pybokeh/gist:5560799

## gistfile1.txt
{
 "metadata": {
  "name": "Weibull_Analysis-Copy0"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<h1 align='center'>Weibull Analysis</h1><br>\n<center>Created by Daniel J. Kim</center>"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<strong>Table of Contents</strong>\n<li>Part 1 - Weibull analysis with complete failure data</li>\n<li>Part 2 - Weibull analysis with failure data and unfailed data (suspensions)</li>\n<li>Part 3 - Weibull analysis with Maximum Likelihood Estimation (MLE)</li>"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Weibull analysis is the process of modelling data that we suspect follows a Weibull distribution.  &nbsp;Most failures or \"life data\" follow the Weibull distribution due to its versatile nature and therefore it is probably the most used distribution to model such failures.  It is has many applications, but I use it to forecast failures.<br><br>To determine if a set of data follows a Weibull distribution, the graphical method is the most popular method.  The graphical method entails graphing the failure times against a probability scale with a model that best fits the data using linear regression.  In Part 1 of this 3-part series, I will cover how to perform Weibull analysis when we have complete failure data.  That is, we waited for all of our units in the test or in the field to fail.  &nbsp;Part 2 in the series covers how to do Weibull analysis when we have data that also includes data for unfailed units or units that failed due to a different reason.  &nbsp;In Part 3, I will cover how to estimate the Weibull parameters using MLE method.  &nbsp;To be honest, I do not have a strong enough statistics and mathematics background to go into details and explain the theory on which method to use, although the general consensus has been to use rank regression method if you have small-ish sample sizes (< 30).  If you have very large quantities of suspensions, MLE method seems to be the preferred method.<br><br>I created this IPython notebook as a benefit to me as I will very soon have to train fellow data analysts at my place of occupation. &nbsp;I think this notebook format helps me organize my thoughts as I am explaining things and it also allows for me to interact with the data and charts as I go along.  Therefore, I believe the IPython notebook format provides a pedagogic benefit to me and hopefully for others as well.  &nbsp;This Weibull analysis series assumes you have some statistics background."
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Part 1 - Weibull analysis with complete failure data"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "The Weibull distribution is a statistical distribution (Normal distribution being the most known) that is commonly used to model life data or failure times of various types of failures.  The 2-parameter version of the Weibull distribution is the most widely-used version of the Weibull distribution."
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<h3><strong>2-parameter Weibull Cumulative Distribution Function (CDF):</strong></h3><center>$\\huge{F(x) = 1 - e^{-(\\frac{x}{\\lambda})^k}}$,</center><br>\n<center><p>where k is the shape parameter and $\\lambda$ is the scale parameter.</p></center>"
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "<center>Let's say we were to model car battery failures and we found the failures follow a Weibull distribution.  &nbsp;It allows us to answer questions such as \"What percent of the batteries will have failed after 200 days?\"</center>"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<p>We will plot data points (failure times) and try to fit them onto a straight line in order to estimate our 2 Weibull parameters (k and $\\lambda$).  Since the Weibull CDF is a logarithmic function, if we attempt to plot the data ploints on 1-1 scale x and y-axis, the data will not fall onto a straight line.  To address this, we need to apply linear transformation to the Weibull CDF equation by using laws of exponents and laws of logarithms:</p>"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<center>$\\large{F(x) = 1 - e^{-(\\frac{x}{\\lambda})^k}}$</center><br><br>\n<center>$1-F(x)=e^{-(\\frac{x}{\\lambda})^k}$</center><br><br>\n<center>$ln(1-F(x))=-(\\frac{x}{\\lambda})^k$</center><br><br>\n<center>$ln\\left(\\frac{1}{1-F(x)}\\right)=(\\frac{x}{\\lambda})^k$</center><br><br>\n<center>$ln\\left(ln\\left(\\frac{1}{1-F(x)}\\right)\\right)=k{\\space}ln(\\frac{x}{\\lambda})$</center><br><br>\n<center>$\\underbrace{ln\\left(ln\\left(\\frac{1}{1-F(x)}\\right)\\right)}=\\underbrace{k{\\space}lnx}-\\underbrace{k{\\space}ln\\lambda}$</center><br>\n<center>$\\space\\space\\space y\\space\\space\\space\\space\\space\\space\\space\\space\\space\\space=\\space mx\\space+\\space\\space b$</center><br>\n<center>(\"linearized\" Weibull CDF)</center><br><br>\nWith the Weibull CDF in its linear form, <strong>y</strong> is then equal to $ln\\left(ln\\left(\\frac{1}{1-F(x)}\\right)\\right){\\space}$,&nbsp;the slope <strong>m</strong> equals k,&nbsp;<strong>x</strong> equals ln(x), and the y-intercept <strong>b</strong> equals $-k{\\space}ln\\lambda\\space\\space$.<br><br>\nSince<br><br>$b=-k{\\space}ln\\lambda{\\space}{\\space}$&nbsp;&nbsp;, then solving for $\\lambda$ :<br><br>\n$\\large{\\lambda=e^{-(\\frac{b}{k})}}$<br><br>\n<p>So now that we know how to estimate the 2 Weibull parameters ($\\lambda$ and k), we are almost ready to create a Weibull probability plot later on.<br><br>A Weibull probability plot is simply plotting ln(x) versus $ln\\left(ln\\left(\\frac{1}{1-F(x)}\\right)\\right)$<br><br>\nBut what is F(x)?  F(x) is based on calcuations for the \"Median Ranks\".  There are different ways to calculate median ranks.  But for Weibull distribution, it is suggested to use Bernard's formula for median ranks:</p><br>\n<center>$\\huge{\\frac{(rank - 0.3)}{(n + 0.4)}}$</center><br>\n<center>where rank is the rank of the data from smallest to largest and n equals the total number of data points</center><br><br>\nNow we are ready to make a table with the necessary calcuations to plot a Weibull plot.  Let's say we have 10 failures with failure times measured in minutes:<br>\n<strong>150, 85, 135, 150, 240, 190, 240, 200, 250, 200</strong><br>"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "The following is the table containing necessary calculations for our x and y cordinates of the data that we are going to use to create the Weibull 1-1 scale probability plot:"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<center><table border=\"1\">\n<tr>\n<th style=\"text-align: center;\">Data<br>$x$</th>\n<th style=\"text-align: center;\">x<br>$ln(x)$</th>\n<th>Rank</th>\n<th style=\"text-align: center;\">Median Rank F(x)<br>$\\frac{(rank - 0.3)}{(n + 0.4)}$</th>\n    <th style=\"text-align: center;\">y<br>$ln\\left(ln\\left(\\frac{1}{1-F(x)}\\right)\\right)$</th>\n</tr>\n<tr>\n<td>85</td>\n<td>4.44265126</td>\n<td style=\"text-align: center;\">1</td>\n<td>0.06730769</td>\n<td>-2.66384309</td>\n</tr>\n<tr>\n<td>135</td>\n<td>4.90527478</td>\n<td style=\"text-align: center;\">2</td>\n<td>0.16346154</td>\n<td>-1.72326315</td>\n</tr>\n<tr>\n<td>150</td>\n<td>5.01063529</td>\n<td style=\"text-align: center;\">3</td>\n<td>0.25961538</td>\n<td>-1.20202312</td>\n</tr>\n<tr>\n<td>150</td>\n<td>5.01063529</td>\n<td style=\"text-align: center;\">4</td>\n<td>0.35576923</td>\n<td>-0.82166652</td>\n</tr>\n<tr>\n<td>190</td>\n<td>5.24702407</td>\n<td style=\"text-align: center;\">5</td>\n<td>0.45192308</td>\n<td>-0.50859539</td>\n</tr>\n<tr>\n<td>200</td>\n<td>5.29831737</td>\n<td style=\"text-align: center;\">6</td>\n<td>0.54807692</td>\n<td>-0.23036544</td>\n</tr>\n<tr>\n<td>200</td>\n<td>5.29831737</td>\n<td style=\"text-align: center;\">7</td>\n<td>0.64423077</td>\n<td>0.03292496</td>\n</tr>\n<tr>\n<td>240</td>\n<td>5.48063892</td>\n<td style=\"text-align: center;\">8</td>\n<td>0.74038462</td>\n<td>0.29903293</td>\n</tr>\n<tr>\n<td>240</td>\n<td>5.48063892</td>\n<td style=\"text-align: center;\">9</td>\n<td>0.83653846</td>\n<td>0.59397722</td>\n</tr>\n<tr>\n<td>250</td>\n<td>5.52146092</td>\n<td style=\"text-align: center;\">10</td>\n<td>0.93269231</td>\n<td>0.99268893</td>\n</tr>\n</table></center><br>\n<strong>NOTE</strong>-We have to sort our failure times from smallest to greatest when performing the calculations."
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "With Python, Numpy/Scipy numerical/scientific packages, and MATPLOTLIB plotting package, we can generate the calculations and create the plot easily"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nfrom numpy import random\nfrom numpy import log as ln\n\ndata = np.array([85,135,150,150,190,200,200,240,240,250])\ny = ln(data)\nrank = np.arange(1,data.size+1)  # ranks = {1, 2, 3, ... 10}\nmedian_rank = (rank - 0.3)/(rank.size + 0.4)\nx = ln(-ln(1 - median_rank))\n\nscatter(x,y)\ntitle(\"Weibull Probability Plot of Failure Times\", weight='bold')\ngrid()\nshow()\n\nprint \"x and y coordinates of the Weibull probability plot:\"\nfor value in zip(x,y):\n    print \"( \" + str(value[0]) + \" , \" + str(value[1]) + \" )\"\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "x and y coordinates of the Weibull probability plot:\n( -2.66384308539 , 4.44265125649 )\n( -1.72326315028 , 4.90527477844 )\n( -1.20202311525 , 5.0106352941 )\n( -0.821666515129 , 5.0106352941 )\n( -0.508595393734 , 5.24702407216 )\n( -0.230365444733 , 5.29831736655 )\n( 0.0329249619143 , 5.29831736655 )\n( 0.299032931862 , 5.48063892334 )\n( 0.59397721666 , 5.48063892334 )\n( 0.99268892949 , 5.52146091786 )\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Also note above, we are plotting the failure times along the y-axis, instead of the x-axis because according to prominent Weibull analysts, we want to do regression analysis on the x direction, instead of the y direction.  This is called \"X on Y\" median rank regression."
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "With least-squares linear regression method, let's generate a line that will \"fit\" through the data points as best as possible.  From this \"ideal\" line, we are going to use the line's slope and y-intercept to calcuate the shape and scale parameter of the ideal Weibull distribution:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import scipy.stats as stats # scipy is a statistical package for Python\n\n# Use Scipy's stats package to perform least-squares fit\nslope, intercept, r_value, p_value, std_err = stats.linregress(x,y)\n\nline = slope*x+intercept\nscatter(x,y)\nplot(x,line)\ntitle(\"Linear Regression - Least Squares Method\", weight='bold')\ngrid()\nshow()\n\n# Since we plot failure times on the y-axis, the actual slope is inverted\nshape = 1/slope\n# Since we plot failure times on the y-axis, we want the x-intercept, not the y-intercept\n# x-intercept is equal to the negative y-intercept divided by the slope/shape parameter\n# Basically you are solving for x: 0 = mx + b, equation of the line where y = 0\nx_intercept = - intercept / shape\n\nprint \"r^2 value:\", r_value**2\nprint \"slope/shape parameter:\", shape\nscale = exp(-x_intercept/slope)\nprint \"scale parameter:\", scale\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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Olrq6wqxZ8IfXdsLGbPYhpqysLDIyMgDIzMxkw4YNtGrVqsA6J0+e5NSpU5w6\ndYoBAwawYMGCAoVdr+58K6YXeswlmSxT2TIdPqyd9RIbq12rdOfO8ivslW2s9KjEnntqairR0dEA\n5OTkMHToULp160Z8fDwAsbGV40KyQojfnT8Pr7+unbP+yivw1Vfaq3Zxb5G5ZYQQAKSna+eoL1gA\nTz+tzQNTs2bpPydsR+aWEUKUWXY2zJ+vTReQkqJdv3T6dCns9zqHLe567a/pMZdkssy9lkkp+OIL\naNFCmypg/XpISIDAQPvmshc9ZrKGfJZMCAe0Y4d2BszNmzBvHnTrZu9EorxJz10IB3L8uNZL37sX\npk6FYcPAiutaCxuTnrsQokSXL8Nzz0FEBLRrp82tPmKEFPbKzGGLu177a3rMJZkso8dM69aZmDZN\nuxC1k5N2qbuJE8HNrfSftSU9jpUeM1lDeu5C6FRaWhoZGRn4+/tjNN7d67DcXFiyRJtbvXNn2Lkz\nj6pVz+PiUgOQ02AcgfTchdAZpRQvv/wqc+e+h5NTNQID/di0aRX+/v4W/Kx21svf/qadyvjOO3Df\nfefo3LkXFy78TG7uTeLi4pgx480KuCfCWtJzF6ISWbFiBe+//xW3b5/il18ucOJELwYPHl3qzx04\nAFFR8MIL2sHSxERo3x7+8penOH26H7/8coHbt08yb97/WLVqVQXcE2FPDlvc9dpf02MuyWSZ8sq0\nb99+MjMHAnUAA7m5sRw8eKDY9c+cgSeegMcegwEDtDlh+vTRroRkMpk4dOgAubljAAPgTVZWP/bv\nL357FaEyP3564bDFXQi9Cg5uiLv7ZiD7t+9spF69BoXWu35da7+0bQsNG2oXzBgzBlxcCq4XGNgA\n2Pjbrdu4u2+hYcPC2xOVi/TchdCZnJwcHntsIDt2HMXJKQCD4QdMprWEhoYC8Ouv8K9/aVME9O0L\nU6bAffcVv73vvvuOzp17Ai3IyTnLQw+1ZtWqT3GS8yB1r8Lmcy8rKe5C3J28vDx2797NjRs3aNeu\nHV5eXuTlwfLlMGmSNmXAjBnav5a4cuUK+/bto2bNmnTo0KHYK6YJfZEDqmWg1/6aHnNJJsuUZyaj\n0UhERATdu3fHy8uLLVugQwft7JdFi2DVKssKe36mOnXq0L17dyIiInRR2Cv746cHDlvchSgvhw8f\npnHjNnTt2o3Gjdtw+PDhctv2Dz9A794QEwNxcbBnj3beuhClkbaMEFa4efMmQUHNuXp1KjAQWI6X\n1+ucOXOtWjEPAAAd9klEQVQMDw+PMm/34kWYPFm7UMbEiTBuHFSpUm6xxT1C2jJC2MmxY8fIzvYC\nYgAPYCTZ2bU5duxYmbZ386ZW1Fu21D6EdOwYvPiiFHZx9xy2uOu1v6bHXJKpeF5eXty+fR5IA0xA\nGrdvX8DLy+uutpOTA++/D40bw4kTsH+/djHq2rWty6eXcbqTHnPpMZM1ZG4ZIazQoEEDnnxyOEuW\nPMCvv4ZQpcr3jBw5gqCgIIt+XintQhkTJ4Kfn3bd0vvvt21m4RhK7bkHBQVRo0YNnJyccHFxYc+e\nPQWWf/zxx8ycOROlFNWrV2fBggW0bt264E6k5y4qMaUUa9eu5ejRozRv3pwePXpYdEbK7t3aBTOu\nXdOuXdqjh/apUiHy2fQ89wYNGrB//35qF/P+cOfOnYSEhFCzZk3WrVvHlClT2LVrV7kFFKKyOXFC\nO1d92zZ4803tTBj5PJEois0PqJa08YiICGr+diXd9u3bk5KSUqYgFU2v/TU95pJMlikt09Wr2qRe\n7dtDq1badAFPPWXbwq7HcQJ95tJjJmuU2nM3GAx07doVJycnYmNjGT26+NnpFi1aRM+ePYtcFhMT\nY+5Denp6EhYWRmRkJPD7oFbk7aSkJLvu/166nZSUpKs8en388t25fP16E198AZ9/Hslf/gILF5qo\nVQs8PPSVXx4/7J7HZDKRkJAAYPFxm+KU2pa5ePEifn5+XL58maioKObOnUunTp0Krbd582bGjRvH\n9u3bqVWrVsGdSFtGOKC8PFi6FF59Vbu03bRp0LSpvVOJe4k1tbPUV+5+fn4AeHt7Ex0dzZ49ewoV\n90OHDjF69GjWrVtXqLAL4Yg2btRmbHRzg//+Fzp2tHci4WhK7LlnZWWRkZEBQGZmJhs2bKBVq1YF\n1jl79iz9+vVj6dKlNGrUyHZJy9mdb8X0Qo+5JJNlTCYThw5B9+7wzDPaK/bt2+1b2PU4TqDPXHrM\nZI0SX7mnpqYSHR0NaNOQDh06lG7duhEfHw9AbGwsb775JtevX2fs2LEARZ4uKURll5ICb78N332n\nFfXY2MLzqgtRkWRuGSGscOOGVtTj47WCPmGCNm2AEOVB5pYRooLdvg1z50KTJnDpEhw8qB0wlcIu\n9MJhi7te+2t6zCWZfqcUfPaZNpf6mjXagdMPPoCAABmnu6HHXHrMZA2ZW0YIC23fDi+9BLduwYIF\n0LWrvRMJUTzpuQtRiuRk+PvftZka//EPGDoUjA77nldUJOm5C2EDqanaRTIefFC7xF1yMjzxhBR2\ncW9w2KepXvtreszlaJkyM7VX6C1agKurdsGMv/0Nqla1X6ay0mMm0GcuPWayhsMWdyHulJurXXy6\naVP4/nvteqX//Cfc5XU3hNAF6bkLh6cUrF2rvTr38tKugPSnP9k7lRA2nltGiMps/37tghkXL2oX\nzOjVSy6YISoHh23L6LW/psdclTHT6dPaWS+9e8OgQXD4sPZ/awp7ZRwnW9FjLj1msobDFnfhmK5f\n185Vv/9+7dOlP/4ITz8NzvIeVlQy0nMXDuHXX2H+fJgxA/r1g8mTtQtSC6Fn0nMXohh5ebBsGbzy\nCrRuDVu2QPPm9k4lhO05bFtGr/01Pea6VzNt3qyd9TJ7NiQkwIoVti3s9+o42YMec+kxkzXklbuo\ndL7/Xpt694cfYPp0GDhQPlUqHI/03EWlceGC1ktfsQImTYKxY6FKFXunEqLsZG4Z4dAyMuD116FV\nK6hdWzsD5oUXpLALx+awxV2v/TU95tJrpuxsberdJk2089YPHNCuiuTpab9MeqPHTKDPXHrMZA3p\nuQu7yX+7abjLTw4pBdu2wZgx2kUy1qyBNm0s3+fd7k+Ie5IqRf369VWrVq1UWFiYateuXZHrPPfc\nc6pRo0aqdevW6sCBA4WWW7Ab4UBu3bqlBg0aqZydq6oqVaqryZP/ofLy8iz62Z07lXrwQaVatVJq\n7VqlLPwxFR+/UFWr5qWcnFxU1659VFpamhX3QIiKYU3tLPUng4KC1NWrV4tdvnr1atWjRw+llFK7\ndu1S7du3L9eAovL5619fVm5ujylIU3BGeXi0UEuXflzizxw/rtSAAUr5+yv1wQdK5eRYvj+TyaTc\n3QMUHFGQpVxdn1S9ew+y8l4IYXvW1E6Leu6qhKO1K1euZMSIEQC0b9+etLQ0UlNTrX9LYWN67a/p\nMVd5Z1qzZhO//PIqUBOoR2bms6xZs7nIda9cgeef1y6W0aaNdrB05EjYutXyTJs3b+aXX0YALQA3\nbt9+ky1bit6fNRzhsSsvesylx0zWKLXnbjAY6Nq1K05OTsTGxjJ69OgCy8+fP09gYKD5dkBAACkp\nKfj6+hZYLyYmhqCgIAA8PT0JCwsjMjIS+H1QK/J2UlKSXfd/L91OSkoq1+1VreoE/A/oAICT01py\nc6uRz2Qy8euvcOBAJO++Cw89ZOI//4G+fX/f3t08fmlpabi47OH2bQUYgKW4u7sX2F953L/y3l5l\nvq3H37989sxjMplISEgAMNfLMivtpf2FCxeUUkr9/PPPKjQ0VCUmJhZY3qtXL7Vt2zbz7UceeUTt\n37+/3N5aiMrnu+++U9Wr+yg3txHKw6OP8vdvrC5fvqyU0totixcrFRCgVP/+SiUnW7+/zMxM1bLl\nn5SHxyPKzW2UcnevozZu3Gj9hoWwMWtqZ6mv3P1+m13J29ub6Oho9uzZQ6dOnczL/f39OXfunPl2\nSkoK/v7+1v3FEZVaWFgYR47sZe3atbi6utKv3xJq1qzJ+vXaBTM8PODTT+GBB8pnf+7u7uzdu4XP\nP/+cGzdu0KXLeJo1a1Y+GxdCr0qq/JmZmSo9PV0ppdTNmzfVAw88oNavX19gnT8eUN25c+c9c0B1\n8+bN9o5QJD3msnWmpCSloqKUatxYqc8/t+wMGEccp7LQYyal9JlLj5msqZ0lvnJPTU0lOjoagJyc\nHIYOHUq3bt2Ij48HIDY2lp49e7JmzRoaNWqEh4cHixcvtvXfI1FJnDsHr74K69fDa69p86q7uNg7\nlRCVg8wtIyrcjRvahF4LF2ofRJowAWrUsHcqIfRH5pYR94Tbt2HOHG26gMuX4eBBeOstKexC2ILD\nFvc7T3/SCz3msjaTUrB8uTaX+vr18M03sGiRNnWAvTLZgmSynB5z6TGTNWRuGWFTW7dq1yzNzoZ/\n/xseecTeiYRwDNJzFzZx7BhMnAjffae1XoYMkQtmCHG3pOcudOPSJe0iGZ06QceOkJwMw4ZJYRei\nojnsr5xe+2vlmSsnJ4etW7eyfv16bty4YdNMmZnw5pvQogW4uWmv3F9+GapWLfNurc5U0SST5fSY\nS4+ZrCE990rq1q1bREY+xvffX8ZorE2VKqfYseNbGjVqVK77ycmBxYthyhR46CHYtw8aNCjXXQgh\nykB67pXUrFnv8PrrW7l16wvACaPxXR58cBNbtqwul+0rBatXa+eoe3vDrFnQrl25bFoI8Rtraqe8\ncq+kjh07xa1bjwBOAOTlRXHy5KJy2fa+fVrLJTUVZs6Exx4DubiREPoiPXedKa9cDzzQFnf3j4F0\nIA8Xl3/Trt39VmU6dUo766VPH+3fQ4egVy/7FHY9Pn6SyXJ6zKXHTNZw2OJe2Y0cOZJBg8JxdQ2g\natW6tGiRxH/+M6dM20pPh/HjITwcmjXTzoAZPRqc5X2fELolPfdK7vr16/zyyy/4+fnd9YWhb92C\nefPg7bdhwACYPBnq1rVRUCFEIdJzF8WqVasWtWrVuqufycuD//4XXnkFwsIgMVGbOkAIce9w2LaM\nXvtr9s61aZN21st778GHH8JXX0Fqqn0zFcXe41QUyWQ5PebSYyZryCt3AcCRI9pVkJKTtel4Bw6U\nM2CEuJdJz93BnT+v9dJXrYJJk7SpA1xd7Z1KCAEyt4wog/R07SpIrVtDnTraK/bnn5fCLkRl4bDF\nXa/9NVvnys6Gf/0LmjbVLnP33XcwYwZ4etovU1lIJsvoMRPoM5ceM1lDeu4OQint4OjEiVC/Pqxd\nq50JI4SonCzquefm5hIeHk5AQACrVq0qsOzKlSsMGzaMS5cukZOTw0svvURMTEzBnUjP3a527tSm\nC8jI0OaA6dbN3omEEJawec99zpw5hISEFPkhmHnz5tGmTRuSkpIwmUyMHz+enJycMoUR5ev4ce2s\nlz//WftE6YEDUtiFcBSlFveUlBTWrFnDqFGjivwL4ufnR3p6OgDp6el4eXnhfA98Ll2v/bXyyHX5\nMvz1r/DAA3D//fDjjzBiBDg52S9TeZNMltFjJtBnLj1mskapVTguLo5Zs2aZC/idRo8eTZcuXbjv\nvvvIyMhg+fLlRa4XExNDUFAQAJ6enoSFhREZGQn8PqgVeTspKcmu+7fF7T/9KZLZs+Htt0107Qo/\n/BCJt7f1209KStLF/dP745dPL3n0fFsev6Jvm0wmEhISAMz1sqxK7Ll//fXXrF27lvnz52MymXj3\n3XcL9dz/8Y9/cOXKFWbPns2JEyeIiori4MGDVK9e/fedSM/dpnJztU+Tvv46dOigfQipnK/JIYSw\nA5v13Hfs2MHKlStp0KABgwcPZtOmTQwfPrzQOgMHDgQgODiYBg0akJycXKYw4u4oBevWQZs2sGgR\n/O9/2pcUdiFEicV92rRpnDt3jlOnTrFs2TK6dOnChx9+WGCdZs2a8c033wCQmppKcnIyDRs2tF3i\ncnLnWzG9sDTXd99pB0eff167dunWrdqrdntmqkiSyTJ6zAT6zKXHTNa4qw8x5Z8tEx8fT3x8PACT\nJk1i3759hIaG0rVrV2bOnEnt2rXLP6kA4OxZGD4cevaEfv20OWH69pV5YIQQBcncMveItDStl/6f\n/8C4cdp56384rCGEqIRkbplK7NdfYfZsaNIErl2Dw4e1NowUdiFESRy2uOu1v5afSyn49FMICYFv\nvtHmWV+4EO67z36Z9EQyWUaPmUCfufSYyRr6/7SRA0pMhJde0k5x/M9/oHNneycSQtxrpOeuI0eP\nwoQJWuvlrbdg0CAwOux7KyGE9NzvcZcuQWwsPPQQPPwwHDsGQ4ZIYRdClJ3Dlg899Ndu3oQpU6BF\nC+0AaXIy3H+/iSpV7J2sID2M1Z0kk2X0mAn0mUuPmazhsMXdnnJyID5eOwPm+HHYvx/eeQfk4wFC\niPIiPfcKpJR2rdIJE8DPT5tb/f777Z1KCKFX1tROOVumguzdq50Bc/UqvPsu9OghnyoVQtiOw7Zl\nKqq/dvKkdtZL377atAFJSdrUAcUVdj32/SSTZSST5fSYS4+ZrOGwxd3Wrl6FuDho1047YPrjj/DU\nU3APXMdECFEJSM+9nP3yC8ydq/XT//xnbY51X197pxJC3Iuk564DeXnw8cfw6qvQti1s2wZNm9o7\nlRDCUTlsW6Y8+2vffKOd9fKvf2kF/ssvy17Y9dj3k0yWkUyW02MuPWayhrxyt8KhQ/C3v8FPP8GM\nGdC/v5wBI4TQB+m5l0FKitZLX71aa8PExoKrq71TCSEqG5lbpoLcuAGvvAKhoVC3rnYGzHPPSWEX\nQuiPwxb3u+mv3b4N8+ZpffQLF+DgQZg2DWrWtG+uiiKZLCOZLKfHXHrMZA3puZdAKfjiC5g4EYKD\nYf167VW7EELonUU999zcXMLDwwkICGDVqlWFlptMJuLi4sjOzqZOnTqF/gLeiz337du165RmZWnn\nrEdF2TuREMLR2Pw89zlz5hASEkJGRkahZWlpaYwbN47169cTEBDAlStXyhREL5KT4e9/h3374B//\ngGHDZF51IcS9p9SylZKSwpo1axg1alSRf0E++eQT+vfvT0BAAAB16tQp/5Q2cOe7i59/hnHjoGNH\naN9eK/LDh1d8Yddj308yWUYyWU6PufSYyRqlvnKPi4tj1qxZpKenF7n8+PHjZGdn07lzZzIyMnj+\n+ed54oknCq0XExNDUFAQAJ6enoSFhREZGQn8PqgVeTspKYnIyEgyM+GvfzXx2WcwcmQkx47BkSMm\ndu+u2Dx6vp2UlKSrPH98/PSS54/0kkfPt+XxK/q2yWQiISEBwFwvy6rEnvvXX3/N2rVrmT9/PiaT\niXfffbdQz/3ZZ5/lwIEDfPvtt2RlZREREcHq1atp3Ljx7zvRYc89NxcSEmDyZO3V+rRp2kFTIYTQ\nC5v13Hfs2MHKlStZs2YNt27dIj09neHDh/Phhx+a1wkMDKROnTq4ubnh5ubGQw89xMGDBwsUdz1R\nCtau1T5ZWrs2fP651oYRQojKpMSO8rRp0zh37hynTp1i2bJldOnSpUBhB+jTpw/btm0jNzeXrKws\ndu/eTUhIiE1Dl9X+/dC1K4wfD4MHm9iyRX+F/c63iHogmSwjmSynx1x6zGSNuzpcaPht4pT4+Hji\n4+MBaNasGd27d6d169a0b9+e0aNH6664nz4NQ4dCr17aNLyHD2utGJkHRghRWVXquWWuX9d66R98\noE0TMH48VK9e4TGEEKJMZG6ZO/z6q3ad0iZNtPlgjhyBKVOksAshHEelKu55efDf/0KzZrBli/b1\n73+Dn1/hdfXaX9NjLslkGclkOT3m0mMma1SauWWSkmDUKK2Pvngx/HYKqRBCOKRK03P/8Uc4cEA7\nYGqsVO9HhBCOypraWWmKuxBCVDZyQLUM9Npf02MuyWQZyWQ5PebSYyZrOGxxF0KIykzaMkIIoVPS\nlhFCCFGAwxZ3vfbX9JhLMllGMllOj7n0mMkaDlvchRCiMpOeuxBC6JT03IUQQhTgsMVdr/01PeaS\nTJaRTJbTYy49ZrJGpSju27dv5+GHe3H//V1477350gISQji8e77nnpSURMeOUWRlzQL8cHd/mddf\nH8GECeNtsj8hhKgoDt1z/+ij//LLL+OAGOBRsrIWMX/+YjunEkII+7rni7uLizMGw60/fOcWTk5O\npf6cXvtreswlmSwjmSynx1x6zGSNe764jxo1Enf3DzAYpgGLcXcfzmuvvWDvWEIIYVcW9dxzc3MJ\nDw8nICCAVatWFbnO3r17iYiIYPny5fTr16/gTmx8nvvRo0eZPn026emZDB/en379om22LyGEqCjW\n1E6LrsQ0Z84cQkJCyMjIKHJ5bm4uEyZMoHv37nY5U6V58+Z8+GF8he9XCCH0qtS2TEpKCmvWrGHU\nqFHFFu65c+cyYMAAvL29yz2grei1v6bHXJLJMpLJcnrMpcdM1ij1lXtcXByzZs0iPT29yOXnz59n\nxYoVbNq0ib1792IwGIpcLyYmhqCgIAA8PT0JCwsj8rcLneYPakXeTkpKsuv+76XbSUlJusqj18cv\nn17y6Pm2PH5F3zaZTCQkJACY62VZldhz//rrr1m7di3z58/HZDLx7rvvFuq5Dxw4kJdeeon27dsT\nExND79696d+/f8GdyNwyQghx12x2DdVJkybx0Ucf4ezszK1bt0hPT6d///58+OGH5nUaNmxo3vmV\nK1dwd3dn4cKFPP744+USUAghHJXNPsQ0bdo0zp07x6lTp1i2bBldunQpUNgBTp48yalTpzh16hQD\nBgxgwYIFBQq7Xt35Vkwv9JhLMllGMllOj7n0mMkad3Wee34/PT4+nvh4OTtFCCH06p6fW0YIISor\nh55bRgghRGEOW9z12l/TYy7JZBnJZDk95tJjJms4bHEXQojKTHruQgihU9JzF0IIUYDDFne99tf0\nmEsyWUYyWU6PufSYyRoOW9yFEKIyk567EELolPTchRBCFOCwxV2v/TU95pJMlpFMltNjLj1msobD\nFnchhKjMpOcuhBA6JT13IYQQBThscddrf02PuSSTZSST5fSYS4+ZrOGwxV0IISoz6bkLIYROSc9d\nCCFEAQ5b3PXaX9NjLslkGclkOT3m0mMmazhscU9KSrJ3hCLpMZdksoxkspwec+kxkzUsKu65ubm0\nadOG3r17F1r28ccfExoaSuvWrenYsSOHDh0q95C2kJaWZu8IRdJjLslkGclkOT3m0mMmazhbstKc\nOXMICQkhIyOj0LKGDRuSmJhIzZo1WbduHU8//TS7du0q96BCCCEsV+or95SUFNasWcOoUaOKPGob\nERFBzZo1AWjfvj0pKSnln9IGTp8+be8IRdJjLslkGclkOT3m0mMmq6hSDBgwQB04cECZTCbVq1ev\nEtedNWuWGj16dKHvA/IlX/IlX/JVhq+yKrEt8/XXX+Pj40ObNm1KPZK8efNmPvjgA7Zv315oWVGv\n+IUQQthOiR9imjRpEh999BHOzs7cunWL9PR0+vfvz4cfflhgvUOHDtGvXz/WrVtHo0aNbB5aCCFE\nySz+hOqWLVt45513WLVqVYHvnz17li5durB06VI6dOhgk5BCCCHujkVny+QzGAwAxMfHAxAbG8ub\nb77J9evXGTt2LAAuLi7s2bOnnGMKIYS4K2Xu1pfg1VdfVa1bt1ahoaGqS5cu6uzZs0Wut3btWtW0\naVPVqFEjNWPGDFtEKeCll15SzZo1U61bt1bR0dEqLS2tyPXq16+vWrVqpcLCwlS7du10kakix2r5\n8uUqJCREGY1GtX///mLXq8hxsjRTRY7T1atXVdeuXVXjxo1VVFSUun79epHrVdQ4WXLfn3vuOdWo\nUSPVunVrdeDAAZtlsTTT5s2bVY0aNVRYWJgKCwtTU6dOtWmekSNHKh8fH9WyZcti16noMSotU1nH\nyCbFPT093fz/9957Tz311FOF1snJyVHBwcHq1KlT6vbt2yo0NFT98MMPtohjtmHDBpWbm6uUUmrC\nhAlqwoQJRa4XFBSkrl69atMsd5Oposfq6NGjKjk5WUVGRpZYSCtynCzJVNHj9PLLL6u3335bKaXU\njBkz7Pp8suS+r169WvXo0UMppdSuXbtU+/bt7Z5p8+bNqnfv3jbN8UeJiYnqwIEDxRbSih4jSzKV\ndYxsMv1A9erVzf+/efMmderUKbTOnj17aNSoEUFBQbi4uDBo0CBWrFhhizhmUVFRGI3aXS7tnHxV\nQWf4WJKposeqWbNmNGnSxKJ1K2qcLMlU0eO0cuVKRowYAcCIESP46quvil3X1uNkyX3/Y9727duT\nlpZGamqqXTNBxZ5N16lTJ2rVqlXs8ooeI0syQdnGyGZzy7zyyivUq1ePJUuWMHHixELLz58/T2Bg\noPl2QEAA58+ft1WcQj744AN69uxZ5DKDwUDXrl0JDw9n4cKFds9k77Eqjr3GqTgVPU6pqan4+voC\n4OvrW2wRqIhxsuS+F7WOLT90aEkmg8HAjh07CA0NpWfPnvzwww82y2OJih4jS5R1jO7qgOofRUVF\ncenSpULfnzZtGr179+att97irbfeYsaMGcTFxbF48eJCgW2htFwAb731Fq6urgwZMqTIbWzfvh0/\nPz8uX75MVFQUzZo1o1OnTnbLZIuxsiRTaewxTiWpyHF66623Cu27uP2X9zgVxdL7fucrQFv9Hlq6\n7bZt23Lu3Dnc3d1Zu3Ytffv25ccff7RZJktU5BhZoqxjVObivnHjRovWGzJkSJGvRv39/Tl37pz5\n9rlz5wgICChrHItzJSQksGbNGr799tti1/Hz8wPA29ub6Oho9uzZY9Uvo7WZbDFWlj5+JanocSpN\nRY+Tr68vly5dom7duly8eBEfH58i1yvvcSqKJff9znVSUlLw9/cv1xx3m+mPLdwePXrwzDPPcO3a\nNWrXrm2zXCWp6DGyRFnHyCZtmePHj5v/v2LFCtq0aVNonfDwcI4fP87p06e5ffs2n376KY8//rgt\n4pitW7eOWbNmsWLFCqpWrVrkOllZWeYJ0jIzM9mwYQOtWrWyayZ7jFW+4np9FT1OlmSq6HF6/PHH\nWbJkCQBLliyhb9++hdapqHGy5L4//vjj5g8g7tq1C09PT3NbyRYsyZSammp+PPfs2YNSym6FHSp+\njCxR5jEqw8HdUvXv31+1bNlShYaGqn79+qnU1FSllFLnz59XPXv2NK+3Zs0a1aRJExUcHKymTZtm\niygFNGrUSNWrV898StHYsWML5Tpx4oQKDQ1VoaGhqkWLFjbPZUkmpSp2rL744gsVEBCgqlatqnx9\nfVX37t0LZarocbIkk1IVO05Xr15VjzzySKFTIe01TkXd9/fff1+9//775nXGjRungoODVevWrUs8\nE6qiMs2bN0+1aNFChYaGqoiICLVz506b5hk0aJDy8/NTLi4uKiAgQC1atMjuY1RaprKOUYVcQ1UI\nIUTFctgrMQkhRGUmxV0IISohKe5CCFEJSXEXQohKSIq7EEJUQlLchRCiEvp/H0QBfBxMchkAAAAA\nSUVORK5CYII=\n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "r^2 value: 0.953902860399\nslope/shape parameter: 3.41595091809\nscale parameter: 204.936017721\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "From the least-squares fit method above, we now have the Weibull shape and scale parameter.  Next we can plot the actual failure times versus the \"ideal\" Weibull distribution.  We will plot on a more useful log-log scale where the x axis is the failure time and y axis is the cumulative distribuion function."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nfrom numpy import random\nfrom matplotlib.ticker import FuncFormatter\n\n# I'm used to  the ln notation for the natural log\nfrom numpy import log as ln\n\n# Since we are going to plot failure times on log scale, we don't need to take the log of the failure times\nx = data\nrank = np.arange(1,x.size+1)  # ranks = {1, 2, 3, ... 10}\nmedian_rank = (rank - 0.3)/(rank.size + 0.4)\ny = ln(-ln(1 - median_rank))\n\n# Generate 1000 numbers following a Weibull distribution that we think ideally fits our data using the shape and scale parameter\nx_ideal = scale *random.weibull(shape, size=100)\nx_ideal.sort()\nF = 1 - exp( -(x_ideal/scale)**shape )\ny_ideal = ln(-ln(1 - F))\n\n# Weibull plot\nax = subplot(111)\nsemilogx(x, y, \"bs\")\nplot(x_ideal, y_ideal, 'r-', label=\"beta= %5G\\neta = %.5G\" % (shape, scale) )\ntitle(\"Weibull Probability Plot on Log Scale\", weight=\"bold\")\nxlabel('x (time)', weight=\"bold\")\nylabel('Cumulative Distribution Function', weight=\"bold\")\nlegend(loc='lower right')\n\n# Generate ticks\ndef weibull_CDF(y, pos):\n    return \"%G %%\" % (100*(1-exp(-exp(y))))\n\nformatter = FuncFormatter(weibull_CDF)\nax.yaxis.set_major_formatter(formatter)\n\nyt_F = array([ 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5,\n           0.6, 0.7, 0.8, 0.9, 0.95, 0.99])\nyt_lnF = ln( -ln(1-yt_F))\nyticks(yt_lnF)\nax.yaxis.grid()\nax.xaxis.grid(which='both')\nshow()\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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A4uctp2GrdResr9UUdX1XQJPIGebSNwsrZ1Y2kFatWmH16tUoVaqUzC6EXbt2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\nhQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Since it can be difficult to read certain x and y (CDF) values from the Weibull log-log scale plot above, let's create an output containing x values and their corresponding y (CDF) values:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x2 = np.arange(0,400)\ny2 = 1-exp(-(x2/scale)**shape) # This is the equation for Weibull CDF\n\nplot(x2,y2)\ntitle(\"Weibull CDF - Prediction\",weight='bold')\ngrid()\nshow()\n\nprint \"Coordinates ( x, y ) of the CDF:\"\nfor value in zip(x2,y2):\n    print \"( \" + str(value[0]) + \" , \" + str(value[1]*100) + \" )\"\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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UxNPHsrJJTn25WjvL7MGnpqYSFxdHYmIiAFOnTsXLy4vnnnvOsc8dd9zh6BHl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\nRU5ErkJggg==\n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Coordinates ( x, y ) of the CDF:\n( 0 , 0.0 )\n( 1 , 1.26947855561e-06 )\n( 2 , 1.3549679756e-05 )\n( 3 , 5.41312481284e-05 )\n( 4 , 0.000144621358389 )\n( 5 , 0.000309935929765 )\n( 6 , 0.000577764154452 )\n( 7 , 0.000978220301773 )\n( 8 , 0.00154359402438 )\n( 9 , 0.00230816012697 )\n( 10 , 0.00330802745295 )\n( 11 , 0.00458101508177 )\n( 12 , 0.00616654844551 )\n( 13 , 0.00810557046718 )\n( 14 , 0.0104404643293 )\n( 15 , 0.0132149854387 )\n( 16 , 0.016474200788 )\n( 17 , 0.0202644343514 )\n( 18 , 0.0246332174596 )\n( 19 , 0.0296292433219 )\n( 20 , 0.0353023250307 )\n( 21 , 0.0417033565062 )\n( 22 , 0.0488842759366 )\n( 23 , 0.0568980313435 )\n( 24 , 0.0657985479594 )\n( 25 , 0.0756406971548 )\n( 26 , 0.086480266686 )\n( 27 , 0.0983739320694 )\n( 28 , 0.111379228911 )\n( 29 , 0.125554526044 )\n( 30 , 0.140958999338 )\n( 31 , 0.157652606073 )\n( 32 , 0.175696059762 )\n( 33 , 0.195150805339 )\n( 34 , 0.216078994626 )\n( 35 , 0.238543462002 )\n( 36 , 0.262607700203 )\n( 37 , 0.288335836199 )\n( 38 , 0.315792607082 )\n( 39 , 0.345043335917 )\n( 40 , 0.376153907505 )\n( 41 , 0.409190744022 )\n( 42 , 0.444220780478 )\n( 43 , 0.481311439974 )\n( 44 , 0.520530608715 )\n( 45 , 0.561946610737 )\n( 46 , 0.605628182341 )\n( 47 , 0.651644446187 )\n( 48 , 0.700064885019 )\n( 49 , 0.750959315022 )\n( 50 , 0.80439785876 )\n( 51 , 0.860450917692 )\n( 52 , 0.919189144237 )\n( 53 , 0.980683413385 )\n( 54 , 1.04500479382 )\n( 55 , 1.11222451853 )\n( 56 , 1.18241395499 )\n( 57 , 1.25564457469 )\n( 58 , 1.33198792224 )\n( 59 , 1.41151558394 )\n( 60 , 1.49429915569 )\n( 61 , 1.58041021048 )\n( 62 , 1.66992026525 )\n( 63 , 1.76290074713 )\n( 64 , 1.85942295929 )\n( 65 , 1.95955804597 )\n( 66 , 2.06337695716 )\n( 67 , 2.17095041259 )\n( 68 , 2.28234886515 )\n( 69 , 2.39764246378 )\n( 70 , 2.51690101578 )\n( 71 , 2.64019394854 )\n( 72 , 2.76759027073 )\n( 73 , 2.89915853295 )\n( 74 , 3.0349667878 )\n( 75 , 3.17508254949 )\n( 76 , 3.31957275283 )\n( 77 , 3.46850371177 )\n( 78 , 3.62194107747 )\n( 79 , 3.77994979583 )\n( 80 , 3.94259406455 )\n( 81 , 4.10993728979 )\n( 82 , 4.28204204236 )\n( 83 , 4.45897001351 )\n( 84 , 4.64078197029 )\n( 85 , 4.82753771059 )\n( 86 , 5.01929601777 )\n( 87 , 5.21611461505 )\n( 88 , 5.4180501195 )\n( 89 , 5.62515799578 )\n( 90 , 5.83749250972 )\n( 91 , 6.05510668154 )\n( 92 , 6.27805223899 )\n( 93 , 6.50637957029 )\n( 94 , 6.74013767693 )\n( 95 , 6.97937412643 )\n( 96 , 7.22413500495 )\n( 97 , 7.47446487003 )\n( 98 , 7.73040670318 )\n( 99 , 7.99200186263 )\n( 100 , 8.25929003616 )\n( 101 , 8.53230919404 )\n( 102 , 8.81109554215 )\n( 103 , 9.09568347535 )\n( 104 , 9.3861055311 )\n( 105 , 9.68239234334 )\n( 106 , 9.98457259684 )\n( 107 , 10.2926729818 )\n( 108 , 10.6067181491 )\n( 109 , 10.9267306658 )\n( 110 , 11.2527309714 )\n( 111 , 11.5847373345 )\n( 112 , 11.9227658104 )\n( 113 , 12.2668301993 )\n( 114 , 12.6169420047 )\n( 115 , 12.9731103937 )\n( 116 , 13.3353421571 )\n( 117 , 13.7036416711 )\n( 118 , 14.0780108597 )\n( 119 , 14.458449158 )\n( 120 , 14.8449534769 )\n( 121 , 15.2375181689 )\n( 122 , 15.6361349946 )\n( 123 , 16.0407930909 )\n( 124 , 16.4514789408 )\n( 125 , 16.8681763436 )\n( 126 , 17.2908663875 )\n( 127 , 17.719527423 )\n( 128 , 18.1541350382 )\n( 129 , 18.5946620354 )\n( 130 , 19.0410784099 )\n( 131 , 19.4933513293 )\n( 132 , 19.951445116 )\n( 133 , 20.4153212305 )\n( 134 , 20.8849382568 )\n( 135 , 21.3602518898 )\n( 136 , 21.8412149247 )\n( 137 , 22.3277772478 )\n( 138 , 22.8198858304 )\n( 139 , 23.3174847237 )\n( 140 , 23.8205150564 )\n( 141 , 24.3289150346 )\n( 142 , 24.8426199434 )\n( 143 , 25.3615621512 )\n( 144 , 25.885671116 )\n( 145 , 26.4148733943 )\n( 146 , 26.9490926519 )\n( 147 , 27.4882496776 )\n( 148 , 28.0322623994 )\n( 149 , 28.581045902 )\n( 150 , 29.1345124485 )\n( 151 , 29.6925715032 )\n( 152 , 30.2551297577 )\n( 153 , 30.8220911589 )\n( 154 , 31.3933569402 )\n( 155 , 31.9688256549 )\n( 156 , 32.548393212 )\n( 157 , 33.131952915 )\n( 158 , 33.719395503 )\n( 159 , 34.3106091943 )\n( 160 , 34.9054797327 )\n( 161 , 35.5038904366 )\n( 162 , 36.1057222499 )\n( 163 , 36.7108537963 )\n( 164 , 37.3191614356 )\n( 165 , 37.9305193227 )\n( 166 , 38.5447994688 )\n( 167 , 39.1618718054 )\n( 168 , 39.7816042507 )\n( 169 , 40.4038627777 )\n( 170 , 41.0285114858 )\n( 171 , 41.6554126735 )\n( 172 , 42.2844269144 )\n( 173 , 42.9154131346 )\n( 174 , 43.5482286923 )\n( 175 , 44.1827294604 )\n( 176 , 44.8187699099 )\n( 177 , 45.4562031961 )\n( 178 , 46.094881246 )\n( 179 , 46.7346548486 )\n( 180 , 47.3753737457 )\n( 181 , 48.0168867252 )\n( 182 , 48.6590417159 )\n( 183 , 49.301685883 )\n( 184 , 49.9446657266 )\n( 185 , 50.5878271796 )\n( 186 , 51.2310157086 )\n( 187 , 51.8740764146 )\n( 188 , 52.5168541356 )\n( 189 , 53.1591935495 )\n( 190 , 53.8009392785 )\n( 191 , 54.4419359935 )\n( 192 , 55.0820285194 )\n( 193 , 55.7210619414 )\n( 194 , 56.3588817106 )\n( 195 , 56.9953337508 )\n( 196 , 57.6302645653 )\n( 197 , 58.2635213432 )\n( 198 , 58.8949520661 )\n( 199 , 59.5244056143 )\n( 200 , 60.151731873 )\n( 201 , 60.7767818378 )\n( 202 , 61.3994077196 )\n( 203 , 62.0194630487 )\n( 204 , 62.6368027784 )\n( 205 , 63.2512833874 )\n( 206 , 63.862762981 )\n( 207 , 64.4711013915 )\n( 208 , 65.0761602767 )\n( 209 , 65.6778032176 )\n( 210 , 66.2758958138 )\n( 211 , 66.870305778 )\n( 212 , 67.4609030278 )\n( 213 , 68.0475597763 )\n( 214 , 68.6301506205 )\n( 215 , 69.2085526272 )\n( 216 , 69.7826454168 )\n( 217 , 70.3523112449 )\n( 218 , 70.9174350814 )\n( 219 , 71.4779046865 )\n( 220 , 72.033610685 )\n( 221 , 72.5844466365 )\n( 222 , 73.1303091041 )\n( 223 , 73.6710977192 )\n( 224 , 74.2067152433 )\n( 225 , 74.7370676275 )\n( 226 , 75.2620640677 )\n( 227 , 75.7816170573 )\n( 228 , 76.2956424363 )\n( 229 , 76.8040594367 )\n( 230 , 77.3067907252 )\n( 231 , 77.8037624415 )\n( 232 , 78.2949042338 )\n( 233 , 78.78014929 )\n( 234 , 79.2594343661 )\n( 235 , 79.7326998099 )\n( 236 , 80.1998895822 )\n( 237 , 80.6609512731 )\n( 238 , 81.1158361154 )\n( 239 , 81.5644989938 )\n( 240 , 82.0068984511 )\n( 241 , 82.4429966894 )\n( 242 , 82.8727595686 )\n( 243 , 83.2961566011 )\n( 244 , 83.7131609423 )\n( 245 , 84.123749378 )\n( 246 , 84.5279023074 )\n( 247 , 84.9256037238 )\n( 248 , 85.3168411902 )\n( 249 , 85.7016058125 )\n( 250 , 86.0798922091 )\n( 251 , 86.4516984763 )\n( 252 , 86.8170261516 )\n( 253 , 87.175880173 )\n( 254 , 87.528268835 )\n( 255 , 87.8742037418 )\n( 256 , 88.2136997577 )\n( 257 , 88.5467749541 )\n( 258 , 88.8734505537 )\n( 259 , 89.1937508726 )\n( 260 , 89.5077032585 )\n( 261 , 89.8153380281 )\n( 262 , 90.1166884002 )\n( 263 , 90.4117904279 )\n( 264 , 90.700682928 )\n( 265 , 90.9834074083 )\n( 266 , 91.260007993 )\n( 267 , 91.5305313464 )\n( 268 , 91.7950265947 )\n( 269 , 92.0535452459 )\n( 270 , 92.3061411092 )\n( 271 , 92.552870212 )\n( 272 , 92.793790716 )\n( 273 , 93.0289628329 )\n( 274 , 93.2584487377 )\n( 275 , 93.4823124828 )\n( 276 , 93.7006199103 )\n( 277 , 93.9134385642 )\n( 278 , 94.1208376018 )\n( 279 , 94.3228877053 )\n( 280 , 94.5196609931 )\n( 281 , 94.7112309303 )\n( 282 , 94.8976722405 )\n( 283 , 95.079060817 )\n( 284 , 95.2554736345 )\n( 285 , 95.4269886612 )\n( 286 , 95.5936847714 )\n( 287 , 95.7556416593 )\n( 288 , 95.9129397526 )\n( 289 , 96.0656601281 )\n( 290 , 96.2138844273 )\n( 291 , 96.3576947738 )\n( 292 , 96.4971736916 )\n( 293 , 96.6324040249 )\n( 294 , 96.7634688585 )\n( 295 , 96.8904514412 )\n( 296 , 97.0134351093 )\n( 297 , 97.1325032121 )\n( 298 , 97.2477390399 )\n( 299 , 97.3592257527 )\n( 300 , 97.4670463112 )\n( 301 , 97.5712834099 )\n( 302 , 97.672019412 )\n( 303 , 97.7693362861 )\n( 304 , 97.8633155451 )\n( 305 , 97.9540381874 )\n( 306 , 98.0415846401 )\n( 307 , 98.1260347041 )\n( 308 , 98.2074675019 )\n( 309 , 98.2859614272 )\n( 310 , 98.3615940969 )\n( 311 , 98.4344423058 )\n( 312 , 98.5045819822 )\n( 313 , 98.572088148 )\n( 314 , 98.6370348785 )\n( 315 , 98.6994952667 )\n( 316 , 98.7595413887 )\n( 317 , 98.8172442712 )\n( 318 , 98.8726738622 )\n( 319 , 98.925899003 )\n( 320 , 98.9769874031 )\n( 321 , 99.0260056164 )\n( 322 , 99.0730190209 )\n( 323 , 99.1180917988 )\n( 324 , 99.1612869204 )\n( 325 , 99.2026661289 )\n( 326 , 99.2422899274 )\n( 327 , 99.2802175685 )\n( 328 , 99.3165070446 )\n( 329 , 99.3512150818 )\n( 330 , 99.3843971335 )\n( 331 , 99.4161073779 )\n( 332 , 99.4463987156 )\n( 333 , 99.4753227695 )\n( 334 , 99.5029298866 )\n( 335 , 99.5292691408 )\n( 336 , 99.5543883372 )\n( 337 , 99.5783340185 )\n( 338 , 99.6011514718 )\n( 339 , 99.6228847376 )\n( 340 , 99.6435766193 )\n( 341 , 99.6632686946 )\n( 342 , 99.6820013271 )\n( 343 , 99.6998136802 )\n( 344 , 99.7167437305 )\n( 345 , 99.7328282837 )\n( 346 , 99.7481029902 )\n( 347 , 99.7626023617 )\n( 348 , 99.7763597894 )\n( 349 , 99.7894075618 )\n( 350 , 99.8017768835 )\n( 351 , 99.8134978953 )\n( 352 , 99.8245996935 )\n( 353 , 99.8351103508 )\n( 354 , 99.8450569371 )\n( 355 , 99.8544655408 )\n( 356 , 99.8633612904 )\n( 357 , 99.871768376 )\n( 358 , 99.8797100718 )\n( 359 , 99.8872087583 )\n( 360 , 99.8942859442 )\n( 361 , 99.9009622892 )\n( 362 , 99.9072576267 )\n( 363 , 99.9131909855 )\n( 364 , 99.9187806131 )\n( 365 , 99.9240439976 )\n( 366 , 99.9289978899 )\n( 367 , 99.9336583263 )\n( 368 , 99.9380406498 )\n( 369 , 99.9421595324 )\n( 370 , 99.9460289964 )\n( 371 , 99.9496624358 )\n( 372 , 99.9530726372 )\n( 373 , 99.9562718005 )\n( 374 , 99.9592715595 )\n( 375 , 99.9620830018 )\n( 376 , 99.9647166884 )\n( 377 , 99.9671826736 )\n( 378 , 99.9694905232 )\n( 379 , 99.9716493337 )\n( 380 , 99.9736677503 )\n( 381 , 99.9755539845 )\n( 382 , 99.9773158317 )\n( 383 , 99.9789606879 )\n( 384 , 99.9804955664 )\n( 385 , 99.9819271137 )\n( 386 , 99.983261625 )\n( 387 , 99.9845050598 )\n( 388 , 99.9856630563 )\n( 389 , 99.9867409455 )\n( 390 , 99.9877437655 )\n( 391 , 99.9886762747 )\n( 392 , 99.9895429647 )\n( 393 , 99.9903480727 )\n( 394 , 99.9910955941 )\n( 395 , 99.9917892934 )\n( 396 , 99.9924327165 )\n( 397 , 99.9930292003 )\n( 398 , 99.9935818843 )\n( 399 , 99.9940937197 )\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Finally,&nbsp;the point of doing all of this is to allow us to predict failures after x units of time.<br><br>Based on the output above, if someone were to ask us \"What percent of the population will have failed after 200 days?\"  The answer would be approximately 60%."
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Part 2 - Weibull Analysis with Suspensions/Censored Data"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "In this Part 2 of the series, I will cover how to do Weibull analysis when our data set also includes data from units that didn't fail or failed for a different reason or for a different failure mode.  This scenario where our data set includes data from units that have not failed yet is very common in the industry since most of the time it would be unfeasible or time consuming to wait for all units to have failed. When our data includes data such as these, the data set as a whole is what is referred to as \"failure data with suspensions or censored data\".  This is just fancy talk by statisticians.<br><br>\nTo perform Weibull analysis on data with suspensions, the \"rank\" of the data has to be adjusted due to the suspension data.  Then we can accordingly calculate the proper median ranks using Bernard's formula.<br><br>\nLet's get some failure data that is saved in a csv file:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import pandas\n\n# Open csv file\ndf = pandas.read_csv(r'C:\\Documents and Settings\\ma17151\\Desktop\\Weibull_Suspensions.csv')\n# Ensure that the data is sorted by DTF in ascending order\ndf.sort(columns=\"DTF\")\nprint \"What the CSV data looks like:\"\nprint df\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "What the CSV data looks like:\n   VIN  DTF     STATUS\n0    6   10  SUSPENDED\n1    1   30     FAILED\n2    7   45  SUSPENDED\n3    2   49     FAILED\n4    3   82     FAILED\n5    4   90     FAILED\n6    5   96     FAILED\n7    8  100  SUSPENDED\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "From the output above, we see that we have 8 rows of data, where we have 5 failed units and 3 suspensions.<br><br>\nThe equation for calculating the adjusted rank is as follows:<br><br>\n<center>$\\large{Adjusted Rank = \\frac{(Reverse Rank)(Previous AdjustedRank)+(N+1)}{(Reverse Rank)+1}}$</center>"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Now we are ready to create 4 additional columns.  We need: rank, reverse rank, adjusted rank, and median rank.  The Python script below will create those 4 columns for us using the dataframe's apply() method, which allows us to create Excel-like functions to create new columns:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# Reference material on how to use the apply() function in a dataframe:\n# http://stackoverflow.com/questions/13331698/how-to-apply-a-function-to-two-columns-of-pandas-dataframe  or\n# http://manishamde.github.io/blog/2013/03/07/pandas-and-python-top-10/\n\n# Make sure the data set is sorted by DTF in ascending order\ndf.sort(columns=\"DTF\")\n\nglobal prev_adj_rank\nprev_adj_rank = [0]\n\ndef adj_rank(series):\n    if series[\"STATUS\"] == \"SUSPENDED\":\n        return \"SUSPENSION\"\n    else:\n        adjusted_rank = (series[\"REV_RANK\"] * 1.0 * prev_adj_rank[-1] + (len(df) + 1))/(series[\"REV_RANK\"] + 1)\n        prev_adj_rank.append(adjusted_rank)\n        return adjusted_rank\n        \ndef median_rank(series):\n    if series[\"ADJ_RANK\"] == \"SUSPENSION\":\n        return NaN\n    else:\n        median_rank = (series[\"ADJ_RANK\"] - 0.3)/(len(df) + 0.4)\n        return median_rank\n\ndf[\"RANK\"]=df.index+1\ndf[\"REV_RANK\"]=len(df)+1-df[\"RANK\"]\ndf[\"ADJ_RANK\"] = df.apply(adj_rank,axis=1)\ndf[\"MEDIAN_RANK\"] = df.apply(median_rank, axis=1)\nprint \"What the data looks like with the 4 additional columns(\\\"NaN\\\"=Not A Number):\"\nprint df\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "What the data looks like with the 4 additional columns(\"NaN\"=Not A Number):\n   VIN  DTF     STATUS  RANK  REV_RANK    ADJ_RANK  MEDIAN_RANK\n0    6   10  SUSPENDED     1         8  SUSPENSION          NaN\n1    1   30     FAILED     2         7       1.125     0.098214\n2    7   45  SUSPENDED     3         6  SUSPENSION          NaN\n3    2   49     FAILED     4         5      2.4375     0.254464\n4    3   82     FAILED     5         4        3.75     0.410714\n5    4   90     FAILED     6         3      5.0625     0.566964\n6    5   96     FAILED     7         2       6.375     0.723214\n7    8  100  SUSPENDED     8         1  SUSPENSION          NaN\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Since we will actually only plot data from failed units and not the suspensions, we want to limit our data set to those 5 rows where status equals \"FAILED\":"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "print \"What the data looks like with just failed data:\"\ndf_final = df[df.STATUS == \"FAILED\"]\nprint df_final\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "What the data looks like with just failed data:\n   VIN  DTF  STATUS  RANK  REV_RANK ADJ_RANK  MEDIAN_RANK\n1    1   30  FAILED     2         7    1.125     0.098214\n3    2   49  FAILED     4         5   2.4375     0.254464\n4    3   82  FAILED     5         4     3.75     0.410714\n5    4   90  FAILED     6         3   5.0625     0.566964\n6    5   96  FAILED     7         2    6.375     0.723214\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Now we can start creating the usual probability plots:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nfrom numpy import random\nfrom numpy import log as ln\n\ndata = df_final[\"DTF\"].values\ny = ln(data)\nmedian_rank = df_final[\"MEDIAN_RANK\"].values\nx = ln(-ln(1 - median_rank))\n\nscatter(x,y)\ntitle(\"Weibull Probability Plot of Failure Times\", weight='bold')\ngrid()\nshow()\n\nprint \"x and y coordinates of the Weibull plot:\"\nfor value in zip(x,y):\n    print \"( \" + str(value[0]) + \" , \" + str(value[1]) + \" )\"\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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dDGTv+zGf9ZI5GyB/PlOwuBMRSYg9dyIiC8WeOxERGWBxNwPZ+37MZ71kzgbI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\n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "x and y coordinates of the Weibull plot:\n( -2.26935967679 , 3.40119738166 )\n( -1.22535907083 , 3.89182029811 )\n( -0.637061542208 , 4.40671924726 )\n( -0.178008782168 , 4.49980967033 )\n( 0.25037862029 , 4.56434819147 )\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import scipy.stats as stats # scipy is a statistical package for Python\n\n# Use Scipy's stats package to perform least-squares fit\nslope, intercept, r_value, p_value, std_err = stats.linregress(x,y)\n\nline = slope*x+intercept\nscatter(x,y)\nplot(x,line)\ntitle(\"Linear Regression - Least Squares Method\", weight='bold')\ngrid()\nshow()\n\n# Since we plot failure times on the y-axis, the actual slope is inverted\nshape = 1/slope\n# Since we plot failure times on the y-axis, we want the x-intercept, not the y-intercept\n# x-intercept is equal to the negative y-intercept divided by the slope/shape parameter\n# Basically you are solving for x: 0 = mx + b, equation of the line where y = 0\nx_intercept = - intercept / shape\n\nprint \"r^2 value:\", r_value**2\nprint \"slope/shape parameter:\", shape\nscale = exp(-x_intercept/slope)\nprint \"scale parameter:\", scale\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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sXLmS4cOHW7aRC6pC3Lrr168zZMg4tm/fg8FQnQ4dWvP115uo74DZtcxmbQ6Y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\nQmCC\n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "r^2 value: 0.953148083657\nslope/shape parameter: 2.02425855437\nscale parameter: 94.9979428891\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import numpy as np\nfrom numpy import random\nfrom matplotlib.ticker import FuncFormatter\n\n# I'm used to  the ln notation for the natural log\nfrom numpy import log as ln\n\n# 10 failures that we are assuming follow a Weibull distribution\nx = df_final[\"DTF\"].values\nrank = np.arange(1,data.size+1)  # ranks = {1, 2, 3, ... 21}\nmedian_rank = df_final[\"MEDIAN_RANK\"].values\ny = ln(-ln(1 - median_rank))\n\n# Generate 1000 numbers following a Weibull distribution that we think ideally fits our data using the shape and scale parameter\nx_ideal = scale *random.weibull(shape, size=100)\nx_ideal.sort()\nF = 1 - exp( -(x_ideal/scale)**shape )\ny_ideal = ln(-ln(1 - F))\n\n# Weibull plot\nax = subplot(111)\nsemilogx(x, y, \"bs\")\nplot(x_ideal, y_ideal, 'r-', label=\"beta= %5G\\neta = %.5G\" % (shape, scale) )\ntitle(\"Weibull Probability Plot on Log Scale\", weight=\"bold\")\nxlabel('x (time)', weight=\"bold\")\nylabel('Cumulative Distribution Function', weight=\"bold\")\nlegend(loc='lower right')\n\n# Generate ticks\ndef weibull_CDF(y, pos):\n    return \"%G %%\" % (100*(1-exp(-exp(y))))\n\nformatter = FuncFormatter(weibull_CDF)\nax.yaxis.set_major_formatter(formatter)\n\nyt_F = array([ 0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5,\n           0.6, 0.7, 0.8, 0.9, 0.95, 0.99])\nyt_lnF = ln( -ln(1-yt_F))\nyticks(yt_lnF)\nax.yaxis.grid()\nax.xaxis.grid(which='both')\nshow()\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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27dpwdXWFq6sr3Nzc5Ka/d+8eNm7ciL///htXr15FXl4edu3aBYDXwmIYlfjn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\n6l7c+kbQyvwAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x2 = np.arange(0,300)\ny2 = 1-exp(-(x2/scale)**shape) # This is the equation for Weibull CDF\n\nplot(x2,y2)\ntitle(\"Weibull CDF - Prediction\",weight='bold')\ngrid()\nshow()\n\nprint \"Coordinates ( x, y ) of the CDF:\"\nfor value in zip(x2,y2):\n    print \"( \" + str(value[0]) + \" , \" + str(value[1]*100) + \" )\"\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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paWlKKaWGDRumVq5cedl2rrAbt7d582aHbevIEaUaNlQqO9thm7SbI/NzNUbO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\nQmCC\n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Coordinates ( x, y ) of the CDF:\n( 0 , 0.0 )\n( 1 , 0.00992141384496 )\n( 2 , 0.0403524599601 )\n( 3 , 0.0916669461903 )\n( 4 , 0.164045278272 )\n( 5 , 0.257591285995 )\n( 6 , 0.372361358298 )\n( 7 , 0.508376861109 )\n( 8 , 0.665630660682 )\n( 9 , 0.844091007278 )\n( 10 , 1.04370405814 )\n( 11 , 1.26439563001 )\n( 12 , 1.50607248547 )\n( 13 , 1.76862332291 )\n( 14 , 2.05191957143 )\n( 15 , 2.35581605364 )\n( 16 , 2.68015155758 )\n( 17 , 3.02474934532 )\n( 18 , 3.38941761722 )\n( 19 , 3.77394994546 )\n( 20 , 4.17812568641 )\n( 21 , 4.6017103789 )\n( 22 , 5.04445613367 )\n( 23 , 5.50610201782 )\n( 24 , 5.98637443721 )\n( 25 , 6.48498751886 )\n( 26 , 7.00164349512 )\n( 27 , 7.53603309064 )\n( 28 , 8.08783591303 )\n( 29 , 8.65672084788 )\n( 30 , 9.2423464583 )\n( 31 , 9.84436138946 )\n( 32 , 10.4624047779 )\n( 33 , 11.096106666 )\n( 34 , 11.7450884206 )\n( 35 , 12.408963157 )\n( 36 , 13.0873361666 )\n( 37 , 13.7798053483 )\n( 38 , 14.4859616445 )\n( 39 , 15.2053894787 )\n( 40 , 15.9376671976 )\n( 41 , 16.6823675138 )\n( 42 , 17.4390579512 )\n( 43 , 18.2073012917 )\n( 44 , 18.9866560225 )\n( 45 , 19.7766767831 )\n( 46 , 20.576914813 )\n( 47 , 21.3869183982 )\n( 48 , 22.2062333158 )\n( 49 , 23.0344032775 )\n( 50 , 23.8709703705 )\n( 51 , 24.7154754951 )\n( 52 , 25.567458799 )\n( 53 , 26.426460108 )\n( 54 , 27.2920193517 )\n( 55 , 28.1636769842 )\n( 56 , 29.0409743998 )\n( 57 , 29.9234543422 )\n( 58 , 30.8106613076 )\n( 59 , 31.7021419405 )\n( 60 , 32.5974454228 )\n( 61 , 33.4961238545 )\n( 62 , 34.3977326265 )\n( 63 , 35.3018307851 )\n( 64 , 36.2079813868 )\n( 65 , 37.1157518448 )\n( 66 , 38.0247142648 )\n( 67 , 38.9344457721 )\n( 68 , 39.8445288268 )\n( 69 , 40.7545515301 )\n( 70 , 41.6641079189 )\n( 71 , 42.5727982492 )\n( 72 , 43.480229269 )\n( 73 , 44.386014479 )\n( 74 , 45.2897743817 )\n( 75 , 46.1911367195 )\n( 76 , 47.0897366998 )\n( 77 , 47.9852172086 )\n( 78 , 48.8772290119 )\n( 79 , 49.7654309447 )\n( 80 , 50.6494900878 )\n( 81 , 51.5290819323 )\n( 82 , 52.4038905317 )\n( 83 , 53.2736086415 )\n( 84 , 54.137937847 )\n( 85 , 54.9965886779 )\n( 86 , 55.8492807119 )\n( 87 , 56.6957426648 )\n( 88 , 57.5357124698 )\n( 89 , 58.368937344 )\n( 90 , 59.1951738436 )\n( 91 , 60.014187907 )\n( 92 , 60.8257548871 )\n( 93 , 61.6296595713 )\n( 94 , 62.4256961915 )\n( 95 , 63.2136684221 )\n( 96 , 63.9933893684 )\n( 97 , 64.7646815433 )\n( 98 , 65.5273768351 )\n( 99 , 66.2813164641 )\n( 100 , 67.0263509305 )\n( 101 , 67.7623399522 )\n( 102 , 68.489152394 )\n( 103 , 69.2066661873 )\n( 104 , 69.9147682419 )\n( 105 , 70.6133543491 )\n( 106 , 71.3023290774 )\n( 107 , 71.9816056597 )\n( 108 , 72.6511058744 )\n( 109 , 73.3107599185 )\n( 110 , 73.9605062748 )\n( 111 , 74.6002915721 )\n( 112 , 75.2300704405 )\n( 113 , 75.8498053601 )\n( 114 , 76.4594665047 )\n( 115 , 77.0590315811 )\n( 116 , 77.6484856631 )\n( 117 , 78.2278210215 )\n( 118 , 78.7970369506 )\n( 119 , 79.3561395905 )\n( 120 , 79.9051417463 )\n( 121 , 80.4440627048 )\n( 122 , 80.9729280483 )\n( 123 , 81.4917694659 )\n( 124 , 82.0006245633 )\n( 125 , 82.4995366706 )\n( 126 , 82.9885546491 )\n( 127 , 83.4677326968 )\n( 128 , 83.9371301531 )\n( 129 , 84.3968113034 )\n( 130 , 84.846845183 )\n( 131 , 85.2873053817 )\n( 132 , 85.7182698482 )\n( 133 , 86.1398206954 )\n( 134 , 86.5520440064 )\n( 135 , 86.9550296421 )\n( 136 , 87.3488710491 )\n( 137 , 87.7336650704 )\n( 138 , 88.1095117566 )\n( 139 , 88.4765141804 )\n( 140 , 88.8347782519 )\n( 141 , 89.1844125373 )\n( 142 , 89.5255280798 )\n( 143 , 89.8582382226 )\n( 144 , 90.1826584359 )\n( 145 , 90.4989061458 )\n( 146 , 90.807100567 )\n( 147 , 91.1073625387 )\n( 148 , 91.3998143631 )\n( 149 , 91.6845796488 )\n( 150 , 91.9617831567 )\n( 151 , 92.2315506498 )\n( 152 , 92.4940087468 )\n( 153 , 92.7492847801 )\n( 154 , 92.9975066568 )\n( 155 , 93.2388027242 )\n( 156 , 93.4733016396 )\n( 157 , 93.701132243 )\n( 158 , 93.9224234357 )\n( 159 , 94.1373040611 )\n( 160 , 94.3459027914 )\n( 161 , 94.5483480167 )\n( 162 , 94.7447677403 )\n( 163 , 94.9352894759 )\n( 164 , 95.120040151 )\n( 165 , 95.299146013 )\n( 166 , 95.4727325402 )\n( 167 , 95.6409243564 )\n( 168 , 95.80384515 )\n( 169 , 95.9616175968 )\n( 170 , 96.1143632871 )\n( 171 , 96.2622026561 )\n( 172 , 96.4052549188 )\n( 173 , 96.5436380088 )\n( 174 , 96.67746852 )\n( 175 , 96.806861653 )\n( 176 , 96.9319311646 )\n( 177 , 97.0527893207 )\n( 178 , 97.1695468535 )\n( 179 , 97.2823129211 )\n( 180 , 97.3911950709 )\n( 181 , 97.4962992067 )\n( 182 , 97.5977295578 )\n( 183 , 97.6955886526 )\n( 184 , 97.7899772941 )\n( 185 , 97.8809945388 )\n( 186 , 97.9687376786 )\n( 187 , 98.0533022245 )\n( 188 , 98.1347818945 )\n( 189 , 98.2132686025 )\n( 190 , 98.2888524507 )\n( 191 , 98.3616217237 )\n( 192 , 98.4316628857 )\n( 193 , 98.4990605788 )\n( 194 , 98.5638976244 )\n( 195 , 98.626255026 )\n( 196 , 98.6862119743 )\n( 197 , 98.7438458536 )\n( 198 , 98.7992322508 )\n( 199 , 98.852444965 )\n( 200 , 98.9035560197 )\n( 201 , 98.9526356758 )\n( 202 , 98.999752446 )\n( 203 , 99.0449731112 )\n( 204 , 99.0883627375 )\n( 205 , 99.1299846942 )\n( 206 , 99.1699006739 )\n( 207 , 99.2081707123 )\n( 208 , 99.24485321 )\n( 209 , 99.2800049546 )\n( 210 , 99.3136811438 )\n( 211 , 99.3459354092 )\n( 212 , 99.3768198405 )\n( 213 , 99.406385011 )\n( 214 , 99.4346800029 )\n( 215 , 99.4617524332 )\n( 216 , 99.4876484806 )\n( 217 , 99.512412912 )\n( 218 , 99.53608911 )\n( 219 , 99.5587191 )\n( 220 , 99.5803435778 )\n( 221 , 99.6010019378 )\n( 222 , 99.6207323006 )\n( 223 , 99.639571541 )\n( 224 , 99.6575553162 )\n( 225 , 99.6747180934 )\n( 226 , 99.6910931784 )\n( 227 , 99.7067127429 )\n( 228 , 99.7216078528 )\n( 229 , 99.7358084953 )\n( 230 , 99.7493436066 )\n( 231 , 99.7622410994 )\n( 232 , 99.7745278895 )\n( 233 , 99.7862299228 )\n( 234 , 99.7973722017 )\n( 235 , 99.8079788113 )\n( 236 , 99.8180729454 )\n( 237 , 99.8276769318 )\n( 238 , 99.8368122577 )\n( 239 , 99.8454995943 )\n( 240 , 99.8537588212 )\n( 241 , 99.8616090509 )\n( 242 , 99.8690686516 )\n( 243 , 99.8761552711 )\n( 244 , 99.8828858592 )\n( 245 , 99.8892766902 )\n( 246 , 99.8953433847 )\n( 247 , 99.9011009308 )\n( 248 , 99.9065637057 )\n( 249 , 99.9117454956 )\n( 250 , 99.916659516 )\n( 251 , 99.9213184315 )\n( 252 , 99.9257343746 )\n( 253 , 99.9299189646 )\n( 254 , 99.9338833257 )\n( 255 , 99.9376381049 )\n( 256 , 99.9411934891 )\n( 257 , 99.9445592221 )\n( 258 , 99.947744621 )\n( 259 , 99.9507585919 )\n( 260 , 99.9536096455 )\n( 261 , 99.9563059125 )\n( 262 , 99.9588551576 )\n( 263 , 99.9612647941 )\n( 264 , 99.9635418974 )\n( 265 , 99.9656932187 )\n( 266 , 99.9677251975 )\n( 267 , 99.9696439742 )\n( 268 , 99.9714554026 )\n( 269 , 99.9731650611 )\n( 270 , 99.9747782642 )\n( 271 , 99.9763000738 )\n( 272 , 99.9777353091 )\n( 273 , 99.9790885576 )\n( 274 , 99.9803641844 )\n( 275 , 99.9815663421 )\n( 276 , 99.9826989795 )\n( 277 , 99.9837658511 )\n( 278 , 99.9847705252 )\n( 279 , 99.9857163921 )\n( 280 , 99.9866066724 )\n( 281 , 99.9874444241 )\n( 282 , 99.9882325504 )\n( 283 , 99.9889738066 )\n( 284 , 99.9896708065 )\n( 285 , 99.9903260295 )\n( 286 , 99.9909418266 )\n( 287 , 99.9915204263 )\n( 288 , 99.9920639404 )\n( 289 , 99.9925743697 )\n( 290 , 99.9930536091 )\n( 291 , 99.9935034528 )\n( 292 , 99.993925599 )\n( 293 , 99.9943216549 )\n( 294 , 99.9946931408 )\n( 295 , 99.9950414945 )\n( 296 , 99.9953680755 )\n( 297 , 99.9956741687 )\n( 298 , 99.9959609882 )\n( 299 , 99.9962296812 )\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Now, we're done!"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Actually, there's more to this. &nbsp;There are considerations that needs to be made in determining if our line through the data points is a \"good\" fit. &nbsp;Also, when dealing with suspensions as outlined in this part 2, I have found that if I have very large quantities of suspensions compared to actual failures, X on Y median rank regression method did not work very well.  &nbsp;After brief <a href=\"http://www.weibull.com/hotwire/issue16/relbasics16.htm\">research</a>, I have found that in this case, it is recommended that I use a non-graphical method called maximum likelihood estimation (MLE).  &nbsp;When I have time, I will look into estimating Weibull paramenters using MLE method.  &nbsp;I guess that will be my Part 3."
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Part 3 - Estimating Weibull parameters using Maximum Likelihood Estimation (MLE)"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "To solve for our scale parameter (k) using MLE, we need to solve for this equation below:"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<center>$\\huge{\\sum\\limits_{i=1}^r \\frac{ln(x_i)}{r}=\\frac{\\sum\\limits_{i=1}^n (x_i)^kln(x_i)}{\\sum\\limits_{i=1}^n (x_i)^k}-\\frac{1}{k}\\approx0}$</center> ,<br><br>\n<center>Where $x_i$ is the ith failure time,</center><br>\n<center>r is the number of failures,</center><br>\n<center>and n is the total number of failure times, both failed and suspended</center>"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "The equation above basically means we need to find a value of k such that the left of the equation equals the right equation or in other words, the value of k such that the difference between the left of the equation and right of the equation is as close to zero as possible.  Once we find the value of k, the scale parameter can be calculated as:"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<center>$\\large{\\lambda=\\left(\\sum\\limits_{i=1}^n \\frac{(x_i)^k}{r}\\right)^\\frac{1}{k}}$</center>"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Let's get data from an external file and calculate the left side of the equation $\\left(\\large{\\sum\\limits_{i=1}^r \\frac{ln(x_i)}{r}}\\right)$:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import pandas\nimport openpyxl\nfrom numpy import log as ln\n\n# Open csv file\nxls = pandas.ExcelFile(r'C:\\Documents and Settings\\ma17151\\Desktop\\72148_Replaced.xlsx')\ndf = xls.parse(\"Weibull\")\n\ndf_failed = df[df.STATUS=='FAILED']\n\ndtf_failed = df_failed[\"DTF\"].values\n\ndef ln_x_div_r(series):\n    return ln(series[\"DTF\"])/len(df_failed)\n\nleft_eq_sum = np.sum( ln(dtf_failed)/len(df_failed) )\n\ndf_failed[\"ln_x_div_r\"] = df_failed.apply(ln_x_div_r, axis=1)\n\nprint df_failed.to_string(),\"\\n\"\nprint \"Sum of \\\"ln_x_div_r\\\" column =\", left_eq_sum\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "                 VIN_NO   DTF  STATUS  ln_x_div_r\n0     19UUA86589A005214  1534  FAILED    0.007013\n1     19UUA86559A017742  1521  FAILED    0.007005\n2     19UUA86549A007638  1501  FAILED    0.006992\n3     19UUA96589A000861  1480  FAILED    0.006979\n4     19UUA96559A001028  1466  FAILED    0.006970\n5     19UUA86529A003958  1455  FAILED    0.006962\n6     19UUA96509A004922  1452  FAILED    0.006961\n7     19UUA86519A013879  1445  FAILED    0.006956\n8     19UUA86579A005589  1441  FAILED    0.006953\n9     19UUA86529A010974  1427  FAILED    0.006944\n10    19UUA96589A005008  1424  FAILED    0.006942\n11    19UUA96599A001520  1423  FAILED    0.006941\n12    19UUA86509A011413  1416  FAILED    0.006937\n13    19UUA86569A007222  1416  FAILED    0.006937\n14    19UUA86599A009918  1412  FAILED    0.006934\n15    19UUA96529A001049  1412  FAILED    0.006934\n16    19UUA86529A005788  1412  FAILED    0.006934\n17    19UUA86579A018990  1411  FAILED    0.006933\n18    19UUA86529A013101  1410  FAILED    0.006932\n19    19UUA86569A022867  1395  FAILED    0.006922\n20    19UUA86529A009064  1395  FAILED    0.006922\n21    19UUA86559A017949  1392  FAILED    0.006920\n22    19UUA96599A004160  1387  FAILED    0.006917\n23    19UUA86509A016949  1385  FAILED    0.006915\n24    19UUA86559A013111  1383  FAILED    0.006914\n25    19UUA96569A000244  1382  FAILED    0.006913\n26    19UUA96589A002111  1381  FAILED    0.006913\n27    19UUA96549A005913  1381  FAILED    0.006913\n28    19UUA86549A013682  1379  FAILED    0.006911\n29    19UUA96589A002674  1378  FAILED    0.006911\n30    19UUA86579A008072  1372  FAILED    0.006906\n31    19UUA86579A010906  1365  FAILED    0.006901\n32    19UUA86529A007749  1361  FAILED    0.006899\n33    19UUA86579A004703  1360  FAILED    0.006898\n34    19UUA86529A024714  1359  FAILED    0.006897\n35    19UUA86519A016667  1358  FAILED    0.006897\n36    19UUA86579A014843  1357  FAILED    0.006896\n37    19UUA86509A012528  1353  FAILED    0.006893\n38    19UUA96579A003508  1353  FAILED    0.006893\n39    19UUA86519A003935  1348  FAILED    0.006889\n40    19UUA86539A009607  1345  FAILED    0.006887\n41    19UUA96589A002996  1345  FAILED    0.006887\n42    19UUA86509A026686  1344  FAILED    0.006887\n43    19UUA96599A000237  1343  FAILED    0.006886\n44    19UUA96569A002060  1341  FAILED    0.006884\n45    19UUA96519A002371  1340  FAILED    0.006884\n46    19UUA96519A004444  1340  FAILED    0.006884\n47    19UUA86559A026554  1339  FAILED    0.006883\n48    19UUA96579A001628  1339  FAILED    0.006883\n49    19UUA86569A010038  1339  FAILED    0.006883\n50    19UUA86589A019145  1336  FAILED    0.006881\n51    19UUA86539A006965  1336  FAILED    0.006881\n52    19UUA86569A012792  1336  FAILED    0.006881\n53    19UUA86549A008143  1335  FAILED    0.006880\n54    19UUA96519A003715  1335  FAILED    0.006880\n55    19UUA86519A005748  1333  FAILED    0.006879\n56    19UUA96579A004514  1332  FAILED    0.006878\n57    19UUA96589A001251  1331  FAILED    0.006877\n58    19UUA96589A004960  1330  FAILED    0.006877\n59    19UUA96529A002427  1328  FAILED    0.006875\n60    19UUA86519A009296  1327  FAILED    0.006874\n61    19UUA86539A022681  1327  FAILED    0.006874\n62    19UUA96569A001037  1327  FAILED    0.006874\n63    19UUA86549A016422  1325  FAILED    0.006873\n64    19UUA86539A005671  1325  FAILED    0.006873\n65    19UUA86599A006033  1325  FAILED    0.006873\n66    19UUA86599A011667  1324  FAILED    0.006872\n67    19UUA86589A017301  1324  FAILED    0.006872\n68    19UUA96549A002588  1321  FAILED    0.006870\n69    19UUA86549A009325  1321  FAILED    0.006870\n70    19UUA96559A003510  1316  FAILED    0.006866\n71    19UUA86509A013503  1315  FAILED    0.006866\n72    19UUA86599A020899  1313  FAILED    0.006864\n73    19UUA96589A001489  1313  FAILED    0.006864\n74    19UUA86579A004524  1312  FAILED    0.006864\n75    19UUA865X9A001665  1311  FAILED    0.006863\n76    19UUA96569A002656  1309  FAILED    0.006861\n77    19UUA96509A006203  1307  FAILED    0.006860\n78    19UUA86509A009063  1307  FAILED    0.006860\n79    19UUA86529A009338  1303  FAILED    0.006857\n80    19UUA86579A009951  1302  FAILED    0.006856\n81    19UUA96539A005790  1299  FAILED    0.006854\n82    19UUA86579A013529  1299  FAILED    0.006854\n83    19UUA86569A025915  1297  FAILED    0.006853\n84    19UUA86549A014458  1295  FAILED    0.006851\n85    19UUA86529A013860  1293  FAILED    0.006850\n86    19UUA96589A000875  1292  FAILED    0.006849\n87    19UUA965X9A001123  1287  FAILED    0.006845\n88    19UUA86569A007088  1287  FAILED    0.006845\n89    19UUA86579A011585  1286  FAILED    0.006844\n90    19UUA86559A005798  1286  FAILED    0.006844\n91    19UUA86519A005345  1285  FAILED    0.006844\n92    19UUA86579A022473  1284  FAILED    0.006843\n93    19UUA96589A004392  1283  FAILED    0.006842\n94    19UUA86529A014863  1283  FAILED    0.006842\n95    19UUA96509A004614  1282  FAILED    0.006841\n96    19UUA96519A006064  1279  FAILED    0.006839\n97    19UUA86539A016315  1279  FAILED    0.006839\n98    19UUA86559A013500  1279  FAILED    0.006839\n99    19UUA86519A009735  1278  FAILED    0.006838\n100   19UUA96509A005231  1278  FAILED    0.006838\n101   19UUA86569A004420  1278  FAILED    0.006838\n102   19UUA86549A008210  1276  FAILED    0.006837\n103   19UUA86569A011366  1276  FAILED    0.006837\n104   19UUA96509A006122  1275  FAILED    0.006836\n105   19UUA86579A008377  1275  FAILED    0.006836\n106   19UUA86539A008487  1275  FAILED    0.006836\n107   19UUA86579A001669  1275  FAILED    0.006836\n108   19UUA86589A005777  1275  FAILED    0.006836\n109   19UUA86559A006725  1274  FAILED    0.006835\n110   19UUA86509A014022  1272  FAILED    0.006834\n111   19UUA86529A010313  1272  FAILED    0.006834\n112   19UUA86549A017635  1271  FAILED    0.006833\n113   19UUA86569A026725  1270  FAILED    0.006832\n114   19UUA96599A005504  1270  FAILED    0.006832\n115   19UUA86589A002720  1270  FAILED    0.006832\n116   19UUA965X9A006354  1269  FAILED    0.006832\n117   19UUA96509A004144  1269  FAILED    0.006832\n118   19UUA96589A001167  1269  FAILED    0.006832\n119   19UUA86509A016708  1268  FAILED    0.006831\n120   19UUA86549A002083  1268  FAILED    0.006831\n121   19UUA86589A010669  1267  FAILED    0.006830\n122   19UUA86509A019706  1267  FAILED    0.006830\n123   19UUA86519A004308  1265  FAILED    0.006829\n124   19UUA96539A000296  1265  FAILED    0.006829\n125   19UUA86589A011692  1265  FAILED    0.006829\n126   19UUA86599A021065  1264  FAILED    0.006828\n127   19UUA86579A010887  1263  FAILED    0.006827\n128   19UUA865X9A004551  1262  FAILED    0.006826\n129   19UUA96559A005094  1261  FAILED    0.006826\n130   19UUA96569A006707  1260  FAILED    0.006825\n131   19UUA86569A026739  1260  FAILED    0.006825\n132   19UUA86559A006126  1260  FAILED    0.006825\n133   19UUA96519A004167  1258  FAILED    0.006823\n134   19UUA96589A006482  1258  FAILED    0.006823\n135   19UUA96599A006359  1257  FAILED    0.006823\n136   19UUA96519A004024  1256  FAILED    0.006822\n137   19UUA86519A018354  1255  FAILED    0.006821\n138   19UUA86509A007605  1255  FAILED    0.006821\n139   19UUA86549A021734  1254  FAILED    0.006820\n140   19UUA96589A004473  1253  FAILED    0.006820\n141   19UUA86509A009239  1252  FAILED    0.006819\n142   19UUA86579A023820  1250  FAILED    0.006817\n143   19UUA86569A026675  1250  FAILED    0.006817\n144   19UUA86509A020158  1250  FAILED    0.006817\n145   19UUA96579A001144  1250  FAILED    0.006817\n146   19UUA86509A023660  1249  FAILED    0.006817\n147   19UUA86539A011938  1249  FAILED    0.006817\n148   19UUA865X9A014108  1249  FAILED    0.006817\n149   19UUA965X9A001462  1249  FAILED    0.006817\n150   19UUA865X9A011595  1249  FAILED    0.006817\n151   19UUA86539A004942  1247  FAILED    0.006815\n152   19UUA86559A008958  1247  FAILED    0.006815\n153   19UUA86599A007148  1247  FAILED    0.006815\n154   19UUA965X9A001221  1246  FAILED    0.006814\n155   19UUA96579A003735  1245  FAILED    0.006813\n156   19UUA86569A013361  1245  FAILED    0.006813\n157   19UUA86509A020287  1244  FAILED    0.006813\n158   19UUA96569A004245  1242  FAILED    0.006811\n159   19UUA96519A005206  1242  FAILED    0.006811\n160   19UUA86539A026651  1241  FAILED    0.006810\n161   19UUA96599A002392  1241  FAILED    0.006810\n162   19UUA86589A009411  1238  FAILED    0.006808\n163   19UUA96589A001847  1238  FAILED    0.006808\n164   19UUA86539A016671  1235  FAILED    0.006806\n165   19UUA86559A005297  1235  FAILED    0.006806\n166   19UUA86519A011694  1233  FAILED    0.006804\n167   19UUA86559A004540  1233  FAILED    0.006804\n168   19UUA96599A006698  1230  FAILED    0.006802\n169   19UUA86589A004340  1229  FAILED    0.006801\n170   19UUA86579A010274  1229  FAILED    0.006801\n171   19UUA86589A004984  1228  FAILED    0.006800\n172   19UUA96549A006785  1227  FAILED    0.006800\n173   19UUA86569A012484  1227  FAILED    0.006800\n174   19UUA86579A010064  1227  FAILED    0.006800\n175   19UUA86569A005311  1227  FAILED    0.006800\n176   19UUA86589A011241  1226  FAILED    0.006799\n177   19UUA86509A017728  1225  FAILED    0.006798\n178   19UUA86559A005977  1225  FAILED    0.006798\n179   19UUA86529A023658  1223  FAILED    0.006796\n180   19UUA86589A024331  1223  FAILED    0.006796\n181   19UUA86569A010671  1223  FAILED    0.006796\n182   19UUA86559A006143  1223  FAILED    0.006796\n183   19UUA965X9A006385  1222  FAILED    0.006796\n184   19UUA86589A007464  1222  FAILED    0.006796\n185   19UUA865X9A010849  1222  FAILED    0.006796\n186   19UUA86579A013434  1222  FAILED    0.006796\n187   19UUA86519A025904  1221  FAILED    0.006795\n188   19UUA96539A003781  1221  FAILED    0.006795\n189   19UUA86519A024008  1220  FAILED    0.006794\n190   19UUA86539A017979  1219  FAILED    0.006793\n191   19UUA86539A026472  1219  FAILED    0.006793\n192   19UUA86549A016808  1219  FAILED    0.006793\n193   19UUA86579A004569  1219  FAILED    0.006793\n194   19UUA86539A006531  1218  FAILED    0.006793\n195   19UUA865X9A026727  1217  FAILED    0.006792\n196   19UUA86549A026142  1217  FAILED    0.006792\n197   19UUA96569A001197  1217  FAILED    0.006792\n198   19UUA86599A009577  1217  FAILED    0.006792\n199   19UUA86599A011443  1216  FAILED    0.006791\n200   19UUA86599A009028  1215  FAILED    0.006790\n201   19UUA86539A023829  1213  FAILED    0.006789\n202   19UUA86569A023873  1213  FAILED    0.006789\n203   19UUA86529A010764  1213  FAILED    0.006789\n204   19UUA96569A001023  1213  FAILED    0.006789\n205   19UUA86589A015127  1212  FAILED    0.006788\n206   19UUA86549A012144  1211  FAILED    0.006787\n207   19UUA86579A023624  1210  FAILED    0.006786\n208   19UUA96519A003813  1210  FAILED    0.006786\n209   19UUA86509A025005  1210  FAILED    0.006786\n210   19UUA86559A026604  1210  FAILED    0.006786\n211   19UUA86519A006267  1210  FAILED    0.006786\n212   19UUA86529A019206  1209  FAILED    0.006785\n213   19UUA86599A016402  1209  FAILED    0.006785\n214   19UUA86539A024897  1207  FAILED    0.006784\n215   19UUA96569A006738  1206  FAILED    0.006783\n216   19UUA96519A003519  1206  FAILED    0.006783\n217   19UUA86569A024246  1205  FAILED    0.006782\n218   19UUA86599A008025  1205  FAILED    0.006782\n219   19UUA86589A009151  1204  FAILED    0.006781\n220   19UUA86539A005055  1202  FAILED    0.006780\n221   19UUA96539A000265  1200  FAILED    0.006778\n222   19UUA96599A000335  1199  FAILED    0.006777\n223   19UUA86519A002140  1199  FAILED    0.006777\n224   19UUA96599A000187  1198  FAILED    0.006777\n225   19UUA86529A006973  1197  FAILED    0.006776\n226   19UUA96579A003265  1197  FAILED    0.006776\n227   19UUA86529A010103  1197  FAILED    0.006776\n228   19UUA86539A016931  1196  FAILED    0.006775\n229   19UUA96569A003886  1195  FAILED    0.006774\n230   19UUA865X9A006512  1195  FAILED    0.006774\n231   19UUA86529A026561  1194  FAILED    0.006773\n232   19UUA965X9A005284  1194  FAILED    0.006773\n233   19UUA86549A018588  1194  FAILED    0.006773\n234   19UUA86589A008078  1192  FAILED    0.006772\n235   19UUA96539A000248  1192  FAILED    0.006772\n236   19UUA86589A013684  1192  FAILED    0.006772\n237   19UUA86539A011910  1192  FAILED    0.006772\n238   19UUA86569A025669  1191  FAILED    0.006771\n239   19UUA965X9A001512  1190  FAILED    0.006770\n240   19UUA86529A019867  1189  FAILED    0.006769\n241   19UUA86549A018333  1188  FAILED    0.006769\n242   19UUA86509A019110  1187  FAILED    0.006768\n243   19UUA86569A014879  1186  FAILED    0.006767\n244   19UUA86589A009649  1186  FAILED    0.006767\n245   19UUA86589A010008  1186  FAILED    0.006767\n246   19UUA96589A006675  1185  FAILED    0.006766\n247   19UUA86549A011480  1184  FAILED    0.006765\n248   19UUA96559A002423  1184  FAILED    0.006765\n249   19UUA86519A004566  1184  FAILED    0.006765\n250   19UUA96579A000835  1184  FAILED    0.006765\n251   19UUA86529A004236  1184  FAILED    0.006765\n252   19UUA86539A002432  1184  FAILED    0.006765\n253   19UUA86549A023855  1183  FAILED    0.006765\n254   19UUA86529A005404  1183  FAILED    0.006765\n255   19UUA86599A026265  1182  FAILED    0.006764\n256   19UUA96589A006496  1182  FAILED    0.006764\n257   19UUA96589A004814  1182  FAILED    0.006764\n258   19UUA86529A009260  1182  FAILED    0.006764\n259   19UUA86509A005000  1182  FAILED    0.006764\n260   19UUA96519A006002  1181  FAILED    0.006763\n261   19UUA86579A004149  1181  FAILED    0.006763\n262   19UUA96589A005686  1181  FAILED    0.006763\n263   19UUA86509A005353  1181  FAILED    0.006763\n264   19UUA96529A001035  1181  FAILED    0.006763\n265   19UUA96509A006654  1180  FAILED    0.006762\n266   19UUA86599A005559  1180  FAILED    0.006762\n267   19UUA96599A003302  1179  FAILED    0.006761\n268   19UUA86549A006232  1179  FAILED    0.006761\n269   19UUA86519A012179  1178  FAILED    0.006761\n270   19UUA86509A017485  1178  FAILED    0.006761\n271   19UUA96539A006583  1177  FAILED    0.006760\n272   19UUA86579A006130  1177  FAILED    0.006760\n273   19UUA965X9A006080  1175  FAILED    0.006758\n274   19UUA86569A005938  1175  FAILED    0.006758\n275   19UUA86529A007587  1174  FAILED    0.006757\n276   19UUA86599A006209  1174  FAILED    0.006757\n277   19UUA86549A007249  1174  FAILED    0.006757\n278   19UUA86539A009686  1173  FAILED    0.006757\n279   19UUA96549A005586  1172  FAILED    0.006756\n280   19UUA86539A017996  1172  FAILED    0.006756\n281   19UUA96559A001840  1171  FAILED    0.006755\n282   19UUA865X9A003898  1169  FAILED    0.006753\n283   19UUA86509A026087  1169  FAILED    0.006753\n284   19UUA86519A001778  1168  FAILED    0.006752\n285   19UUA96569A000423  1168  FAILED    0.006752\n286   19UUA86579A019539  1167  FAILED    0.006752\n287   19UUA86549A009163  1167  FAILED    0.006752\n288   19UUA96559A006696  1166  FAILED    0.006751\n289   19UUA96539A006230  1166  FAILED    0.006751\n290   19UUA96599A003056  1166  FAILED    0.006751\n291   19UUA86559A011634  1166  FAILED    0.006751\n292   19UUA86589A007500  1166  FAILED    0.006751\n293   19UUA86519A013235  1165  FAILED    0.006750\n294   19UUA86549A007302  1165  FAILED    0.006750\n295   19UUA86599A011829  1164  FAILED    0.006749\n296   19UUA86569A004496  1164  FAILED    0.006749\n297   19UUA96519A001656  1164  FAILED    0.006749\n298   19UUA86589A004421  1164  FAILED    0.006749\n299   19UUA96519A001091  1162  FAILED    0.006748\n300   19UUA96599A005700  1161  FAILED    0.006747\n301   19UUA965X9A000764  1161  FAILED    0.006747\n302   19UUA96529A000693  1161  FAILED    0.006747\n303   19UUA86569A002795  1159  FAILED    0.006745\n304   19UUA86579A001798  1159  FAILED    0.006745\n305   19UUA86599A002144  1159  FAILED    0.006745\n306   19UUA96599A001971  1157  FAILED    0.006743\n307   19UUA865X9A018501  1157  FAILED    0.006743\n308   19UUA86559A011889  1155  FAILED    0.006742\n309   19UUA86559A003257  1155  FAILED    0.006742\n310   19UUA965X9A004653  1154  FAILED    0.006741\n311   19UUA86539A009459  1153  FAILED    0.006740\n312   19UUA86559A013027  1153  FAILED    0.006740\n313   19UUA86589A012289  1152  FAILED    0.006739\n314   19UUA86569A005440  1151  FAILED    0.006738\n315   19UUA96589A000519  1151  FAILED    0.006738\n316   19UUA86549A002682  1150  FAILED    0.006738\n317   19UUA865X9A006770  1150  FAILED    0.006738\n318   19UUA86579A006824  1149  FAILED    0.006737\n319   19UUA86579A026748  1149  FAILED    0.006737\n320   19UUA86569A016616  1149  FAILED    0.006737\n321   19UUA96529A004257  1149  FAILED    0.006737\n322   19UUA86549A019207  1149  FAILED    0.006737\n323   19UUA86549A006697  1149  FAILED    0.006737\n324   19UUA86529A008559  1148  FAILED    0.006736\n325   19UUA86559A024948  1147  FAILED    0.006735\n326   19UUA865X9A017395  1147  FAILED    0.006735\n327   19UUA86589A005732  1147  FAILED    0.006735\n328   19UUA86579A011814  1147  FAILED    0.006735\n329   19UUA86519A008519  1147  FAILED    0.006735\n330   19UUA86599A011801  1146  FAILED    0.006734\n331   19UUA86539A020560  1146  FAILED    0.006734\n332   19UUA86589A002118  1146  FAILED    0.006734\n333   19UUA86549A010037  1146  FAILED    0.006734\n334   19UUA86589A007769  1146  FAILED    0.006734\n335   19UUA86589A001793  1146  FAILED    0.006734\n336   19UUA86539A013642  1145  FAILED    0.006733\n337   19UUA86509A014859  1145  FAILED    0.006733\n338   19UUA86599A005478  1145  FAILED    0.006733\n339   19UUA86559A009897  1144  FAILED    0.006733\n340   19UUA86599A011748  1143  FAILED    0.006732\n341   19UUA96579A000317  1143  FAILED    0.006732\n342   19UUA86599A009885  1142  FAILED    0.006731\n343   19UUA86599A009806  1142  FAILED    0.006731\n344   19UUA86549A005601  1142  FAILED    0.006731\n345   19UUA86559A010998  1142  FAILED    0.006731\n346   19UUA86599A006467  1142  FAILED    0.006731\n347   19UUA96589A004618  1141  FAILED    0.006730\n348   19UUA96529A002475  1141  FAILED    0.006730\n349   19UUA86559A012704  1141  FAILED    0.006730\n350   19UUA86539A004567  1140  FAILED    0.006729\n351   19UUA86599A009613  1138  FAILED    0.006728\n352   19UUA965X9A000974  1137  FAILED    0.006727\n353   19UUA86539A017819  1137  FAILED    0.006727\n354   19UUA86599A001866  1135  FAILED    0.006725\n355   19UUA86599A015704  1135  FAILED    0.006725\n356   19UUA86569A014915  1135  FAILED    0.006725\n357   19UUA96549A000985  1135  FAILED    0.006725\n358   19UUA865X9A006672  1135  FAILED    0.006725\n359   19UUA86569A013957  1134  FAILED    0.006724\n360   19UUA86509A005272  1133  FAILED    0.006723\n361   19UUA96519A001169  1133  FAILED    0.006723\n362   19UUA86559A007003  1133  FAILED    0.006723\n363   19UUA96589A005428  1132  FAILED    0.006723\n364   19UUA86599A014293  1132  FAILED    0.006723\n365   19UUA865X9A011919  1132  FAILED    0.006723\n366   19UUA86549A006456  1132  FAILED    0.006723\n367   19UUA96519A001673  1131  FAILED    0.006722\n368   19UUA96519A002323  1130  FAILED    0.006721\n369   19UUA96519A004153  1129  FAILED    0.006720\n370   19UUA86529A019870  1129  FAILED    0.006720\n371   19UUA865X9A001827  1128  FAILED    0.006719\n372   19UUA86579A018147  1128  FAILED    0.006719\n373   19UUA86539A015567  1128  FAILED    0.006719\n374   19UUA86559A024562  1127  FAILED    0.006718\n375   19UUA86549A019708  1127  FAILED    0.006718\n376   19UUA96519A001821  1127  FAILED    0.006718\n377   19UUA86519A014093  1127  FAILED    0.006718\n378   19UUA86589A011711  1127  FAILED    0.006718\n379   19UUA86549A007333  1126  FAILED    0.006717\n380   19UUA86599A014858  1126  FAILED    0.006717\n381   19UUA86519A011811  1126  FAILED    0.006717\n382   19UUA86539A011406  1125  FAILED    0.006717\n383   19UUA86599A013113  1125  FAILED    0.006717\n384   19UUA86569A014154  1124  FAILED    0.006716\n385   19UUA86539A004892  1123  FAILED    0.006715\n386   19UUA865X9A010561  1123  FAILED    0.006715\n387   19UUA86549A008255  1123  FAILED    0.006715\n388   19UUA865X9A007045  1122  FAILED    0.006714\n389   19UUA86539A007775  1120  FAILED    0.006712\n390   19UUA86579A011411  1120  FAILED    0.006712\n391   19UUA86579A007682  1120  FAILED    0.006712\n392   19UUA86539A011857  1119  FAILED    0.006711\n393   19UUA865X9A022693  1119  FAILED    0.006711\n394   19UUA86569A007866  1119  FAILED    0.006711\n395   19UUA86519A013915  1119  FAILED    0.006711\n396   19UUA965X9A001574  1119  FAILED    0.006711\n397   19UUA86559A003209  1117  FAILED    0.006710\n398   19UUA86589A017766  1117  FAILED    0.006710\n399   19UUA86529A015267  1117  FAILED    0.006710\n400   19UUA86519A017950  1117  FAILED    0.006710\n401   19UUA86509A004915  1117  FAILED    0.006710\n402   19UUA96539A006289  1116  FAILED    0.006709\n403   19UUA86599A025729  1116  FAILED    0.006709\n404   19UUA86569A011903  1116  FAILED    0.006709\n405   19UUA96509A002037  1116  FAILED    0.006709\n406   19UUA86539A006402  1116  FAILED    0.006709\n407   19UUA86509A013078  1116  FAILED    0.006709\n408   19UUA86569A016289  1116  FAILED    0.006709\n409   19UUA96529A000953  1115  FAILED    0.006708\n410   19UUA86599A013905  1115  FAILED    0.006708\n411   19UUA96559A006519  1114  FAILED    0.006707\n412   19UUA86579A014308  1114  FAILED    0.006707\n413   19UUA86559A013769  1114  FAILED    0.006707\n414   19UUA96529A006459  1113  FAILED    0.006706\n415   19UUA86569A024831  1113  FAILED    0.006706\n416   19UUA86579A015183  1112  FAILED    0.006705\n417   19UUA96519A001592  1112  FAILED    0.006705\n418   19UUA86599A004864  1112  FAILED    0.006705\n419   19UUA96549A005507  1111  FAILED    0.006705\n420   19UUA86569A009438  1111  FAILED    0.006705\n421   19UUA96539A004882  1111  FAILED    0.006705\n422   19UUA86549A006442  1111  FAILED    0.006705\n423   19UUA86599A002631  1111  FAILED    0.006705\n424   19UUA96549A002672  1110  FAILED    0.006704\n425   19UUA865X9A024072  1109  FAILED    0.006703\n426   19UUA86519A017060  1109  FAILED    0.006703\n427   19UUA96549A003370  1109  FAILED    0.006703\n428   19UUA96549A003658  1108  FAILED    0.006702\n429   19UUA96579A000737  1108  FAILED    0.006702\n430   19UUA86509A012710  1108  FAILED    0.006702\n431   19UUA86599A020322  1107  FAILED    0.006701\n432   19UUA86579A023705  1106  FAILED    0.006700\n433   19UUA965X9A001526  1106  FAILED    0.006700\n434   19UUA96549A000758  1106  FAILED    0.006700\n435   19UUA86579A004443  1106  FAILED    0.006700\n436   19UUA86539A003970  1106  FAILED    0.006700\n437   19UUA86539A011227  1105  FAILED    0.006699\n438   19UUA86519A003045  1104  FAILED    0.006699\n439   19UUA86569A007219  1103  FAILED    0.006698\n440   19UUA86589A004533  1103  FAILED    0.006698\n441   19UUA86539A005041  1103  FAILED    0.006698\n442   19UUA96549A006656  1102  FAILED    0.006697\n443   19UUA86579A007679  1102  FAILED    0.006697\n444   19UUA86509A022752  1101  FAILED    0.006696\n445   19UUA86509A009371  1101  FAILED    0.006696\n446   19UUA86559A014128  1101  FAILED    0.006696\n447   19UUA86519A019035  1101  FAILED    0.006696\n448   19UUA86509A017910  1100  FAILED    0.006695\n449   19UUA86529A022364  1100  FAILED    0.006695\n450   19UUA86569A020746  1100  FAILED    0.006695\n451   19UUA86579A006774  1100  FAILED    0.006695\n452   19UUA86599A007991  1099  FAILED    0.006694\n453   19UUA86539A008053  1099  FAILED    0.006694\n454   19UUA86549A015058  1098  FAILED    0.006693\n455   19UUA86569A008094  1098  FAILED    0.006693\n456   19UUA86549A006778  1098  FAILED    0.006693\n457   19UUA86589A008260  1097  FAILED    0.006692\n458   19UUA86509A014151  1097  FAILED    0.006692\n459   19UUA86509A014974  1097  FAILED    0.006692\n460   19UUA86519A005586  1096  FAILED    0.006692\n461   19UUA96559A002633  1096  FAILED    0.006692\n462   19UUA96539A001836  1096  FAILED    0.006692\n463   19UUA86509A013680  1096  FAILED    0.006692\n464   19UUA86549A014461  1095  FAILED    0.006691\n465   19UUA96529A002279  1095  FAILED    0.006691\n466   19UUA86549A025489  1094  FAILED    0.006690\n467   19UUA86539A016377  1094  FAILED    0.006690\n468   19UUA96519A002127  1094  FAILED    0.006690\n469   19UUA86539A018226  1094  FAILED    0.006690\n470   19UUA86589A002443  1093  FAILED    0.006689\n471   19UUA865X9A015632  1092  FAILED    0.006688\n472   19UUA96519A000264  1091  FAILED    0.006687\n473   19UUA86559A006773  1091  FAILED    0.006687\n474   19UUA86559A025890  1090  FAILED    0.006686\n475   19UUA86549A009633  1090  FAILED    0.006686\n476   19UUA86549A025444  1089  FAILED    0.006685\n477   19UUA86519A021688  1089  FAILED    0.006685\n478   19UUA86569A001694  1088  FAILED    0.006685\n479   19UUA96589A003503  1088  FAILED    0.006685\n480   19UUA86599A005349  1087  FAILED    0.006684\n481   19UUA865X9A004436  1087  FAILED    0.006684\n482   19UUA86539A017612  1086  FAILED    0.006683\n483   19UUA86509A014120  1086  FAILED    0.006683\n484   19UUA86509A007023  1086  FAILED    0.006683\n485   19UUA86539A003130  1086  FAILED    0.006683\n486   19UUA86599A006694  1085  FAILED    0.006682\n487   19UUA86519A005197  1085  FAILED    0.006682\n488   19UUA86569A026255  1084  FAILED    0.006681\n489   19UUA86529A023028  1084  FAILED    0.006681\n490   19UUA96549A002462  1084  FAILED    0.006681\n491   19UUA86569A009049  1082  FAILED    0.006679\n492   19UUA96549A004826  1082  FAILED    0.006679\n493   19UUA86509A013100  1082  FAILED    0.006679\n494   19UUA86599A013659  1082  FAILED    0.006679\n495   19UUA96559A001000  1081  FAILED    0.006678\n496   19UUA86549A006053  1080  FAILED    0.006678\n497   19UUA96589A000648  1080  FAILED    0.006678\n498   19UUA96539A000685  1080  FAILED    0.006678\n499   19UUA865X9A020152  1079  FAILED    0.006677\n500   19UUA86549A010121  1079  FAILED    0.006677\n501   19UUA86569A002621  1078  FAILED    0.006676\n502   19UUA86529A001692  1077  FAILED    0.006675\n503   19UUA86509A016370  1077  FAILED    0.006675\n504   19UUA86529A026141  1076  FAILED    0.006674\n505   19UUA96559A003202  1076  FAILED    0.006674\n506   19UUA86569A015059  1076  FAILED    0.006674\n507   19UUA865X9A016697  1076  FAILED    0.006674\n508   19UUA86599A011863  1075  FAILED    0.006673\n509   19UUA86549A013648  1075  FAILED    0.006673\n510   19UUA865X9A024010  1074  FAILED    0.006672\n511   19UUA86569A008340  1074  FAILED    0.006672\n512   19UUA86599A019736  1074  FAILED    0.006672\n513   19UUA86549A006330  1074  FAILED    0.006672\n514   19UUA96519A000233  1074  FAILED    0.006672\n515   19UUA86529A014183  1072  FAILED    0.006670\n516   19UUA86549A010135  1071  FAILED    0.006670\n517   19UUA86559A010807  1071  FAILED    0.006670\n518   19UUA86559A003825  1071  FAILED    0.006670\n519   19UUA86509A006499  1071  FAILED    0.006670\n520   19UUA96529A000242  1071  FAILED    0.006670\n521   19UUA86529A019528  1071  FAILED    0.006670\n522   19UUA86519A019729  1071  FAILED    0.006670\n523   19UUA86529A002129  1071  FAILED    0.006670\n524   19UUA86599A011975  1070  FAILED    0.006669\n525   19UUA86559A003663  1070  FAILED    0.006669\n526   19UUA86569A010119  1069  FAILED    0.006668\n527   19UUA86509A007944  1069  FAILED    0.006668\n528   19UUA86579A018245  1068  FAILED    0.006667\n529   19UUA86509A022380  1068  FAILED    0.006667\n530   19UUA86579A025759  1067  FAILED    0.006666\n531   19UUA86579A011375  1067  FAILED    0.006666\n532   19UUA86519A012618  1066  FAILED    0.006665\n533   19UUA86539A026634  1066  FAILED    0.006665\n534   19UUA86519A014966  1066  FAILED    0.006665\n535   19UUA86509A018653  1065  FAILED    0.006664\n536   19UUA865X9A003741  1065  FAILED    0.006664\n537   19UUA96559A000221  1065  FAILED    0.006664\n538   19UUA86589A006850  1064  FAILED    0.006663\n539   19UUA86549A007624  1064  FAILED    0.006663\n540   19UUA96519A001818  1064  FAILED    0.006663\n541   19UUA86559A015280  1062  FAILED    0.006661\n542   19UUA86599A004847  1062  FAILED    0.006661\n543   19UUA86569A013571  1061  FAILED    0.006661\n544   19UUA86529A002731  1061  FAILED    0.006661\n545   19UUA96579A005422  1060  FAILED    0.006660\n546   19UUA86589A022661  1060  FAILED    0.006660\n547   19UUA86509A008477  1060  FAILED    0.006660\n548   19UUA96549A004986  1057  FAILED    0.006657\n549   19UUA96569A000888  1057  FAILED    0.006657\n550   19UUA86539A009915  1057  FAILED    0.006657\n551   19UUA865X9A020555  1056  FAILED    0.006656\n552   19UUA96599A004479  1056  FAILED    0.006656\n553   19UUA86599A011457  1056  FAILED    0.006656\n554   19UUA86569A009388  1055  FAILED    0.006655\n555   19UUA86569A002120  1055  FAILED    0.006655\n556   19UUA96579A004772  1054  FAILED    0.006654\n557   19UUA86509A012836  1054  FAILED    0.006654\n558   19UUA86559A009611  1054  FAILED    0.006654\n559   19UUA865X9A019583  1054  FAILED    0.006654\n560   19UUA86539A013656  1053  FAILED    0.006653\n561   19UUA86579A018343  1053  FAILED    0.006653\n562   19UUA96599A001470  1053  FAILED    0.006653\n563   19UUA86509A002999  1053  FAILED    0.006653\n564   19UUA86539A014130  1052  FAILED    0.006652\n565   19UUA86599A009501  1052  FAILED    0.006652\n566   19UUA86589A022501  1051  FAILED    0.006652\n567   19UUA865X9A013721  1049  FAILED    0.006650\n568   19UUA86509A009094  1049  FAILED    0.006650\n569   19UUA86549A015982  1048  FAILED    0.006649\n570   19UUA865X9A015243  1048  FAILED    0.006649\n571   19UUA96549A002851  1047  FAILED    0.006648\n572   19UUA96539A001545  1047  FAILED    0.006648\n573   19UUA96579A003895  1046  FAILED    0.006647\n574   19UUA86579A013188  1044  FAILED    0.006645\n575   19UUA86569A009746  1044  FAILED    0.006645\n576   19UUA86509A025375  1042  FAILED    0.006643\n577   19UUA96519A003911  1042  FAILED    0.006643\n578   19UUA86569A003686  1042  FAILED    0.006643\n579   19UUA86509A016305  1042  FAILED    0.006643\n580   19UUA96579A002763  1041  FAILED    0.006642\n581   19UUA86579A005981  1041  FAILED    0.006642\n582   19UUA96549A000873  1041  FAILED    0.006642\n583   19UUA86519A017995  1040  FAILED    0.006641\n584   19UUA96509A003883  1038  FAILED    0.006640\n585   19UUA96509A002782  1038  FAILED    0.006640\n586   19UUA86559A010855  1037  FAILED    0.006639\n587   19UUA86529A026513  1037  FAILED    0.006639\n588   19UUA96579A003573  1037  FAILED    0.006639\n589   19UUA86549A014072  1037  FAILED    0.006639\n590   19UUA86569A012579  1037  FAILED    0.006639\n591   19UUA86579A002823  1037  FAILED    0.006639\n592   19UUA86559A015215  1037  FAILED    0.006639\n593   19UUA86549A008370  1036  FAILED    0.006638\n594   19UUA86529A024955  1035  FAILED    0.006637\n595   19UUA965X9A006077  1035  FAILED    0.006637\n596   19UUA86589A016794  1035  FAILED    0.006637\n597   19UUA86559A016350  1034  FAILED    0.006636\n598   19UUA86519A007953  1034  FAILED    0.006636\n599   19UUA86539A011793  1033  FAILED    0.006635\n600   19UUA86539A019683  1033  FAILED    0.006635\n601   19UUA86599A017016  1033  FAILED    0.006635\n602   19UUA86559A012265  1032  FAILED    0.006634\n603   19UUA86529A008948  1032  FAILED    0.006634\n604   19UUA86529A004690  1032  FAILED    0.006634\n605   19UUA86529A001689  1031  FAILED    0.006633\n606   19UUA86559A009933  1031  FAILED    0.006633\n607   19UUA86559A008510  1029  FAILED    0.006631\n608   19UUA86519A017608  1028  FAILED    0.006630\n609   19UUA86539A004021  1028  FAILED    0.006630\n610   19UUA96559A001076  1028  FAILED    0.006630\n611   19UUA86509A026347  1027  FAILED    0.006629\n612   19UUA86569A013523  1027  FAILED    0.006629\n613   19UUA865X9A007661  1027  FAILED    0.006629\n614   19UUA86519A001280  1027  FAILED    0.006629\n615   19UUA865X9A013847  1027  FAILED    0.006629\n616   19UUA86519A015163  1026  FAILED    0.006629\n617   19UUA86579A018942  1026  FAILED    0.006629\n618   19UUA86549A005677  1026  FAILED    0.006629\n619   19UUA96529A005053  1025  FAILED    0.006628\n620   19UUA86539A021000  1025  FAILED    0.006628\n621   19UUA96529A002296  1025  FAILED    0.006628\n622   19UUA96549A001618  1023  FAILED    0.006626\n623   19UUA86529A018332  1022  FAILED    0.006625\n624   19UUA86599A008297  1022  FAILED    0.006625\n625   19UUA865X9A022788  1021  FAILED    0.006624\n626   19UUA96579A005081  1021  FAILED    0.006624\n627   19UUA86569A005633  1021  FAILED    0.006624\n628   19UUA86509A004722  1021  FAILED    0.006624\n629   19UUA86539A003029  1020  FAILED    0.006623\n630   19UUA96549A004003  1020  FAILED    0.006623\n631   19UUA96559A003393  1020  FAILED    0.006623\n632   19UUA96549A004339  1019  FAILED    0.006622\n633   19UUA86579A023641  1019  FAILED    0.006622\n634   19UUA86589A007996  1019  FAILED    0.006622\n635   19UUA865X9A023374  1018  FAILED    0.006621\n636   19UUA96529A004372  1018  FAILED    0.006621\n637   19UUA86519A010691  1018  FAILED    0.006621\n638   19UUA86559A005249  1018  FAILED    0.006621\n639   19UUA86569A002649  1018  FAILED    0.006621\n640   19UUA86509A002081  1017  FAILED    0.006620\n641   19UUA86569A024571  1015  FAILED    0.006618\n642   19UUA86549A004304  1015  FAILED    0.006618\n643   19UUA86579A009674  1015  FAILED    0.006618\n644   19UUA86539A007789  1014  FAILED    0.006617\n645   19UUA865X9A013539  1013  FAILED    0.006616\n646   19UUA96579A000981  1011  FAILED    0.006614\n647   19UUA86529A006892  1011  FAILED    0.006614\n648   19UUA86579A006936  1010  FAILED    0.006613\n649   19UUA86569A011898  1010  FAILED    0.006613\n650   19UUA86549A016355  1009  FAILED    0.006613\n651   19UUA86559A007132  1009  FAILED    0.006613\n652   19UUA96529A004288  1009  FAILED    0.006613\n653   19UUA86599A004900  1009  FAILED    0.006613\n654   19UUA86549A026450  1008  FAILED    0.006612\n655   19UUA96559A005659  1008  FAILED    0.006612\n656   19UUA86569A009102  1008  FAILED    0.006612\n657   19UUA86569A017152  1007  FAILED    0.006611\n658   19UUA86579A011439  1007  FAILED    0.006611\n659   19UUA96569A004861  1007  FAILED    0.006611\n660   19UUA86569A007172  1005  FAILED    0.006609\n661   19UUA86549A021068  1004  FAILED    0.006608\n662   19UUA86519A019679  1004  FAILED    0.006608\n663   19UUA86599A023611  1003  FAILED    0.006607\n664   19UUA86569A014266  1003  FAILED    0.006607\n665   19UUA86509A018605  1001  FAILED    0.006605\n666   19UUA86569A013599  1001  FAILED    0.006605\n667   19UUA96519A004332  1001  FAILED    0.006605\n668   19UUA86579A011912  1000  FAILED    0.006604\n669   19UUA86529A009369  1000  FAILED    0.006604\n670   19UUA86539A013494   999  FAILED    0.006603\n671   19UUA86549A013164   999  FAILED    0.006603\n672   19UUA86599A002659   998  FAILED    0.006602\n673   19UUA86539A023135   998  FAILED    0.006602\n674   19UUA865X9A003464   997  FAILED    0.006601\n675   19UUA86539A004276   997  FAILED    0.006601\n676   19UUA86579A012235   996  FAILED    0.006600\n677   19UUA96579A004531   996  FAILED    0.006600\n678   19UUA86589A016424   996  FAILED    0.006600\n679   19UUA96579A004139   995  FAILED    0.006599\n680   19UUA86539A003614   995  FAILED    0.006599\n681   19UUA865X9A011242   995  FAILED    0.006599\n682   19UUA86579A022506   994  FAILED    0.006598\n683   19UUA86569A012016   994  FAILED    0.006598\n684   19UUA865X9A015565   994  FAILED    0.006598\n685   19UUA86549A021412   994  FAILED    0.006598\n686   19UUA86559A009415   993  FAILED    0.006597\n687   19UUA86529A002616   993  FAILED    0.006597\n688   19UUA86559A007454   993  FAILED    0.006597\n689   19UUA86599A006078   992  FAILED    0.006596\n690   19UUA86529A016287   991  FAILED    0.006595\n691   19UUA86579A018150   991  FAILED    0.006595\n692   19UUA96569A003998   990  FAILED    0.006594\n693   19UUA86549A016792   990  FAILED    0.006594\n694   19UUA86569A010282   990  FAILED    0.006594\n695   19UUA86509A016319   989  FAILED    0.006593\n696   19UUA86539A008926   989  FAILED    0.006593\n697   19UUA86529A003605   988  FAILED    0.006592\n698   19UUA86599A009224   988  FAILED    0.006592\n699   19UUA96509A002281   988  FAILED    0.006592\n700   19UUA86599A018487   988  FAILED    0.006592\n701   19UUA86589A004676   988  FAILED    0.006592\n702   19UUA86559A024349   987  FAILED    0.006591\n703   19UUA86519A023439   987  FAILED    0.006591\n704   19UUA86599A015119   987  FAILED    0.006591\n705   19UUA86589A012308   986  FAILED    0.006590\n706   19UUA865X9A015209   986  FAILED    0.006590\n707   19UUA86509A007961   986  FAILED    0.006590\n708   19UUA86529A017827   985  FAILED    0.006590\n709   19UUA86579A015572   984  FAILED    0.006589\n710   19UUA86589A007688   984  FAILED    0.006589\n711   19UUA86589A016679   983  FAILED    0.006588\n712   19UUA86529A013308   983  FAILED    0.006588\n713   19UUA86569A024098   982  FAILED    0.006587\n714   19UUA86579A003504   982  FAILED    0.006587\n715   19UUA865X9A021172   982  FAILED    0.006587\n716   19UUA96539A003747   982  FAILED    0.006587\n717   19UUA86549A012533   982  FAILED    0.006587\n718   19UUA865X9A009670   981  FAILED    0.006586\n719   19UUA86539A016976   981  FAILED    0.006586\n720   19UUA86539A005668   981  FAILED    0.006586\n721   19UUA86529A021781   980  FAILED    0.006585\n722   19UUA86559A011603   980  FAILED    0.006585\n723   19UUA86579A009853   979  FAILED    0.006584\n724   19UUA96519A004220   978  FAILED    0.006583\n725   19UUA86519A006124   978  FAILED    0.006583\n726   19UUA86559A022374   978  FAILED    0.006583\n727   19UUA86509A008818   977  FAILED    0.006582\n728   19UUA86579A022201   977  FAILED    0.006582\n729   19UUA86549A017019   976  FAILED    0.006581\n730   19UUA86569A013442   976  FAILED    0.006581\n731   19UUA86559A011732   975  FAILED    0.006580\n732   19UUA86589A022689   975  FAILED    0.006580\n733   19UUA86539A019165   973  FAILED    0.006578\n734   19UUA86599A023429   973  FAILED    0.006578\n735   19UUA86559A012864   973  FAILED    0.006578\n736   19UUA96529A004775   973  FAILED    0.006578\n737   19UUA86559A020933   972  FAILED    0.006577\n738   19UUA96579A002293   972  FAILED    0.006577\n739   19UUA86569A015787   971  FAILED    0.006576\n740   19UUA86519A014868   971  FAILED    0.006576\n741   19UUA86549A008448   971  FAILED    0.006576\n742   19UUA86559A019586   971  FAILED    0.006576\n743   19UUA86589A002636   970  FAILED    0.006575\n744   19UUA86589A014155   970  FAILED    0.006575\n745   19UUA965X9A004863   969  FAILED    0.006574\n746   19UUA86569A013568   969  FAILED    0.006574\n747   19UUA86559A023878   968  FAILED    0.006573\n748   19UUA86539A021787   968  FAILED    0.006573\n749   19UUA86519A016815   968  FAILED    0.006573\n750   19UUA86599A025035   968  FAILED    0.006573\n751   19UUA86539A023460   967  FAILED    0.006572\n752   19UUA86509A015137   967  FAILED    0.006572\n753   19UUA86569A004515   967  FAILED    0.006572\n754   19UUA86579A015975   967  FAILED    0.006572\n755   19UUA96589A001542   966  FAILED    0.006571\n756   19UUA86539A009090   966  FAILED    0.006571\n757   19UUA86599A005481   965  FAILED    0.006570\n758   19UUA86559A023217   965  FAILED    0.006570\n759   19UUA86519A007533   965  FAILED    0.006570\n760   19UUA86509A026767   964  FAILED    0.006569\n761   19UUA86529A023983   964  FAILED    0.006569\n762   19UUA86569A018317   964  FAILED    0.006569\n763   19UUA96509A004175   963  FAILED    0.006568\n764   19UUA86599A021177   963  FAILED    0.006568\n765   19UUA86559A018583   963  FAILED    0.006568\n766   19UUA86539A013107   963  FAILED    0.006568\n767   19UUA86599A022393   963  FAILED    0.006568\n768   19UUA96559A000445   963  FAILED    0.006568\n769   19UUA96549A004714   962  FAILED    0.006567\n770   19UUA86549A023094   962  FAILED    0.006567\n771   19UUA86539A018291   962  FAILED    0.006567\n772   19UUA86509A024906   960  FAILED    0.006565\n773   19UUA86529A010022   960  FAILED    0.006565\n774   19UUA86559A005624   960  FAILED    0.006565\n775   19UUA86539A026648   959  FAILED    0.006564\n776   19UUA86569A014302   959  FAILED    0.006564\n777   19UUA86519A006303   959  FAILED    0.006564\n778   19UUA86589A013734   959  FAILED    0.006564\n779   19UUA86559A023170   958  FAILED    0.006563\n780   19UUA86549A007218   957  FAILED    0.006562\n781   19UUA86589A020232   956  FAILED    0.006561\n782   19UUA86589A026130   955  FAILED    0.006560\n783   19UUA865X9A006686   955  FAILED    0.006560\n784   19UUA86559A007177   955  FAILED    0.006560\n785   19UUA96559A005600   954  FAILED    0.006559\n786   19UUA865X9A020572   952  FAILED    0.006557\n787   19UUA86599A008896   952  FAILED    0.006557\n788   19UUA86559A011701   952  FAILED    0.006557\n789   19UUA965X9A000523   952  FAILED    0.006557\n790   19UUA865X9A008339   951  FAILED    0.006556\n791   19UUA86589A012969   950  FAILED    0.006555\n792   19UUA86589A024992   950  FAILED    0.006555\n793   19UUA86549A017537   950  FAILED    0.006555\n794   19UUA96569A005640   949  FAILED    0.006554\n795   19UUA86569A015627   949  FAILED    0.006554\n796   19UUA86589A017833   949  FAILED    0.006554\n797   19UUA86589A007108   949  FAILED    0.006554\n798   19UUA865X9A013766   948  FAILED    0.006553\n799   19UUA865X9A011080   948  FAILED    0.006553\n800   19UUA86559A006711   947  FAILED    0.006552\n801   19UUA86569A011187   947  FAILED    0.006552\n802   19UUA965X9A005012   946  FAILED    0.006551\n803   19UUA86519A004325   946  FAILED    0.006551\n804   19UUA86599A024578   944  FAILED    0.006549\n805   19UUA86519A021741   943  FAILED    0.006548\n806   19UUA86529A015981   943  FAILED    0.006548\n807   19UUA86519A007158   942  FAILED    0.006547\n808   19UUA86559A015246   942  FAILED    0.006547\n809   19UUA86539A004682   942  FAILED    0.006547\n810   19UUA86589A006492   941  FAILED    0.006546\n811   19UUA86599A017629   941  FAILED    0.006546\n812   19UUA96549A001571   941  FAILED    0.006546\n813   19UUA96589A005879   941  FAILED    0.006546\n814   19UUA86539A023720   941  FAILED    0.006546\n815   19UUA86509A017020   941  FAILED    0.006546\n816   19UUA86569A022951   940  FAILED    0.006545\n817   19UUA86569A010881   939  FAILED    0.006544\n818   19UUA86529A008223   939  FAILED    0.006544\n819   19UUA86549A006134   939  FAILED    0.006544\n820   19UUA86569A011433   938  FAILED    0.006543\n821   19UUA86509A020113   938  FAILED    0.006543\n822   19UUA86569A004434   937  FAILED    0.006542\n823   19UUA86529A017164   936  FAILED    0.006541\n824   19UUA86579A009268   936  FAILED    0.006541\n825   19UUA865X9A021169   934  FAILED    0.006539\n826   19UUA86599A020997   934  FAILED    0.006539\n827   19UUA86559A010287   934  FAILED    0.006539\n828   19UUA86589A023213   933  FAILED    0.006538\n829   19UUA86579A023607   933  FAILED    0.006538\n830   19UUA86569A019189   932  FAILED    0.006537\n831   19UUA86599A018618   932  FAILED    0.006537\n832   19UUA865X9A008809   932  FAILED    0.006537\n833   19UUA86549A015237   932  FAILED    0.006537\n834   19UUA86509A002646   931  FAILED    0.006536\n835   19UUA96589A004134   931  FAILED    0.006536\n836   19UUA86589A024717   931  FAILED    0.006536\n837   19UUA86579A010050   931  FAILED    0.006536\n838   19UUA96559A006505   930  FAILED    0.006535\n839   19UUA865X9A005067   927  FAILED    0.006532\n840   19UUA96569A001958   927  FAILED    0.006532\n841   19UUA86519A011078   927  FAILED    0.006532\n842   19UUA86539A012989   927  FAILED    0.006532\n843   19UUA86589A005388   926  FAILED    0.006530\n844   19UUA865X9A002816   926  FAILED    0.006530\n845   19UUA86549A022222   925  FAILED    0.006529\n846   19UUA86539A009929   925  FAILED    0.006529\n847   19UUA86519A013557   924  FAILED    0.006528\n848   19UUA86549A006716   924  FAILED    0.006528\n849   19UUA86509A010763   923  FAILED    0.006527\n850   19UUA865X9A001875   922  FAILED    0.006526\n851   19UUA86509A018281   922  FAILED    0.006526\n852   19UUA86569A006264   921  FAILED    0.006525\n853   19UUA965X9A003857   920  FAILED    0.006524\n854   19UUA96529A000225   919  FAILED    0.006523\n855   19UUA86509A000301   917  FAILED    0.006521\n856   19UUA86539A004150   917  FAILED    0.006521\n857   19UUA86599A007134   917  FAILED    0.006521\n858   19UUA86539A012572   916  FAILED    0.006520\n859   19UUA86549A014234   916  FAILED    0.006520\n860   19UUA86549A016856   914  FAILED    0.006518\n861   19UUA86519A021626   913  FAILED    0.006517\n862   19UUA86589A016312   913  FAILED    0.006517\n863   19UUA96589A005901   912  FAILED    0.006516\n864   19UUA865X9A023018   912  FAILED    0.006516\n865   19UUA86529A004009   911  FAILED    0.006515\n866   19UUA86539A004746   911  FAILED    0.006515\n867   19UUA86569A009536   910  FAILED    0.006514\n868   19UUA86539A024916   910  FAILED    0.006514\n869   19UUA86569A015188   910  FAILED    0.006514\n870   19UUA86549A020583   910  FAILED    0.006514\n871   19UUA86509A023030   909  FAILED    0.006513\n872   19UUA86509A016322   909  FAILED    0.006513\n873   19UUA86559A014985   909  FAILED    0.006513\n874   19UUA86559A010838   907  FAILED    0.006511\n875   19UUA86589A000398   907  FAILED    0.006511\n876   19UUA96519A005058   906  FAILED    0.006510\n877   19UUA86579A004216   906  FAILED    0.006510\n878   19UUA86519A023988   905  FAILED    0.006509\n879   19UUA86549A021636   905  FAILED    0.006509\n880   19UUA86579A019749   905  FAILED    0.006509\n881   19UUA96569A000647   905  FAILED    0.006509\n882   19UUA86579A024837   903  FAILED    0.006506\n883   19UUA86559A024934   903  FAILED    0.006506\n884   19UUA96589A004005   900  FAILED    0.006503\n885   19UUA96509A003754   899  FAILED    0.006502\n886   19UUA86589A013054   896  FAILED    0.006499\n887   19UUA86569A022576   895  FAILED    0.006498\n888   19UUA86529A005287   894  FAILED    0.006497\n889   19UUA86589A023129   894  FAILED    0.006497\n890   19UUA86519A009959   893  FAILED    0.006496\n891   19UUA86529A022512   893  FAILED    0.006496\n892   19UUA86559A011097   893  FAILED    0.006496\n893   19UUA86599A017274   893  FAILED    0.006496\n894   19UUA865X9A024055   892  FAILED    0.006495\n895   19UUA86579A026510   891  FAILED    0.006494\n896   19UUA86569A023792   891  FAILED    0.006494\n897   19UUA86559A022178   891  FAILED    0.006494\n898   19UUA865X9A023911   890  FAILED    0.006493\n899   19UUA86519A019231   890  FAILED    0.006493\n900   19UUA86569A012209   890  FAILED    0.006493\n901   19UUA86509A017924   890  FAILED    0.006493\n902   19UUA86579A008475   889  FAILED    0.006491\n903   19UUA96579A006411   888  FAILED    0.006490\n904   19UUA86509A016899   888  FAILED    0.006490\n905   19UUA86519A024221   887  FAILED    0.006489\n906   19UUA96519A004704   886  FAILED    0.006488\n907   19UUA86599A021101   884  FAILED    0.006486\n908   19UUA86589A015256   884  FAILED    0.006486\n909   19UUA96579A000592   883  FAILED    0.006485\n910   19UUA86599A018974   883  FAILED    0.006485\n911   19UUA865X9A006462   882  FAILED    0.006484\n912   19UUA86549A007865   881  FAILED    0.006483\n913   19UUA86519A020945   880  FAILED    0.006482\n914   19UUA86539A018601   879  FAILED    0.006481\n915   19UUA86519A010304   878  FAILED    0.006480\n916   19UUA96519A001849   878  FAILED    0.006480\n917   19UUA865X9A005599   877  FAILED    0.006478\n918   19UUA86529A009484   876  FAILED    0.006477\n919   19UUA86569A021878   874  FAILED    0.006475\n920   19UUA86559A026005   873  FAILED    0.006474\n921   19UUA86509A007006   873  FAILED    0.006474\n922   19UUA96549A006558   872  FAILED    0.006473\n923   19UUA86559A025758   871  FAILED    0.006472\n924   19UUA86559A022908   870  FAILED    0.006471\n925   19UUA86529A003829   870  FAILED    0.006471\n926   19UUA86529A010067   870  FAILED    0.006471\n927   19UUA86509A003635   870  FAILED    0.006471\n928   19UUA96579A005002   869  FAILED    0.006470\n929   19UUA86549A021877   866  FAILED    0.006466\n930   19UUA86519A010822   866  FAILED    0.006466\n931   19UUA86599A013449   865  FAILED    0.006465\n932   19UUA86529A007511   865  FAILED    0.006465\n933   19UUA86599A020580   865  FAILED    0.006465\n934   19UUA96559A005273   861  FAILED    0.006461\n935   19UUA86509A009872   861  FAILED    0.006461\n936   19UUA86539A008070   861  FAILED    0.006461\n937   19UUA86579A022943   859  FAILED    0.006459\n938   19UUA86599A002693   859  FAILED    0.006459\n939   19UUA86569A009133   858  FAILED    0.006458\n940   19UUA86539A006223   857  FAILED    0.006456\n941   19UUA86579A009660   853  FAILED    0.006452\n942   19UUA86509A014179   853  FAILED    0.006452\n943   19UUA86599A015606   848  FAILED    0.006446\n944   19UUA96539A004638   847  FAILED    0.006445\n945   19UUA86599A008395   846  FAILED    0.006444\n946   19UUA86579A021162   844  FAILED    0.006442\n947   19UUA86539A006030   842  FAILED    0.006440\n948   19UUA865X9A010074   841  FAILED    0.006438\n949   19UUA86509A005708   841  FAILED    0.006438\n950   19UUA86589A004256   838  FAILED    0.006435\n951   19UUA86549A007798   836  FAILED    0.006433\n952   19UUA865X9A018305   831  FAILED    0.006427\n953   19UUA86519A007032   831  FAILED    0.006427\n954   19UUA965X9A000957   829  FAILED    0.006425\n955   19UUA96529A005327   827  FAILED    0.006422\n956   19UUA96519A004136   826  FAILED    0.006421\n957   19UUA86579A003003   824  FAILED    0.006419\n958   19UUA86589A025415   824  FAILED    0.006419\n959   19UUA86529A005919   823  FAILED    0.006418\n960   19UUA86539A024074   822  FAILED    0.006417\n961   19UUA86519A010299   819  FAILED    0.006413\n962   19UUA86589A024359   818  FAILED    0.006412\n963   19UUA86549A024018   817  FAILED    0.006411\n964   19UUA96589A003971   813  FAILED    0.006406\n965   19UUA865X9A024718   806  FAILED    0.006398\n966   19UUA86509A015087   804  FAILED    0.006395\n967   19UUA86589A017413   802  FAILED    0.006393\n968   19UUA86569A002084   800  FAILED    0.006391\n969   19UUA86569A014462   796  FAILED    0.006386\n970   19UUA86529A024681   794  FAILED    0.006383\n971   19UUA86589A013426   793  FAILED    0.006382\n972   19UUA86539A021756   793  FAILED    0.006382\n973   19UUA86539A003502   786  FAILED    0.006374\n974   19UUA86539A001457   783  FAILED    0.006370\n975   19UUA96539A001982   781  FAILED    0.006368\n976   19UUA96519A006100   781  FAILED    0.006368\n977   19UUA86559A012248   779  FAILED    0.006365\n978   19UUA86549A006182   777  FAILED    0.006363\n979   19UUA86559A017045   772  FAILED    0.006357\n980   19UUA86509A006955   766  FAILED    0.006349\n981   19UUA86549A001824   763  FAILED    0.006345\n982   19UUA86559A020253   763  FAILED    0.006345\n983   19UUA86519A013395   763  FAILED    0.006345\n984   19UUA86589A012597   757  FAILED    0.006338\n985   19UUA86599A011720   748  FAILED    0.006326\n986   19UUA965X9A005768   748  FAILED    0.006326\n987   19UUA86549A013150   741  FAILED    0.006317\n988   19UUA86589A007156   736  FAILED    0.006311\n989   19UUA96569A000390   736  FAILED    0.006311\n990   19UUA86549A025041   735  FAILED    0.006310\n991   19UUA86509A007541   729  FAILED    0.006302\n992   19UUA86599A012687   727  FAILED    0.006299\n993   19UUA865X9A010141   725  FAILED    0.006297\n994   19UUA96509A004161   725  FAILED    0.006297\n995   19UUA86529A012692   723  FAILED    0.006294\n996   19UUA86559A006644   710  FAILED    0.006277\n997   19UUA96599A003106   709  FAILED    0.006275\n998   19UUA86529A026754   694  FAILED    0.006255\n999   19UUA86559A015537   693  FAILED    0.006253\n1000  19UUA96579A006215   680  FAILED    0.006235\n1001  19UUA96589A001105   678  FAILED    0.006232\n1002  19UUA86579A007553   671  FAILED    0.006223\n1003  19UUA86579A005821   666  FAILED    0.006215\n1004  19UUA86539A013611   659  FAILED    0.006205\n1005  19UUA86549A020244   657  FAILED    0.006202\n1006  19UUA865X9A007577   656  FAILED    0.006201\n1007  19UUA86569A004000   644  FAILED    0.006183\n1008  19UUA86549A014816   636  FAILED    0.006171\n1009  19UUA86549A010104   622  FAILED    0.006150\n1010  19UUA96569A006724   615  FAILED    0.006139\n1011  19UUA86509A008365   602  FAILED    0.006119\n1012  19UUA96529A006042   602  FAILED    0.006119\n1013  19UUA86549A004724   602  FAILED    0.006119\n1014  19UUA86549A001788   589  FAILED    0.006098\n1015  19UUA96579A004285   556  FAILED    0.006043\n1016  19UUA86559A018745   553  FAILED    0.006038\n1017  19UUA86519A009685   553  FAILED    0.006038\n1018  19UUA86529A024051   552  FAILED    0.006036\n1019  19UUA86519A026146   546  FAILED    0.006025\n1020  19UUA86569A015269   543  FAILED    0.006020\n1021  19UUA86519A012554   532  FAILED    0.006001\n1022  19UUA96539A004932   525  FAILED    0.005988\n1023  19UUA86539A017528   501  FAILED    0.005943\n1024  19UUA86579A006502   497  FAILED    0.005936\n1025  19UUA86569A017927   493  FAILED    0.005928\n1026  19UUA86519A012330   492  FAILED    0.005926\n1027  19UUA86589A011109   446  FAILED    0.005832\n1028  19UUA86529A000347   405  FAILED    0.005740\n1029  19UUA96519A000877   399  FAILED    0.005726\n1030  19UUA86559A021161   395  FAILED    0.005716\n1031  19UUA865X9A026842   388  FAILED    0.005699\n1032  19UUA86559A015571   347  FAILED    0.005592\n1033  19UUA86559A018194   343  FAILED    0.005581\n1034  19UUA86529A011087   333  FAILED    0.005553\n1035  19UUA86589A023230   317  FAILED    0.005506\n1036  19UUA86549A019238   315  FAILED    0.005500\n1037  19UUA86539A018677   296  FAILED    0.005440\n1038  19UUA86509A007068   228  FAILED    0.005191\n1039  19UUA965X9A003812   205  FAILED    0.005089\n1040  19UUA86519A014109   148  FAILED    0.004777\n1041  19UUA86579A026085   112  FAILED    0.004511\n1042  19UUA96529A002606    88  FAILED    0.004280\n1043  19UUA86549A003704    50  FAILED    0.003740\n1044  19UUA86529A020985     9  FAILED    0.002101\n1045  19UUA86589A026693     4  FAILED    0.001325 \n\nSum of \"ln_x_div_r\" column = 6.92541212554\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<center>left side = $\\large{\\sum\\limits_{i=1}^r \\frac{ln(x_i)}{r}=6.9254}$</center>"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "The left side of the equation was calculated to be 6.9254.  Next we are going to calculate the right side of the equation using 100,000 values of k ranging from 0.1 to 10 and then substract the result from 4.9138.  Basically, what we are trying to achieve is throw a lot of k values into the right side of the equation, and subtract the result from it from 4.9138 until we find the difference as small or close to zero as possible. "
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<center>$\\large{6.9254-\\left(\\frac{\\sum\\limits_{i=1}^n (x_i)^kln(x_i)}{\\sum\\limits_{i=1}^n (x_i)^k}-\\frac{1}{k}\\right) \\approx 0}$</center>"
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "This script below will calculate the 100,000 values that represent the difference of the left side and right side of the equation:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "dtf_all = df[\"DTF\"].values\n\n# Generate 10,0000 k values that is between 0.1 and 10\n# Can't use 0 because it is not a valid value in the right-side equation formula, so we're using 0.1 instead\nk = np.linspace(0.1,10,100000,endpoint=True)\n\nright = []\nfor value in k:\n    right_eq = np.sum( dtf_all**value * ln(dtf_all) ) / np.sum( dtf_all**value ) - (1/value)\n    right.append(right_eq)\n    \nright_values = np.array(right)\n\ndiff = right_values - left_eq_sum\n",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "When it is done, at this point we should have 100,000 difference values and their corresponding k values.  Now let's plot them and see what they look like:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "plot(k,diff)\nylabel(\"Difference\")\nxlabel(\"k\")\ngrid()\nshow()\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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UZ61dunQJmZmZmD17NgDA398fnTp1khyVHB07dkRAQABKS0tRWVmJ0tJSU53I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\n5P8B4gm+XjEZTs8AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "As I've already mentioned, we need to choose a k value where the difference between the left equation and right equation is close to 0 as possible.  From the plot above, it looks like it would be approximately less than 3, maybe 2.8.  But instead of trying to \"eye-ball it\", let's calculate a more precise value for k where the difference is as close to zero as possible:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "ks = np.array(k)\ndiffs = np.array(diff)\n\nd = {'k' : ks,\n     'diff' : diffs}\n    \ndf_k_diff = pandas.DataFrame(d, index=np.arange(1,ks.size+1)) # Create one-based index instead of zero-based\ndf_k_diff = df_k_diff.sort_index(axis=1, ascending=False)  # Re-sorting the columns so that k column in on the left\n\nprint \"What the k values and their diffs look like:\"\nprint df_k_diff.head()\nprint df_k_diff.tail(), \"\\n\"\n\nprint \"The row with the first smallest difference:\"\nk_with_smallest_diff = df_k_diff[ (df_k_diff[\"diff\"] >= 0.000001)][0:1]\nprint k_with_smallest_diff, \"\\n\"\n\nfinal_k = k_with_smallest_diff[\"k\"].values\nk_final = final_k[0]\nprint \"Therefore, the k value we should use where the difference is as close to zero is:\", k_final\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "What the k values and their diffs look like:\n          k      diff\n1  0.100000 -9.662288\n2  0.100099 -9.652397\n3  0.100198 -9.642524\n4  0.100297 -9.632672\n5  0.100396 -9.622838\n                k      diff\n99996    9.999604  0.301151\n99997    9.999703  0.301152\n99998    9.999802  0.301154\n99999    9.999901  0.301155\n100000  10.000000  0.301157 \n\nThe row with the first smallest difference:\n              k      diff\n26892  2.762236  0.000013 \n\nTherefore, the k value we should use where the difference is as close to zero is: 2.76223562236\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "OK so now that we solved for k, we can solve for the scale ($\\lambda$) parameter next:"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "<center>$\\large{\\lambda=\\left(\\sum\\limits_{i=1}^n \\frac{(x_i)^k}{r}\\right)^\\frac{1}{k}}$</center>"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "l = (np.sum((dtf_all**k_final)/len(df_failed)))**(1/k_final)\nprint \"scale parameter:\",l\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "scale parameter: 4452.77055359\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Let's revisit the difference vs k value plot again:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x = []\nfor value in xrange(0,100000):\n    x.append(k_final)\n\nplot(k,diff)\nplot(x,diff)\ntitle(\"The difference is zero when k=2.762\")\nylabel(\"Difference\")\nxlabel(\"k\")\ngrid()\nshow()\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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TE6HX63H//ffXeb/Zs2cj+N8nKvj4+CAqKso8ZNy1ywDTbJdpu/IfRuXt3G78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\n"
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "We're done!  So using MLE method, we calculated the shape parameter to be 2.762 and the scale parameter to be 4452.77.  With the usual Weibull CDF plot below, we are equipped to make failure predictions."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "shape = 2.76223562236\nscale = 4452.77055359\n\nx2 = np.arange(0,9000)\ny2 = 1-exp(-(x2/scale)**shape) # This is the equation for Weibull CDF\n\nplot(x2,y2)\ntitle(\"Weibull CDF - Prediction\",weight='bold')\ngrid()\nshow()\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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CdfVqiI83rnSdNKlyxV7HcQJ9c5nJbQu+EKJ82dlGUW/Z0piAbNMmWLEC7rnHOH9eVF/S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\n"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "print \"Coordinates ( x, y ) of the CDF:\"\nfor value in zip(x2,y2):\n    print \"( \" + str(value[0]) + \" , \" + str(value[1]*100) + \" )\"\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Coordinates ( x, y ) of the CDF:\n( 0 , 0.0 )\n( 1 , 8.34878832734e-09 )\n( 2 , 5.66420688131e-08 )\n( 3 , 1.73597991537e-07 )\n( 4 , 3.84286313881e-07 )\n( 5 , 7.11775782758e-07 )\n( 6 , 1.17776993713e-06 )\n( 7 , 1.80294829066e-06 )\n( 8 , 2.60717805123e-06 )\n( 9 , 3.60965761725e-06 )\n( 10 , 4.82901970633e-06 )\n( 11 , 6.2834089154e-06 )\n( 12 , 7.99054182821e-06 )\n( 13 , 9.96775495476e-06 )\n( 14 , 1.2232043789e-05 )\n( 15 , 1.48000950384e-05 )\n( 16 , 1.76883139025e-05 )\n( 17 , 2.09128471096e-05 )\n( 18 , 2.44896028234e-05 )\n( 19 , 2.84342680179e-05 )\n( 20 , 3.27623234986e-05 )\n( 21 , 3.74890573807e-05 )\n( 22 , 4.26295769018e-05 )\n( 23 , 4.81988190582e-05 )\n( 24 , 5.42115601632e-05 )\n( 25 , 6.06824244298e-05 )\n( 26 , 6.76258917864e-05 )\n( 27 , 7.50563050156e-05 )\n( 28 , 8.29878762709e-05 )\n( 29 , 9.14346929726e-05 )\n( 30 , 0.000100410723392 )\n( 31 , 0.000109929821657 )\n( 32 , 0.000120005732485 )\n( 33 , 0.000130652095498 )\n( 34 , 0.0001418824493 )\n( 35 , 0.000153710235262 )\n( 36 , 0.000166148801006 )\n( 37 , 0.000179211403772 )\n( 38 , 0.00019291121347 )\n( 39 , 0.000207261315599 )\n( 40 , 0.000222274714012 )\n( 41 , 0.00023796433346 )\n( 42 , 0.000254343022066 )\n( 43 , 0.000271423553622 )\n( 44 , 0.000289218629768 )\n( 45 , 0.000307740882044 )\n( 46 , 0.000327002873923 )\n( 47 , 0.000347017102575 )\n( 48 , 0.000367796000744 )\n( 49 , 0.000389351938379 )\n( 50 , 0.000411697224256 )\n( 51 , 0.000434844107544 )\n( 52 , 0.000458804779258 )\n( 53 , 0.000483591373657 )\n( 54 , 0.000509215969613 )\n( 55 , 0.000535690591885 )\n( 56 , 0.000563027212352 )\n( 57 , 0.000591237751224 )\n( 58 , 0.000620334078127 )\n( 59 , 0.000650328013274 )\n( 60 , 0.000681231328448 )\n( 61 , 0.000713055748036 )\n( 62 , 0.000745812950043 )\n( 63 , 0.000779514566951 )\n( 64 , 0.000814172186703 )\n( 65 , 0.000849797353508 )\n( 66 , 0.000886401568745 )\n( 67 , 0.000923996291724 )\n( 68 , 0.000962592940512 )\n( 69 , 0.00100220289265 )\n( 70 , 0.00104283748593 )\n( 71 , 0.00108450801909 )\n( 72 , 0.00112722575246 )\n( 73 , 0.00117100190872 )\n( 74 , 0.00121584767344 )\n( 75 , 0.00126177419579 )\n( 76 , 0.00130879258911 )\n( 77 , 0.00135691393147 )\n( 78 , 0.0014061492663 )\n( 79 , 0.00145650960293 )\n( 80 , 0.00150800591706 )\n( 81 , 0.00156064915141 )\n( 82 , 0.00161445021608 )\n( 83 , 0.00166941998919 )\n( 84 , 0.00172556931726 )\n( 85 , 0.00178290901569 )\n( 86 , 0.00184144986928 )\n( 87 , 0.00190120263259 )\n( 88 , 0.00196217803045 )\n( 89 , 0.0020243867583 )\n( 90 , 0.00208783948268 )\n( 91 , 0.00215254684155 )\n( 92 , 0.00221851944475 )\n( 93 , 0.00228576787437 )\n( 94 , 0.00235430268504 )\n( 95 , 0.00242413440442 )\n( 96 , 0.00249527353345 )\n( 97 , 0.00256773054675 )\n( 98 , 0.00264151589293 )\n( 99 , 0.00271663999492 )\n( 100 , 0.00279311325031 )\n( 101 , 0.00287094603166 )\n( 102 , 0.00295014868681 )\n( 103 , 0.00303073153912 )\n( 104 , 0.0031127048879 )\n( 105 , 0.00319607900852 )\n( 106 , 0.00328086415284 )\n( 107 , 0.00336707054944 )\n( 108 , 0.00345470840384 )\n( 109 , 0.00354378789882 )\n( 110 , 0.00363431919465 )\n( 111 , 0.00372631242935 )\n( 112 , 0.00381977771898 )\n( 113 , 0.00391472515779 )\n( 114 , 0.00401116481853 )\n( 115 , 0.00410910675268 )\n( 116 , 0.00420856099064 )\n( 117 , 0.00430953754197 )\n( 118 , 0.00441204639564 )\n( 119 , 0.0045160975202 )\n( 120 , 0.00462170086404 )\n( 121 , 0.00472886635552 )\n( 122 , 0.00483760390326 )\n( 123 , 0.00494792339629 )\n( 124 , 0.00505983470427 )\n( 125 , 0.00517334767764 )\n( 126 , 0.00528847214787 )\n( 127 , 0.00540521792759 )\n( 128 , 0.00552359481081 )\n( 129 , 0.00564361257308 )\n( 130 , 0.00576528097166 )\n( 131 , 0.00588860974572 )\n( 132 , 0.00601360861648 )\n( 133 , 0.00614028728739 )\n( 134 , 0.00626865544431 )\n( 135 , 0.00639872275561 )\n( 136 , 0.00653049887241 )\n( 137 , 0.0066639934287 )\n( 138 , 0.00679921604146 )\n( 139 , 0.00693617631086 )\n( 140 , 0.00707488382039 )\n( 141 , 0.00721534813699 )\n( 142 , 0.00735757881122 )\n( 143 , 0.00750158537739 )\n( 144 , 0.00764737735368 )\n( 145 , 0.00779496424232 )\n( 146 , 0.00794435552968 )\n( 147 , 0.00809556068641 )\n( 148 , 0.0082485891676 )\n( 149 , 0.0084034504129 )\n( 150 , 0.00856015384658 )\n( 151 , 0.00871870887778 )\n( 152 , 0.00887912490051 )\n( 153 , 0.00904141129384 )\n( 154 , 0.009205577422 )\n( 155 , 0.00937163263449 )\n( 156 , 0.00953958626622 )\n( 157 , 0.00970944763758 )\n( 158 , 0.00988122605462 )\n( 159 , 0.0100549308091 )\n( 160 , 0.0102305711785 )\n( 161 , 0.0104081564265 )\n( 162 , 0.0105876958027 )\n( 163 , 0.0107691985427 )\n( 164 , 0.0109526738685 )\n( 165 , 0.0111381309886 )\n( 166 , 0.0113255790977 )\n( 167 , 0.0115150273771 )\n( 168 , 0.011706484995 )\n( 169 , 0.0118999611061 )\n( 170 , 0.0120954648519 )\n( 171 , 0.0122930053612 )\n( 172 , 0.0124925917493 )\n( 173 , 0.012694233119 )\n( 174 , 0.0128979385603 )\n( 175 , 0.0131037171503 )\n( 176 , 0.0133115779536 )\n( 177 , 0.0135215300223 )\n( 178 , 0.0137335823959 )\n( 179 , 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)\n( 1294 , 3.23883804046 )\n( 1295 , 3.24564302286 )\n( 1296 , 3.25245679222 )\n( 1297 , 3.25927935208 )\n( 1298 , 3.26611070596 )\n( 1299 , 3.27295085737 )\n( 1300 , 3.27979980984 )\n( 1301 , 3.28665756686 )\n( 1302 , 3.29352413195 )\n( 1303 , 3.30039950861 )\n( 1304 , 3.30728370033 )\n( 1305 , 3.31417671059 )\n( 1306 , 3.32107854288 )\n( 1307 , 3.32798920069 )\n( 1308 , 3.33490868749 )\n( 1309 , 3.34183700674 )\n( 1310 , 3.34877416191 )\n( 1311 , 3.35572015646 )\n( 1312 , 3.36267499385 )\n( 1313 , 3.36963867753 )\n( 1314 , 3.37661121093 )\n( 1315 , 3.3835925975 )\n( 1316 , 3.39058284068 )\n( 1317 , 3.39758194389 )\n( 1318 , 3.40458991056 )\n( 1319 , 3.41160674411 )\n( 1320 , 3.41863244795 )\n( 1321 , 3.4256670255 )\n( 1322 , 3.43271048016 )\n( 1323 , 3.43976281532 )\n( 1324 , 3.44682403439 )\n( 1325 , 3.45389414075 )\n( 1326 , 3.46097313779 )\n( 1327 , 3.46806102889 )\n( 1328 , 3.47515781742 )\n( 1329 , 3.48226350675 )\n( 1330 , 3.48937810025 )\n( 1331 , 3.49650160128 )\n( 1332 , 3.50363401319 )\n( 1333 , 3.51077533933 )\n( 1334 , 3.51792558305 )\n( 1335 , 3.52508474768 )\n( 1336 , 3.53225283657 )\n( 1337 , 3.53942985304 )\n( 1338 , 3.54661580041 )\n( 1339 , 3.55381068201 )\n( 1340 , 3.56101450114 )\n( 1341 , 3.56822726113 )\n( 1342 , 3.57544896527 )\n( 1343 , 3.58267961686 )\n( 1344 , 3.5899192192 )\n( 1345 , 3.59716777557 )\n( 1346 , 3.60442528927 )\n( 1347 , 3.61169176356 )\n( 1348 , 3.61896720173 )\n( 1349 , 3.62625160704 )\n( 1350 , 3.63354498276 )\n( 1351 , 3.64084733214 )\n( 1352 , 3.64815865844 )\n( 1353 , 3.65547896491 )\n( 1354 , 3.66280825479 )\n( 1355 , 3.67014653132 )\n( 1356 , 3.67749379773 )\n( 1357 , 3.68485005726 )\n( 1358 , 3.69221531312 )\n( 1359 , 3.69958956853 )\n( 1360 , 3.70697282671 )\n( 1361 , 3.71436509086 )\n( 1362 , 3.72176636419 )\n( 1363 , 3.72917664989 )\n( 1364 , 3.73659595117 )\n( 1365 , 3.74402427119 )\n( 1366 , 3.75146161316 )\n( 1367 , 3.75890798023 )\n( 1368 , 3.7663633756 )\n( 1369 , 3.77382780242 )\n( 1370 , 3.78130126385 )\n( 1371 , 3.78878376306 )\n( 1372 , 3.79627530319 )\n( 1373 , 3.80377588739 )\n( 1374 , 3.8112855188 )\n( 1375 , 3.81880420056 )\n( 1376 , 3.8263319358 )\n( 1377 , 3.83386872765 )\n( 1378 , 3.84141457922 )\n( 1379 , 3.84896949363 )\n( 1380 , 3.85653347399 )\n( 1381 , 3.86410652341 )\n( 1382 , 3.87168864499 )\n( 1383 , 3.87927984182 )\n( 1384 , 3.886880117 )\n( 1385 , 3.8944894736 )\n( 1386 , 3.90210791471 )\n( 1387 , 3.9097354434 )\n( 1388 , 3.91737206273 )\n( 1389 , 3.92501777579 )\n( 1390 , 3.93267258561 )\n( 1391 , 3.94033649526 )\n( 1392 , 3.94800950779 )\n( 1393 , 3.95569162623 )\n( 1394 , 3.96338285364 )\n( 1395 , 3.97108319303 )\n( 1396 , 3.97879264743 )\n( 1397 , 3.98651121988 )\n( 1398 , 3.99423891338 )\n( 1399 , 4.00197573095 )\n( 1400 , 4.00972167559 )\n( 1401 , 4.01747675032 )\n( 1402 , 4.02524095811 )\n( 1403 , 4.03301430197 )\n( 1404 , 4.04079678488 )\n( 1405 , 4.04858840982 )\n( 1406 , 4.05638917977 )\n( 1407 , 4.06419909769 )\n( 1408 , 4.07201816656 )\n( 1409 , 4.07984638933 )\n( 1410 , 4.08768376895 )\n( 1411 , 4.09553030838 )\n( 1412 , 4.10338601056 )\n( 1413 , 4.11125087843 )\n( 1414 , 4.11912491492 )\n( 1415 , 4.12700812296 )\n( 1416 , 4.13490050548 )\n( 1417 , 4.14280206538 )\n( 1418 , 4.15071280559 )\n( 1419 , 4.15863272902 )\n( 1420 , 4.16656183855 )\n( 1421 , 4.1745001371 )\n( 1422 , 4.18244762755 )\n( 1423 , 4.19040431278 )\n( 1424 , 4.19837019569 )\n( 1425 , 4.20634527914 )\n( 1426 , 4.214329566 )\n( 1427 , 4.22232305915 )\n( 1428 , 4.23032576143 )\n( 1429 , 4.23833767571 )\n( 1430 , 4.24635880484 )\n( 1431 , 4.25438915165 )\n( 1432 , 4.26242871899 )\n( 1433 , 4.27047750969 )\n( 1434 , 4.27853552658 )\n( 1435 , 4.28660277248 )\n( 1436 , 4.29467925021 )\n( 1437 , 4.30276496258 )\n( 1438 , 4.31085991239 )\n( 1439 , 4.31896410246 )\n( 1440 , 4.32707753557 )\n( 1441 , 4.33520021451 )\n( 1442 , 4.34333214208 )\n( 1443 , 4.35147332105 )\n( 1444 , 4.3596237542 )\n( 1445 , 4.3677834443 )\n( 1446 , 4.3759523941 )\n( 1447 , 4.38413060637 )\n( 1448 , 4.39231808387 )\n( 1449 , 4.40051482934 )\n( 1450 , 4.40872084552 )\n( 1451 , 4.41693613516 )\n( 1452 , 4.42516070098 )\n( 1453 , 4.43339454571 )\n( 1454 , 4.44163767207 )\n( 1455 , 4.44989008279 )\n( 1456 , 4.45815178056 )\n( 1457 , 4.46642276809 )\n( 1458 , 4.47470304809 )\n( 1459 , 4.48299262325 )\n( 1460 , 4.49129149626 )\n( 1461 , 4.4995996698 )\n( 1462 , 4.50791714655 )\n( 1463 , 4.51624392919 )\n( 1464 , 4.52458002038 )\n( 1465 , 4.53292542278 )\n( 1466 , 4.54128013905 )\n( 1467 , 4.54964417185 )\n( 1468 , 4.55801752382 )\n( 1469 , 4.56640019759 )\n( 1470 , 4.57479219581 )\n( 1471 , 4.58319352111 )\n( 1472 , 4.59160417611 )\n( 1473 , 4.60002416342 )\n( 1474 , 4.60845348567 )\n( 1475 , 4.61689214546 )\n( 1476 , 4.6253401454 )\n( 1477 , 4.63379748807 )\n( 1478 , 4.64226417608 )\n( 1479 , 4.65074021201 )\n( 1480 , 4.65922559845 )\n( 1481 , 4.66772033796 )\n( 1482 , 4.67622443312 )\n( 1483 , 4.68473788649 )\n( 1484 , 4.69326070063 )\n( 1485 , 4.7017928781 )\n( 1486 , 4.71033442145 )\n( 1487 , 4.71888533322 )\n( 1488 , 4.72744561594 )\n( 1489 , 4.73601527215 )\n( 1490 , 4.74459430437 )\n( 1491 , 4.75318271514 )\n( 1492 , 4.76178050695 )\n( 1493 , 4.77038768233 )\n( 1494 , 4.77900424378 )\n( 1495 , 4.7876301938 )\n( 1496 , 4.79626553487 )\n( 1497 , 4.8049102695 )\n( 1498 , 4.81356440016 )\n( 1499 , 4.82222792934 )\n( 1500 , 4.8309008595 )\n( 1501 , 4.8395831931 )\n( 1502 , 4.84827493262 )\n( 1503 , 4.85697608051 )\n( 1504 , 4.86568663921 )\n( 1505 , 4.87440661118 )\n( 1506 , 4.88313599885 )\n( 1507 , 4.89187480465 )\n( 1508 , 4.90062303102 )\n( 1509 , 4.90938068037 )\n( 1510 , 4.91814775513 )\n( 1511 , 4.9269242577 )\n( 1512 , 4.93571019049 )\n( 1513 , 4.9445055559 )\n( 1514 , 4.95331035634 )\n( 1515 , 4.96212459418 )\n( 1516 , 4.97094827181 )\n( 1517 , 4.97978139161 )\n( 1518 , 4.98862395595 )\n( 1519 , 4.9974759672 )\n( 1520 , 5.00633742773 )\n( 1521 , 5.01520833988 )\n( 1522 , 5.02408870602 )\n( 1523 , 5.03297852848 )\n( 1524 , 5.04187780961 )\n( 1525 , 5.05078655173 )\n( 1526 , 5.05970475718 )\n( 1527 , 5.06863242829 )\n( 1528 , 5.07756956736 )\n( 1529 , 5.08651617672 )\n( 1530 , 5.09547225866 )\n( 1531 , 5.1044378155 )\n( 1532 , 5.11341284951 )\n( 1533 , 5.12239736301 )\n( 1534 , 5.13139135826 )\n( 1535 , 5.14039483754 )\n( 1536 , 5.14940780314 )\n( 1537 , 5.15843025732 )\n( 1538 , 5.16746220233 )\n( 1539 , 5.17650364045 )\n( 1540 , 5.18555457391 )\n( 1541 , 5.19461500496 )\n( 1542 , 5.20368493584 )\n( 1543 , 5.21276436879 )\n( 1544 , 5.22185330604 )\n( 1545 , 5.2309517498 )\n( 1546 , 5.2400597023 )\n( 1547 , 5.24917716575 )\n( 1548 , 5.25830414235 )\n( 1549 , 5.2674406343 )\n( 1550 , 5.2765866438 )\n( 1551 , 5.28574217303 )\n( 1552 , 5.29490722419 )\n( 1553 , 5.30408179945 )\n( 1554 , 5.31326590098 )\n( 1555 , 5.32245953094 )\n( 1556 , 5.33166269151 )\n( 1557 , 5.34087538483 )\n( 1558 , 5.35009761305 )\n( 1559 , 5.35932937832 )\n( 1560 , 5.36857068279 )\n( 1561 , 5.37782152857 )\n( 1562 , 5.38708191779 )\n( 1563 , 5.39635185259 )\n( 1564 , 5.40563133508 )\n( 1565 , 5.41492036736 )\n( 1566 , 5.42421895154 )\n( 1567 , 5.43352708971 )\n( 1568 , 5.44284478399 )\n( 1569 , 5.45217203644 )\n( 1570 , 5.46150884916 )\n( 1571 , 5.47085522421 )\n( 1572 , 5.48021116368 )\n( 1573 , 5.48957666962 )\n( 1574 , 5.4989517441 )\n( 1575 , 5.50833638916 )\n( 1576 , 5.51773060686 )\n( 1577 , 5.52713439924 )\n( 1578 , 5.53654776834 )\n( 1579 , 5.54597071618 )\n( 1580 , 5.55540324479 )\n( 1581 , 5.5648453562 )\n( 1582 , 5.57429705241 )\n( 1583 , 5.58375833544 )\n( 1584 , 5.59322920728 )\n( 1585 , 5.60270966993 )\n( 1586 , 5.61219972539 )\n( 1587 , 5.62169937564 )\n( 1588 , 5.63120862266 )\n( 1589 , 5.64072746843 )\n( 1590 , 5.6502559149 )\n( 1591 , 5.65979396405 )\n( 1592 , 5.66934161784 )\n( 1593 , 5.6788988782 )\n( 1594 , 5.6884657471 )\n( 1595 , 5.69804222646 )\n( 1596 , 5.70762831823 )\n( 1597 , 5.71722402432 )\n( 1598 , 5.72682934667 )\n( 1599 , 5.73644428719 )\n( 1600 , 5.74606884779 )\n( 1601 , 5.75570303037 )\n( 1602 , 5.76534683684 )\n( 1603 , 5.77500026909 )\n( 1604 , 5.78466332901 )\n( 1605 , 5.79433601848 )\n( 1606 , 5.80401833938 )\n( 1607 , 5.81371029357 )\n( 1608 , 5.82341188293 )\n( 1609 , 5.83312310931 )\n( 1610 , 5.84284397456 )\n( 1611 , 5.85257448054 )\n( 1612 , 5.86231462908 )\n( 1613 , 5.87206442203 )\n( 1614 , 5.88182386121 )\n( 1615 , 5.89159294844 )\n( 1616 , 5.90137168556 )\n( 1617 , 5.91116007436 )\n( 1618 , 5.92095811665 )\n( 1619 , 5.93076581425 )\n( 1620 , 5.94058316894 )\n( 1621 , 5.95041018251 )\n( 1622 , 5.96024685676 )\n( 1623 , 5.97009319345 )\n( 1624 , 5.97994919436 )\n( 1625 , 5.98981486125 )\n( 1626 , 5.99969019589 )\n( 1627 , 6.00957520004 )\n( 1628 , 6.01946987544 )\n( 1629 , 6.02937422383 )\n( 1630 , 6.03928824696 )\n( 1631 , 6.04921194655 )\n( 1632 , 6.05914532434 )\n( 1633 , 6.06908838204 )\n( 1634 , 6.07904112136 )\n( 1635 , 6.08900354402 )\n( 1636 , 6.09897565172 )\n( 1637 , 6.10895744616 )\n( 1638 , 6.11894892902 )\n( 1639 , 6.12895010199 )\n( 1640 , 6.13896096676 )\n( 1641 , 6.14898152499 )\n( 1642 , 6.15901177835 )\n( 1643 , 6.16905172851 )\n( 1644 , 6.17910137713 )\n( 1645 , 6.18916072584 )\n( 1646 , 6.1992297763 )\n( 1647 , 6.20930853015 )\n( 1648 , 6.21939698902 )\n( 1649 , 6.22949515453 )\n( 1650 , 6.23960302831 )\n( 1651 , 6.24972061197 )\n( 1652 , 6.25984790712 )\n( 1653 , 6.26998491537 )\n( 1654 , 6.28013163831 )\n( 1655 , 6.29028807753 )\n( 1656 , 6.30045423462 )\n( 1657 , 6.31063011116 )\n( 1658 , 6.32081570873 )\n( 1659 , 6.33101102889 )\n( 1660 , 6.34121607321 )\n( 1661 , 6.35143084324 )\n( 1662 , 6.36165534052 )\n( 1663 , 6.37188956662 )\n( 1664 , 6.38213352306 )\n( 1665 , 6.39238721138 )\n( 1666 , 6.40265063311 )\n( 1667 , 6.41292378977 )\n( 1668 , 6.42320668286 )\n( 1669 , 6.43349931391 )\n( 1670 , 6.44380168442 )\n( 1671 , 6.45411379587 )\n( 1672 , 6.46443564977 )\n( 1673 , 6.4747672476 )\n( 1674 , 6.48510859085 )\n( 1675 , 6.49545968097 )\n( 1676 , 6.50582051945 )\n( 1677 , 6.51619110774 )\n( 1678 , 6.5265714473 )\n( 1679 , 6.53696153958 )\n( 1680 , 6.54736138603 )\n( 1681 , 6.55777098808 )\n( 1682 , 6.56819034716 )\n( 1683 , 6.57861946471 )\n( 1684 , 6.58905834214 )\n( 1685 , 6.59950698087 )\n( 1686 , 6.6099653823 )\n( 1687 , 6.62043354784 )\n( 1688 , 6.63091147889 )\n( 1689 , 6.64139917683 )\n( 1690 , 6.65189664305 )\n( 1691 , 6.66240387894 )\n( 1692 , 6.67292088585 )\n( 1693 , 6.68344766517 )\n( 1694 , 6.69398421825 )\n( 1695 , 6.70453054644 )\n( 1696 , 6.7150866511 )\n( 1697 , 6.72565253357 )\n( 1698 , 6.73622819518 )\n( 1699 , 6.74681363727 )\n( 1700 , 6.75740886117 )\n( 1701 , 6.76801386818 )\n( 1702 , 6.77862865963 )\n( 1703 , 6.78925323682 )\n( 1704 , 6.79988760105 )\n( 1705 , 6.81053175363 )\n( 1706 , 6.82118569583 )\n( 1707 , 6.83184942894 )\n( 1708 , 6.84252295424 )\n( 1709 , 6.853206273 )\n( 1710 , 6.86389938649 )\n( 1711 , 6.87460229596 )\n( 1712 , 6.88531500267 )\n( 1713 , 6.89603750787 )\n( 1714 , 6.90676981279 )\n( 1715 , 6.91751191868 )\n( 1716 , 6.92826382676 )\n( 1717 , 6.93902553826 )\n( 1718 , 6.94979705438 )\n( 1719 , 6.96057837636 )\n( 1720 , 6.97136950538 )\n( 1721 , 6.98217044265 )\n( 1722 , 6.99298118936 )\n( 1723 , 7.0038017467 )\n( 1724 , 7.01463211585 )\n( 1725 , 7.02547229799 )\n( 1726 , 7.03632229428 )\n( 1727 , 7.04718210589 )\n( 1728 , 7.05805173398 )\n( 1729 , 7.06893117969 )\n( 1730 , 7.07982044418 )\n( 1731 , 7.09071952857 )\n( 1732 , 7.10162843401 )\n( 1733 , 7.11254716162 )\n( 1734 , 7.12347571252 )\n( 1735 , 7.13441408782 )\n( 1736 , 7.14536228864 )\n( 1737 , 7.15632031608 )\n( 1738 , 7.16728817123 )\n( 1739 , 7.17826585518 )\n( 1740 , 7.18925336903 )\n( 1741 , 7.20025071384 )\n( 1742 , 7.21125789069 )\n( 1743 , 7.22227490065 )\n( 1744 , 7.23330174478 )\n( 1745 , 7.24433842412 )\n( 1746 , 7.25538493974 )\n( 1747 , 7.26644129266 )\n( 1748 , 7.27750748394 )\n( 1749 , 7.28858351458 )\n( 1750 , 7.29966938563 )\n( 1751 , 7.3107650981 )\n( 1752 , 7.321870653 )\n( 1753 , 7.33298605134 )\n( 1754 , 7.3441112941 )\n( 1755 , 7.3552463823 )\n( 1756 , 7.36639131691 )\n( 1757 , 7.37754609892 )\n( 1758 , 7.38871072931 )\n( 1759 , 7.39988520903 )\n( 1760 , 7.41106953906 )\n( 1761 , 7.42226372034 )\n( 1762 , 7.43346775384 )\n( 1763 , 7.4446816405 )\n( 1764 , 7.45590538124 )\n( 1765 , 7.46713897702 )\n( 1766 , 7.47838242875 )\n( 1767 , 7.48963573735 )\n( 1768 , 7.50089890374 )\n( 1769 , 7.51217192882 )\n( 1770 , 7.5234548135 )\n( 1771 , 7.53474755867 )\n( 1772 , 7.54605016523 )\n( 1773 , 7.55736263405 )\n( 1774 , 7.56868496601 )\n( 1775 , 7.58001716198 )\n( 1776 , 7.59135922284 )\n( 1777 , 7.60271114943 )\n( 1778 , 7.61407294261 )\n( 1779 , 7.62544460322 )\n( 1780 , 7.63682613212 )\n( 1781 , 7.64821753012 )\n( 1782 , 7.65961879807 )\n( 1783 , 7.67102993678 )\n( 1784 , 7.68245094706 )\n( 1785 , 7.69388182973 )\n( 1786 , 7.70532258559 )\n( 1787 , 7.71677321544 )\n( 1788 , 7.72823372007 )\n( 1789 , 7.73970410026 )\n( 1790 , 7.7511843568 )\n( 1791 , 7.76267449045 )\n( 1792 , 7.77417450198 )\n( 1793 , 7.78568439216 )\n( 1794 , 7.79720416173 )\n( 1795 , 7.80873381145 )\n( 1796 , 7.82027334206 )\n( 1797 , 7.83182275428 )\n( 1798 , 7.84338204886 )\n( 1799 , 7.85495122652 )\n( 1800 , 7.86653028797 )\n( 1801 , 7.87811923392 )\n( 1802 , 7.88971806508 )\n( 1803 , 7.90132678214 )\n( 1804 , 7.91294538581 )\n( 1805 , 7.92457387676 )\n( 1806 , 7.93621225568 )\n( 1807 , 7.94786052324 )\n( 1808 , 7.9595186801 )\n( 1809 , 7.97118672694 )\n( 1810 , 7.98286466439 )\n( 1811 , 7.99455249312 )\n( 1812 , 8.00625021377 )\n( 1813 , 8.01795782697 )\n( 1814 , 8.02967533335 )\n( 1815 , 8.04140273354 )\n( 1816 , 8.05314002815 )\n( 1817 , 8.0648872178 )\n( 1818 , 8.0766443031 )\n( 1819 , 8.08841128463 )\n( 1820 , 8.100188163 )\n( 1821 , 8.1119749388 )\n( 1822 , 8.12377161259 )\n( 1823 , 8.13557818496 )\n( 1824 , 8.14739465648 )\n( 1825 , 8.1592210277 )\n( 1826 , 8.17105729919 )\n( 1827 , 8.18290347149 )\n( 1828 , 8.19475954515 )\n( 1829 , 8.2066255207 )\n( 1830 , 8.21850139868 )\n( 1831 , 8.2303871796 )\n( 1832 , 8.24228286399 )\n( 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27.5226043894 )\n( 2955 , 27.5444232371 )\n( 2956 , 27.5662485263 )\n( 2957 , 27.5880802504 )\n( 2958 , 27.6099184031 )\n( 2959 , 27.631762978 )\n( 2960 , 27.6536139685 )\n( 2961 , 27.6754713682 )\n( 2962 , 27.6973351707 )\n( 2963 , 27.7192053696 )\n( 2964 , 27.7410819583 )\n( 2965 , 27.7629649305 )\n( 2966 , 27.7848542796 )\n( 2967 , 27.8067499991 )\n( 2968 , 27.8286520827 )\n( 2969 , 27.8505605238 )\n( 2970 , 27.8724753159 )\n( 2971 , 27.8943964525 )\n( 2972 , 27.9163239272 )\n( 2973 , 27.9382577334 )\n( 2974 , 27.9601978647 )\n( 2975 , 27.9821443144 )\n( 2976 , 28.0040970762 )\n( 2977 , 28.0260561435 )\n( 2978 , 28.0480215097 )\n( 2979 , 28.0699931684 )\n( 2980 , 28.0919711129 )\n( 2981 , 28.1139553368 )\n( 2982 , 28.1359458335 )\n( 2983 , 28.1579425965 )\n( 2984 , 28.1799456192 )\n( 2985 , 28.201954895 )\n( 2986 , 28.2239704175 )\n( 2987 , 28.2459921799 )\n( 2988 , 28.2680201758 )\n( 2989 , 28.2900543986 )\n( 2990 , 28.3120948417 )\n( 2991 , 28.3341414984 )\n( 2992 , 28.3561943623 )\n( 2993 , 28.3782534267 )\n( 2994 , 28.400318685 )\n( 2995 , 28.4223901307 )\n( 2996 , 28.444467757 )\n( 2997 , 28.4665515575 )\n( 2998 , 28.4886415254 )\n( 2999 , 28.5107376541 )\n( 3000 , 28.5328399371 )\n( 3001 , 28.5549483676 )\n( 3002 , 28.5770629391 )\n( 3003 , 28.599183645 )\n( 3004 , 28.6213104784 )\n( 3005 , 28.6434434329 )\n( 3006 , 28.6655825018 )\n( 3007 , 28.6877276783 )\n( 3008 , 28.7098789559 )\n( 3009 , 28.7320363278 )\n( 3010 , 28.7541997874 )\n( 3011 , 28.776369328 )\n( 3012 , 28.798544943 )\n( 3013 , 28.8207266256 )\n( 3014 , 28.8429143691 )\n( 3015 , 28.8651081669 )\n( 3016 , 28.8873080122 )\n( 3017 , 28.9095138983 )\n( 3018 , 28.9317258186 )\n( 3019 , 28.9539437663 )\n( 3020 , 28.9761677347 )\n( 3021 , 28.9983977171 )\n( 3022 , 29.0206337067 )\n( 3023 , 29.0428756968 )\n( 3024 , 29.0651236807 )\n( 3025 , 29.0873776516 )\n( 3026 , 29.1096376028 )\n( 3027 , 29.1319035275 )\n( 3028 , 29.154175419 )\n( 3029 , 29.1764532705 )\n( 3030 , 29.1987370752 )\n( 3031 , 29.2210268265 )\n( 3032 , 29.2433225174 )\n( 3033 , 29.2656241413 )\n( 3034 , 29.2879316913 )\n( 3035 , 29.3102451607 )\n( 3036 , 29.3325645426 )\n( 3037 , 29.3548898303 )\n( 3038 , 29.377221017 )\n( 3039 , 29.3995580959 )\n( 3040 , 29.4219010601 )\n( 3041 , 29.4442499029 )\n( 3042 , 29.4666046173 )\n( 3043 , 29.4889651967 )\n( 3044 , 29.5113316342 )\n( 3045 , 29.5337039229 )\n( 3046 , 29.556082056 )\n( 3047 , 29.5784660267 )\n( 3048 , 29.6008558281 )\n( 3049 , 29.6232514534 )\n( 3050 , 29.6456528957 )\n( 3051 , 29.6680601482 )\n( 3052 , 29.690473204 )\n( 3053 , 29.7128920562 )\n( 3054 , 29.735316698 )\n( 3055 , 29.7577471225 )\n( 3056 , 29.7801833228 )\n( 3057 , 29.802625292 )\n( 3058 , 29.8250730233 )\n( 3059 , 29.8475265097 )\n( 3060 , 29.8699857443 )\n( 3061 , 29.8924507204 )\n( 3062 , 29.9149214308 )\n( 3063 , 29.9373978688 )\n( 3064 , 29.9598800274 )\n( 3065 , 29.9823678998 )\n( 3066 , 30.0048614789 )\n( 3067 , 30.0273607578 )\n( 3068 , 30.0498657297 )\n( 3069 , 30.0723763876 )\n( 3070 , 30.0948927245 )\n( 3071 , 30.1174147335 )\n( 3072 , 30.1399424077 )\n( 3073 , 30.1624757401 )\n( 3074 , 30.1850147238 )\n( 3075 , 30.2075593517 )\n( 3076 , 30.2301096169 )\n( 3077 , 30.2526655125 )\n( 3078 , 30.2752270315 )\n( 3079 , 30.2977941669 )\n( 3080 , 30.3203669117 )\n( 3081 , 30.3429452589 )\n( 3082 , 30.3655292016 )\n( 3083 , 30.3881187327 )\n( 3084 , 30.4107138453 )\n( 3085 , 30.4333145323 )\n( 3086 , 30.4559207868 )\n( 3087 , 30.4785326017 )\n( 3088 , 30.50114997 )\n( 3089 , 30.5237728847 )\n( 3090 , 30.5464013388 )\n( 3091 , 30.5690353252 )\n( 3092 , 30.5916748369 )\n( 3093 , 30.6143198669 )\n( 3094 , 30.6369704081 )\n( 3095 , 30.6596264535 )\n( 3096 , 30.682287996 )\n( 3097 , 30.7049550287 )\n( 3098 , 30.7276275443 )\n( 3099 , 30.750305536 )\n( 3100 , 30.7729889965 )\n( 3101 , 30.7956779189 )\n( 3102 , 30.818372296 )\n( 3103 , 30.8410721208 )\n( 3104 , 30.8637773862 )\n( 3105 , 30.8864880851 )\n( 3106 , 30.9092042105 )\n( 3107 , 30.9319257552 )\n( 3108 , 30.9546527121 )\n( 3109 , 30.9773850741 )\n( 3110 , 31.0001228342 )\n( 3111 , 31.0228659852 )\n( 3112 , 31.04561452 )\n( 3113 , 31.0683684315 )\n( 3114 , 31.0911277125 )\n( 3115 , 31.113892356 )\n( 3116 , 31.1366623548 )\n( 3117 , 31.1594377017 )\n( 3118 , 31.1822183897 )\n( 3119 , 31.2050044116 )\n( 3120 , 31.2277957602 )\n( 3121 , 31.2505924285 )\n( 3122 , 31.2733944091 )\n( 3123 , 31.2962016951 )\n( 3124 , 31.3190142791 )\n( 3125 , 31.3418321542 )\n( 3126 , 31.364655313 )\n( 3127 , 31.3874837484 )\n( 3128 , 31.4103174533 )\n( 3129 , 31.4331564204 )\n( 3130 , 31.4560006425 )\n( 3131 , 31.4788501126 )\n( 3132 , 31.5017048233 )\n( 3133 , 31.5245647675 )\n( 3134 , 31.547429938 )\n( 3135 , 31.5703003276 )\n( 3136 , 31.5931759291 )\n( 3137 , 31.6160567352 )\n( 3138 , 31.6389427387 )\n( 3139 , 31.6618339325 )\n( 3140 , 31.6847303092 )\n( 3141 , 31.7076318617 )\n( 3142 , 31.7305385828 )\n( 3143 , 31.7534504651 )\n( 3144 , 31.7763675015 )\n( 3145 , 31.7992896847 )\n( 3146 , 31.8222170075 )\n( 3147 , 31.8451494626 )\n( 3148 , 31.8680870427 )\n( 3149 , 31.8910297406 )\n( 3150 , 31.9139775491 )\n( 3151 , 31.9369304608 )\n( 3152 , 31.9598884685 )\n( 3153 , 31.982851565 )\n( 3154 , 32.0058197428 )\n( 3155 , 32.0287929949 )\n( 3156 , 32.0517713138 )\n( 3157 , 32.0747546923 )\n( 3158 , 32.097743123 )\n( 3159 , 32.1207365988 )\n( 3160 , 32.1437351123 )\n( 3161 , 32.1667386561 )\n( 3162 , 32.189747223 )\n( 3163 , 32.2127608057 )\n( 3164 , 32.2357793968 )\n( 3165 , 32.2588029891 )\n( 3166 , 32.2818315751 )\n( 3167 , 32.3048651476 )\n( 3168 , 32.3279036993 )\n( 3169 , 32.3509472228 )\n( 3170 , 32.3739957108 )\n( 3171 , 32.3970491558 )\n( 3172 , 32.4201075507 )\n( 3173 , 32.443170888 )\n( 3174 , 32.4662391604 )\n( 3175 , 32.4893123604 )\n( 3176 , 32.5123904809 )\n( 3177 , 32.5354735144 )\n( 3178 , 32.5585614534 )\n( 3179 , 32.5816542908 )\n( 3180 , 32.604752019 )\n( 3181 , 32.6278546307 )\n( 3182 , 32.6509621185 )\n( 3183 , 32.6740744751 )\n( 3184 , 32.697191693 )\n( 3185 , 32.7203137649 )\n( 3186 , 32.7434406833 )\n( 3187 , 32.7665724409 )\n( 3188 , 32.7897090302 )\n( 3189 , 32.8128504439 )\n( 3190 , 32.8359966744 )\n( 3191 , 32.8591477145 )\n( 3192 , 32.8823035567 )\n( 3193 , 32.9054641936 )\n( 3194 , 32.9286296177 )\n( 3195 , 32.9517998216 )\n( 3196 , 32.9749747979 )\n( 3197 , 32.9981545392 )\n( 3198 , 33.0213390379 )\n( 3199 , 33.0445282868 )\n( 3200 , 33.0677222782 )\n( 3201 , 33.0909210048 )\n( 3202 , 33.1141244591 )\n( 3203 , 33.1373326337 )\n( 3204 , 33.1605455211 )\n( 3205 , 33.1837631138 )\n( 3206 , 33.2069854043 )\n( 3207 , 33.2302123853 )\n( 3208 , 33.2534440491 )\n( 3209 , 33.2766803884 )\n( 3210 , 33.2999213956 )\n( 3211 , 33.3231670633 )\n( 3212 , 33.346417384 )\n( 3213 , 33.3696723502 )\n( 3214 , 33.3929319543 )\n( 3215 , 33.416196189 )\n( 3216 , 33.4394650466 )\n( 3217 , 33.4627385197 )\n( 3218 , 33.4860166008 )\n( 3219 , 33.5092992824 )\n( 3220 , 33.5325865568 )\n( 3221 , 33.5558784168 )\n( 3222 , 33.5791748546 )\n( 3223 , 33.6024758627 )\n( 3224 , 33.6257814337 )\n( 3225 , 33.6490915601 )\n( 3226 , 33.6724062342 )\n( 3227 , 33.6957254485 )\n( 3228 , 33.7190491955 )\n( 3229 , 33.7423774677 )\n( 3230 , 33.7657102574 )\n( 3231 , 33.7890475572 )\n( 3232 , 33.8123893595 )\n( 3233 , 33.8357356566 )\n( 3234 , 33.8590864412 )\n( 3235 , 33.8824417055 )\n( 3236 , 33.9058014421 )\n( 3237 , 33.9291656433 )\n( 3238 , 33.9525343015 )\n( 3239 , 33.9759074093 )\n( 3240 , 33.9992849589 )\n( 3241 , 34.0226669429 )\n( 3242 , 34.0460533536 )\n( 3243 , 34.0694441835 )\n( 3244 , 34.0928394248 )\n( 3245 , 34.1162390702 )\n( 3246 , 34.1396431118 )\n( 3247 , 34.1630515422 )\n( 3248 , 34.1864643537 )\n( 3249 , 34.2098815388 )\n( 3250 , 34.2333030897 )\n( 3251 , 34.2567289988 )\n( 3252 , 34.2801592587 )\n( 3253 , 34.3035938615 )\n( 3254 , 34.3270327998 )\n( 3255 , 34.3504760658 )\n( 3256 , 34.373923652 )\n( 3257 , 34.3973755506 )\n( 3258 , 34.4208317541 )\n( 3259 , 34.4442922548 )\n( 3260 , 34.4677570451 )\n( 3261 , 34.4912261173 )\n( 3262 , 34.5146994637 )\n( 3263 , 34.5381770767 )\n( 3264 , 34.5616589487 )\n( 3265 , 34.5851450719 )\n( 3266 , 34.6086354387 )\n( 3267 , 34.6321300415 )\n( 3268 , 34.6556288725 )\n( 3269 , 34.6791319241 )\n( 3270 , 34.7026391886 )\n( 3271 , 34.7261506584 )\n( 3272 , 34.7496663257 )\n( 3273 , 34.7731861828 )\n( 3274 , 34.7967102221 )\n( 3275 , 34.8202384359 )\n( 3276 , 34.8437708164 )\n( 3277 , 34.867307356 )\n( 3278 , 34.890848047 )\n( 3279 , 34.9143928816 )\n( 3280 , 34.9379418522 )\n( 3281 , 34.961494951 )\n( 3282 , 34.9850521703 )\n( 3283 , 35.0086135024 )\n( 3284 , 35.0321789397 )\n( 3285 , 35.0557484742 )\n( 3286 , 35.0793220984 )\n( 3287 , 35.1028998045 )\n( 3288 , 35.1264815847 )\n( 3289 , 35.1500674314 )\n( 3290 , 35.1736573368 )\n( 3291 , 35.1972512931 )\n( 3292 , 35.2208492926 )\n( 3293 , 35.2444513275 )\n( 3294 , 35.2680573902 )\n( 3295 , 35.2916674728 )\n( 3296 , 35.3152815675 )\n( 3297 , 35.3388996667 )\n( 3298 , 35.3625217626 )\n( 3299 , 35.3861478474 )\n( 3300 , 35.4097779133 )\n( 3301 , 35.4334119525 )\n( 3302 , 35.4570499573 )\n( 3303 , 35.4806919199 )\n( 3304 , 35.5043378326 )\n( 3305 , 35.5279876875 )\n( 3306 , 35.5516414768 )\n( 3307 , 35.5752991928 )\n( 3308 , 35.5989608277 )\n( 3309 , 35.6226263736 )\n( 3310 , 35.6462958228 )\n( 3311 , 35.6699691675 )\n( 3312 , 35.6936463999 )\n( 3313 , 35.7173275122 )\n( 3314 , 35.7410124965 )\n( 3315 , 35.764701345 )\n( 3316 , 35.78839405 )\n( 3317 , 35.8120906036 )\n( 3318 , 35.835790998 )\n( 3319 , 35.8594952253 )\n( 3320 , 35.8832032778 )\n( 3321 , 35.9069151477 )\n( 3322 , 35.930630827 )\n( 3323 , 35.9543503079 )\n( 3324 , 35.9780735827 )\n( 3325 , 36.0018006434 )\n( 3326 , 36.0255314823 )\n( 3327 , 36.0492660915 )\n( 3328 , 36.0730044631 )\n( 3329 , 36.0967465893 )\n( 3330 , 36.1204924622 )\n( 3331 , 36.144242074 )\n( 3332 , 36.1679954169 )\n( 3333 , 36.1917524829 )\n( 3334 , 36.2155132642 )\n( 3335 , 36.2392777529 )\n( 3336 , 36.2630459412 )\n( 3337 , 36.2868178211 )\n( 3338 , 36.3105933849 )\n( 3339 , 36.3343726246 )\n( 3340 , 36.3581555324 )\n( 3341 , 36.3819421003 )\n( 3342 , 36.4057323205 )\n( 3343 , 36.4295261852 )\n( 3344 , 36.4533236863 )\n( 3345 , 36.4771248161 )\n( 3346 , 36.5009295665 )\n( 3347 , 36.5247379298 )\n( 3348 , 36.5485498981 )\n( 3349 , 36.5723654633 )\n( 3350 , 36.5961846176 )\n( 3351 , 36.6200073532 )\n( 3352 , 36.643833662 )\n( 3353 , 36.6676635362 )\n( 3354 , 36.6914969679 )\n( 3355 , 36.7153339491 )\n( 3356 , 36.739174472 )\n( 3357 , 36.7630185285 )\n( 3358 , 36.7868661108 )\n( 3359 , 36.810717211 )\n( 3360 , 36.834571821 )\n( 3361 , 36.8584299331 )\n( 3362 , 36.8822915391 )\n( 3363 , 36.9061566313 )\n( 3364 , 36.9300252016 )\n( 3365 , 36.9538972422 )\n( 3366 , 36.977772745 )\n( 3367 , 37.0016517021 )\n( 3368 , 37.0255341056 )\n( 3369 , 37.0494199475 )\n( 3370 , 37.0733092199 )\n( 3371 , 37.0972019147 )\n( 3372 , 37.1210980241 )\n( 3373 , 37.1449975401 )\n( 3374 , 37.1689004547 )\n( 3375 , 37.1928067599 )\n( 3376 , 37.2167164478 )\n( 3377 , 37.2406295104 )\n( 3378 , 37.2645459397 )\n( 3379 , 37.2884657278 )\n( 3380 , 37.3123888666 )\n( 3381 , 37.3363153481 )\n( 3382 , 37.3602451645 )\n( 3383 , 37.3841783077 )\n( 3384 , 37.4081147697 )\n( 3385 , 37.4320545425 )\n( 3386 , 37.4559976182 )\n( 3387 , 37.4799439886 )\n( 3388 , 37.5038936459 )\n( 3389 , 37.5278465821 )\n( 3390 , 37.5518027891 )\n( 3391 , 37.5757622588 )\n( 3392 , 37.5997249834 )\n( 3393 , 37.6236909548 )\n( 3394 , 37.647660165 )\n( 3395 , 37.671632606 )\n( 3396 , 37.6956082697 )\n( 3397 , 37.7195871482 )\n( 3398 , 37.7435692333 )\n( 3399 , 37.7675545172 )\n( 3400 , 37.7915429917 )\n( 3401 , 37.8155346488 )\n( 3402 , 37.8395294806 )\n( 3403 , 37.8635274789 )\n( 3404 , 37.8875286358 )\n( 3405 , 37.9115329431 )\n( 3406 , 37.9355403929 )\n( 3407 , 37.9595509771 )\n( 3408 , 37.9835646877 )\n( 3409 , 38.0075815166 )\n( 3410 , 38.0316014558 )\n( 3411 , 38.0556244972 )\n( 3412 , 38.0796506328 )\n( 3413 , 38.1036798545 )\n( 3414 , 38.1277121542 )\n( 3415 , 38.151747524 )\n( 3416 , 38.1757859556 )\n( 3417 , 38.1998274412 )\n( 3418 , 38.2238719726 )\n( 3419 , 38.2479195417 )\n( 3420 , 38.2719701404 )\n( 3421 , 38.2960237608 )\n( 3422 , 38.3200803947 )\n( 3423 , 38.344140034 )\n( 3424 , 38.3682026707 )\n( 3425 , 38.3922682967 )\n( 3426 , 38.4163369039 )\n( 3427 , 38.4404084842 )\n( 3428 , 38.4644830295 )\n( 3429 , 38.4885605318 )\n( 3430 , 38.5126409829 )\n( 3431 , 38.5367243748 )\n( 3432 , 38.5608106994 )\n( 3433 , 38.5848999485 )\n( 3434 , 38.6089921141 )\n( 3435 , 38.6330871881 )\n( 3436 , 38.6571851623 )\n( 3437 , 38.6812860287 )\n( 3438 , 38.7053897791 )\n( 3439 , 38.7294964055 )\n( 3440 , 38.7536058997 )\n( 3441 , 38.7777182537 )\n( 3442 , 38.8018334592 )\n( 3443 , 38.8259515083 )\n( 3444 , 38.8500723927 )\n( 3445 , 38.8741961043 )\n( 3446 , 38.8983226351 )\n( 3447 , 38.9224519769 )\n( 3448 , 38.9465841216 )\n( 3449 , 38.970719061 )\n( 3450 , 38.994856787 )\n( 3451 , 39.0189972915 )\n( 3452 , 39.0431405664 )\n( 3453 , 39.0672866035 )\n( 3454 , 39.0914353947 )\n( 3455 , 39.1155869318 )\n( 3456 , 39.1397412067 )\n( 3457 , 39.1638982112 )\n( 3458 , 39.1880579373 )\n( 3459 , 39.2122203767 )\n( 3460 , 39.2363855214 )\n( 3461 , 39.2605533631 )\n( 3462 , 39.2847238937 )\n( 3463 , 39.3088971051 )\n( 3464 , 39.3330729891 )\n( 3465 , 39.3572515375 )\n( 3466 , 39.3814327422 )\n( 3467 , 39.405616595 )\n( 3468 , 39.4298030878 )\n( 3469 , 39.4539922123 )\n( 3470 , 39.4781839605 )\n( 3471 , 39.5023783242 )\n( 3472 , 39.5265752951 )\n( 3473 , 39.5507748652 )\n( 3474 , 39.5749770262 )\n( 3475 , 39.59918177 )\n( 3476 , 39.6233890883 )\n( 3477 , 39.6475989731 )\n( 3478 , 39.6718114161 )\n( 3479 , 39.6960264091 )\n( 3480 , 39.720243944 )\n( 3481 , 39.7444640126 )\n( 3482 , 39.7686866067 )\n( 3483 , 39.7929117181 )\n( 3484 , 39.8171393385 )\n( 3485 , 39.8413694599 )\n( 3486 , 39.8656020741 )\n( 3487 , 39.8898371727 )\n( 3488 , 39.9140747477 )\n( 3489 , 39.9383147908 )\n( 3490 , 39.9625572939 )\n( 3491 , 39.9868022486 )\n( 3492 , 40.011049647 )\n( 3493 , 40.0352994806 )\n( 3494 , 40.0595517413 )\n( 3495 , 40.083806421 )\n( 3496 , 40.1080635113 )\n( 3497 , 40.1323230041 )\n( 3498 , 40.1565848912 )\n( 3499 , 40.1808491644 )\n( 3500 , 40.2051158153 )\n( 3501 , 40.2293848359 )\n( 3502 , 40.2536562179 )\n( 3503 , 40.2779299531 )\n( 3504 , 40.3022060333 )\n( 3505 , 40.3264844502 )\n( 3506 , 40.3507651955 )\n( 3507 , 40.3750482612 )\n( 3508 , 40.3993336389 )\n( 3509 , 40.4236213205 )\n( 3510 , 40.4479112976 )\n( 3511 , 40.4722035621 )\n( 3512 , 40.4964981057 )\n( 3513 , 40.5207949202 )\n( 3514 , 40.5450939974 )\n( 3515 , 40.5693953289 )\n( 3516 , 40.5936989066 )\n( 3517 , 40.6180047223 )\n( 3518 , 40.6423127677 )\n( 3519 , 40.6666230345 )\n( 3520 , 40.6909355144 )\n( 3521 , 40.7152501994 )\n( 3522 , 40.739567081 )\n( 3523 , 40.7638861511 )\n( 3524 , 40.7882074014 )\n( 3525 , 40.8125308236 )\n( 3526 , 40.8368564095 )\n( 3527 , 40.8611841509 )\n( 3528 , 40.8855140394 )\n( 3529 , 40.9098460669 )\n( 3530 , 40.934180225 )\n( 3531 , 40.9585165055 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)\n( 5863 , 88.2139014549 )\n( 5864 , 88.2257704994 )\n( 5865 , 88.2376311534 )\n( 5866 , 88.2494834186 )\n( 5867 , 88.2613272967 )\n( 5868 , 88.2731627894 )\n( 5869 , 88.2849898985 )\n( 5870 , 88.2968086258 )\n( 5871 , 88.3086189729 )\n( 5872 , 88.3204209418 )\n( 5873 , 88.332214534 )\n( 5874 , 88.3439997515 )\n( 5875 , 88.355776596 )\n( 5876 , 88.3675450692 )\n( 5877 , 88.3793051729 )\n( 5878 , 88.391056909 )\n( 5879 , 88.4028002792 )\n( 5880 , 88.4145352853 )\n( 5881 , 88.4262619292 )\n( 5882 , 88.4379802126 )\n( 5883 , 88.4496901373 )\n( 5884 , 88.4613917051 )\n( 5885 , 88.4730849179 )\n( 5886 , 88.4847697775 )\n( 5887 , 88.4964462858 )\n( 5888 , 88.5081144444 )\n( 5889 , 88.5197742554 )\n( 5890 , 88.5314257205 )\n( 5891 , 88.5430688415 )\n( 5892 , 88.5547036204 )\n( 5893 , 88.566330059 )\n( 5894 , 88.577948159 )\n( 5895 , 88.5895579225 )\n( 5896 , 88.6011593513 )\n( 5897 , 88.6127524471 )\n( 5898 , 88.624337212 )\n( 5899 , 88.6359136477 )\n( 5900 , 88.6474817562 )\n( 5901 , 88.6590415394 )\n( 5902 , 88.6705929991 )\n( 5903 , 88.6821361373 )\n( 5904 , 88.6936709558 )\n( 5905 , 88.7051974566 )\n( 5906 , 88.7167156415 )\n( 5907 , 88.7282255125 )\n( 5908 , 88.7397270715 )\n( 5909 , 88.7512203204 )\n( 5910 , 88.7627052611 )\n( 5911 , 88.7741818956 )\n( 5912 , 88.7856502258 )\n( 5913 , 88.7971102537 )\n( 5914 , 88.8085619811 )\n( 5915 , 88.8200054101 )\n( 5916 , 88.8314405426 )\n( 5917 , 88.8428673805 )\n( 5918 , 88.8542859258 )\n( 5919 , 88.8656961804 )\n( 5920 , 88.8770981464 )\n( 5921 , 88.8884918258 )\n( 5922 , 88.8998772204 )\n( 5923 , 88.9112543322 )\n( 5924 , 88.9226231633 )\n( 5925 , 88.9339837157 )\n( 5926 , 88.9453359913 )\n( 5927 , 88.9566799921 )\n( 5928 , 88.9680157202 )\n( 5929 , 88.9793431775 )\n( 5930 , 88.9906623661 )\n( 5931 , 89.0019732879 )\n( 5932 , 89.013275945 )\n( 5933 , 89.0245703395 )\n( 5934 , 89.0358564732 )\n( 5935 , 89.0471343483 )\n( 5936 , 89.0584039669 )\n( 5937 , 89.0696653308 )\n( 5938 , 89.0809184423 )\n( 5939 , 89.0921633033 )\n( 5940 , 89.1033999159 )\n( 5941 , 89.1146282821 )\n( 5942 , 89.125848404 )\n( 5943 , 89.1370602837 )\n( 5944 , 89.1482639232 )\n( 5945 , 89.1594593246 )\n( 5946 , 89.17064649 )\n( 5947 , 89.1818254215 )\n( 5948 , 89.1929961211 )\n( 5949 , 89.2041585909 )\n( 5950 , 89.2153128331 )\n( 5951 , 89.2264588497 )\n( 5952 , 89.2375966429 )\n( 5953 , 89.2487262146 )\n( 5954 , 89.2598475671 )\n( 5955 , 89.2709607025 )\n( 5956 , 89.2820656228 )\n( 5957 , 89.2931623302 )\n( 5958 , 89.3042508268 )\n( 5959 , 89.3153311148 )\n( 5960 , 89.3264031963 )\n( 5961 , 89.3374670733 )\n( 5962 , 89.3485227482 )\n( 5963 , 89.3595702229 )\n( 5964 , 89.3706094997 )\n( 5965 , 89.3816405806 )\n( 5966 , 89.392663468 )\n( 5967 , 89.4036781638 )\n( 5968 , 89.4146846704 )\n( 5969 , 89.4256829898 )\n( 5970 , 89.4366731242 )\n( 5971 , 89.4476550759 )\n( 5972 , 89.4586288469 )\n( 5973 , 89.4695944395 )\n( 5974 , 89.4805518559 )\n( 5975 , 89.4915010982 )\n( 5976 , 89.5024421686 )\n( 5977 , 89.5133750695 )\n( 5978 , 89.5242998028 )\n( 5979 , 89.535216371 )\n( 5980 , 89.5461247761 )\n( 5981 , 89.5570250204 )\n( 5982 , 89.5679171061 )\n( 5983 , 89.5788010355 )\n( 5984 , 89.5896768107 )\n( 5985 , 89.600544434 )\n( 5986 , 89.6114039077 )\n( 5987 , 89.6222552339 )\n( 5988 , 89.633098415 )\n( 5989 , 89.6439334531 )\n( 5990 , 89.6547603505 )\n( 5991 , 89.6655791095 )\n( 5992 , 89.6763897324 )\n( 5993 , 89.6871922213 )\n( 5994 , 89.6979865786 )\n( 5995 , 89.7087728065 )\n( 5996 , 89.7195509073 )\n( 5997 , 89.7303208834 )\n( 5998 , 89.7410827368 )\n( 5999 , 89.7518364701 )\n( 6000 , 89.7625820854 )\n( 6001 , 89.773319585 )\n( 6002 , 89.7840489712 )\n( 6003 , 89.7947702464 )\n( 6004 , 89.8054834128 )\n( 6005 , 89.8161884728 )\n( 6006 , 89.8268854286 )\n( 6007 , 89.8375742827 )\n( 6008 , 89.8482550372 )\n( 6009 , 89.8589276945 )\n( 6010 , 89.869592257 )\n( 6011 , 89.880248727 )\n( 6012 , 89.8908971068 )\n( 6013 , 89.9015373988 )\n( 6014 , 89.9121696052 )\n( 6015 , 89.9227937285 )\n( 6016 , 89.933409771 )\n( 6017 , 89.9440177351 )\n( 6018 , 89.954617623 )\n( 6019 , 89.9652094373 )\n( 6020 , 89.9757931802 )\n( 6021 , 89.9863688541 )\n( 6022 , 89.9969364613 )\n( 6023 , 90.0074960043 )\n( 6024 , 90.0180474855 )\n( 6025 , 90.0285909072 )\n( 6026 , 90.0391262718 )\n( 6027 , 90.0496535817 )\n( 6028 , 90.0601728392 )\n( 6029 , 90.0706840469 )\n( 6030 , 90.0811872071 )\n( 6031 , 90.0916823222 )\n( 6032 , 90.1021693946 )\n( 6033 , 90.1126484267 )\n( 6034 , 90.123119421 )\n( 6035 , 90.1335823798 )\n( 6036 , 90.1440373056 )\n( 6037 , 90.1544842008 )\n( 6038 , 90.1649230679 )\n( 6039 , 90.1753539093 )\n( 6040 , 90.1857767273 )\n( 6041 , 90.1961915246 )\n( 6042 , 90.2065983034 )\n( 6043 , 90.2169970664 )\n( 6044 , 90.2273878158 )\n( 6045 , 90.2377705542 )\n( 6046 , 90.2481452841 )\n( 6047 , 90.2585120078 )\n( 6048 , 90.2688707279 )\n( 6049 , 90.2792214468 )\n( 6050 , 90.2895641671 )\n( 6051 , 90.2998988911 )\n( 6052 , 90.3102256214 )\n( 6053 , 90.3205443605 )\n( 6054 , 90.3308551108 )\n( 6055 , 90.3411578749 )\n( 6056 , 90.3514526552 )\n( 6057 , 90.3617394542 )\n( 6058 , 90.3720182745 )\n( 6059 , 90.3822891185 )\n( 6060 , 90.3925519887 )\n( 6061 , 90.4028068878 )\n( 6062 , 90.4130538181 )\n( 6063 , 90.4232927823 )\n( 6064 , 90.4335237827 )\n( 6065 , 90.4437468221 )\n( 6066 , 90.4539619028 )\n( 6067 , 90.4641690275 )\n( 6068 , 90.4743681986 )\n( 6069 , 90.4845594188 )\n( 6070 , 90.4947426905 )\n( 6071 , 90.5049180163 )\n( 6072 , 90.5150853987 )\n( 6073 , 90.5252448404 )\n( 6074 , 90.5353963439 )\n( 6075 , 90.5455399117 )\n( 6076 , 90.5556755464 )\n( 6077 , 90.5658032505 )\n( 6078 , 90.5759230267 )\n( 6079 , 90.5860348776 )\n( 6080 , 90.5961388056 )\n( 6081 , 90.6062348134 )\n( 6082 , 90.6163229036 )\n( 6083 , 90.6264030788 )\n( 6084 , 90.6364753415 )\n( 6085 , 90.6465396944 )\n( 6086 , 90.65659614 )\n( 6087 , 90.666644681 )\n( 6088 , 90.67668532 )\n( 6089 , 90.6867180595 )\n( 6090 , 90.6967429023 )\n( 6091 , 90.7067598508 )\n( 6092 , 90.7167689078 )\n( 6093 , 90.7267700758 )\n( 6094 , 90.7367633575 )\n( 6095 , 90.7467487556 )\n( 6096 , 90.7567262726 )\n( 6097 , 90.7666959111 )\n( 6098 , 90.7766576739 )\n( 6099 , 90.7866115636 )\n( 6100 , 90.7965575828 )\n( 6101 , 90.8064957341 )\n( 6102 , 90.8164260203 )\n( 6103 , 90.826348444 )\n( 6104 , 90.8362630078 )\n( 6105 , 90.8461697144 )\n( 6106 , 90.8560685665 )\n( 6107 , 90.8659595667 )\n( 6108 , 90.8758427178 )\n( 6109 , 90.8857180224 )\n( 6110 , 90.8955854831 )\n( 6111 , 90.9054451027 )\n( 6112 , 90.9152968839 )\n( 6113 , 90.9251408293 )\n( 6114 , 90.9349769417 )\n( 6115 , 90.9448052236 )\n( 6116 , 90.9546256779 )\n( 6117 , 90.9644383073 )\n( 6118 , 90.9742431144 )\n( 6119 , 90.9840401019 )\n( 6120 , 90.9938292726 )\n( 6121 , 91.0036106293 )\n( 6122 , 91.0133841745 )\n( 6123 , 91.023149911 )\n( 6124 , 91.0329078416 )\n( 6125 , 91.042657969 )\n( 6126 , 91.0524002958 )\n( 6127 , 91.062134825 )\n( 6128 , 91.0718615591 )\n( 6129 , 91.081580501 )\n( 6130 , 91.0912916533 )\n( 6131 , 91.1009950189 )\n( 6132 , 91.1106906005 )\n( 6133 , 91.1203784008 )\n( 6134 , 91.1300584226 )\n( 6135 , 91.1397306686 )\n( 6136 , 91.1493951416 )\n( 6137 , 91.1590518445 )\n( 6138 , 91.1687007799 )\n( 6139 , 91.1783419506 )\n( 6140 , 91.1879753595 )\n( 6141 , 91.1976010092 )\n( 6142 , 91.2072189026 )\n( 6143 , 91.2168290424 )\n( 6144 , 91.2264314316 )\n( 6145 , 91.2360260727 )\n( 6146 , 91.2456129687 )\n( 6147 , 91.2551921223 )\n( 6148 , 91.2647635363 )\n( 6149 , 91.2743272136 )\n( 6150 , 91.283883157 )\n( 6151 , 91.2934313692 )\n( 6152 , 91.3029718531 )\n( 6153 , 91.3125046114 )\n( 6154 , 91.3220296471 )\n( 6155 , 91.3315469629 )\n( 6156 , 91.3410565617 )\n( 6157 , 91.3505584463 )\n( 6158 , 91.3600526195 )\n( 6159 , 91.3695390841 )\n( 6160 , 91.3790178431 )\n( 6161 , 91.3884888992 )\n( 6162 , 91.3979522553 )\n( 6163 , 91.4074079142 )\n( 6164 , 91.4168558788 )\n( 6165 , 91.4262961519 )\n( 6166 , 91.4357287365 )\n( 6167 , 91.4451536352 )\n( 6168 , 91.4545708511 )\n( 6169 , 91.463980387 )\n( 6170 , 91.4733822458 )\n( 6171 , 91.4827764302 )\n( 6172 , 91.4921629433 )\n( 6173 , 91.5015417878 )\n( 6174 , 91.5109129667 )\n( 6175 , 91.5202764828 )\n( 6176 , 91.529632339 )\n( 6177 , 91.5389805383 )\n( 6178 , 91.5483210835 )\n( 6179 , 91.5576539774 )\n( 6180 , 91.5669792231 )\n( 6181 , 91.5762968234 )\n( 6182 , 91.5856067811 )\n( 6183 , 91.5949090993 )\n( 6184 , 91.6042037808 )\n( 6185 , 91.6134908286 )\n( 6186 , 91.6227702455 )\n( 6187 , 91.6320420344 )\n( 6188 , 91.6413061984 )\n( 6189 , 91.6505627403 )\n( 6190 , 91.659811663 )\n( 6191 , 91.6690529695 )\n( 6192 , 91.6782866626 )\n( 6193 , 91.6875127455 )\n( 6194 , 91.6967312209 )\n( 6195 , 91.7059420918 )\n( 6196 , 91.7151453612 )\n( 6197 , 91.724341032 )\n( 6198 , 91.7335291072 )\n( 6199 , 91.7427095897 )\n( 6200 , 91.7518824825 )\n( 6201 , 91.7610477885 )\n( 6202 , 91.7702055107 )\n( 6203 , 91.779355652 )\n( 6204 , 91.7884982155 )\n( 6205 , 91.797633204 )\n( 6206 , 91.8067606207 )\n( 6207 , 91.8158804683 )\n( 6208 , 91.82499275 )\n( 6209 , 91.8340974687 )\n( 6210 , 91.8431946274 )\n( 6211 , 91.852284229 )\n( 6212 , 91.8613662766 )\n( 6213 , 91.8704407732 )\n( 6214 , 91.8795077217 )\n( 6215 , 91.8885671251 )\n( 6216 , 91.8976189865 )\n( 6217 , 91.9066633089 )\n( 6218 , 91.9157000952 )\n( 6219 , 91.9247293484 )\n( 6220 , 91.9337510717 )\n( 6221 , 91.9427652679 )\n( 6222 , 91.9517719401 )\n( 6223 , 91.9607710914 )\n( 6224 , 91.9697627247 )\n( 6225 , 91.9787468431 )\n( 6226 , 91.9877234495 )\n( 6227 , 91.9966925471 )\n( 6228 , 92.0056541389 )\n( 6229 , 92.0146082278 )\n( 6230 , 92.023554817 )\n( 6231 , 92.0324939095 )\n( 6232 , 92.0414255083 )\n( 6233 , 92.0503496165 )\n( 6234 , 92.0592662371 )\n( 6235 , 92.0681753731 )\n( 6236 , 92.0770770277 )\n( 6237 , 92.0859712038 )\n( 6238 , 92.0948579046 )\n( 6239 , 92.1037371331 )\n( 6240 , 92.1126088924 )\n( 6241 , 92.1214731855 )\n( 6242 , 92.1303300154 )\n( 6243 , 92.1391793854 )\n( 6244 , 92.1480212984 )\n( 6245 , 92.1568557576 )\n( 6246 , 92.1656827659 )\n( 6247 , 92.1745023266 )\n( 6248 , 92.1833144426 )\n( 6249 , 92.1921191171 )\n( 6250 , 92.2009163532 )\n( 6251 , 92.2097061539 )\n( 6252 , 92.2184885224 )\n( 6253 , 92.2272634617 )\n( 6254 , 92.2360309749 )\n( 6255 , 92.2447910652 )\n( 6256 , 92.2535437357 )\n( 6257 , 92.2622889894 )\n( 6258 , 92.2710268295 )\n( 6259 , 92.2797572591 )\n( 6260 , 92.2884802813 )\n( 6261 , 92.2971958992 )\n( 6262 , 92.305904116 )\n( 6263 , 92.3146049347 )\n( 6264 , 92.3232983585 )\n( 6265 , 92.3319843906 )\n( 6266 , 92.340663034 )\n( 6267 , 92.3493342919 )\n( 6268 , 92.3579981675 )\n( 6269 , 92.3666546638 )\n( 6270 , 92.375303784 )\n( 6271 , 92.3839455313 )\n( 6272 , 92.3925799088 )\n( 6273 , 92.4012069196 )\n( 6274 , 92.4098265669 )\n( 6275 , 92.4184388539 )\n( 6276 , 92.4270437836 )\n( 6277 , 92.4356413594 )\n( 6278 , 92.4442315842 )\n( 6279 , 92.4528144614 )\n( 6280 , 92.461389994 )\n( 6281 , 92.4699581853 )\n( 6282 , 92.4785190383 )\n( 6283 , 92.4870725563 )\n( 6284 , 92.4956187425 )\n( 6285 , 92.5041575999 )\n( 6286 , 92.5126891319 )\n( 6287 , 92.5212133416 )\n( 6288 , 92.5297302321 )\n( 6289 , 92.5382398067 )\n( 6290 , 92.5467420686 )\n( 6291 , 92.5552370208 )\n( 6292 , 92.5637246667 )\n( 6293 , 92.5722050095 )\n( 6294 , 92.5806780523 )\n( 6295 , 92.5891437983 )\n( 6296 , 92.5976022507 )\n( 6297 , 92.6060534128 )\n( 6298 , 92.6144972877 )\n( 6299 , 92.6229338787 )\n( 6300 , 92.631363189 )\n( 6301 , 92.6397852218 )\n( 6302 , 92.6481999803 )\n( 6303 , 92.6566074677 )\n( 6304 , 92.6650076872 )\n( 6305 , 92.6734006422 )\n( 6306 , 92.6817863357 )\n( 6307 , 92.6901647711 )\n( 6308 , 92.6985359515 )\n( 6309 , 92.7068998803 )\n( 6310 , 92.7152565605 )\n( 6311 , 92.7236059956 )\n( 6312 , 92.7319481886 )\n( 6313 , 92.740283143 )\n( 6314 , 92.7486108618 )\n( 6315 , 92.7569313484 )\n( 6316 , 92.7652446059 )\n( 6317 , 92.7735506378 )\n( 6318 , 92.7818494471 )\n( 6319 , 92.7901410372 )\n( 6320 , 92.7984254113 )\n( 6321 , 92.8067025727 )\n( 6322 , 92.8149725247 )\n( 6323 , 92.8232352704 )\n( 6324 , 92.8314908133 )\n( 6325 , 92.8397391565 )\n( 6326 , 92.8479803033 )\n( 6327 , 92.856214257 )\n( 6328 , 92.8644410209 )\n( 6329 , 92.8726605982 )\n( 6330 , 92.8808729923 )\n( 6331 , 92.8890782063 )\n( 6332 , 92.8972762437 )\n( 6333 , 92.9054671077 )\n( 6334 , 92.9136508015 )\n( 6335 , 92.9218273285 )\n( 6336 , 92.929996692 )\n( 6337 , 92.9381588952 )\n( 6338 , 92.9463139415 )\n( 6339 , 92.9544618342 )\n( 6340 , 92.9626025765 )\n( 6341 , 92.9707361717 )\n( 6342 , 92.9788626232 )\n( 6343 , 92.9869819343 )\n( 6344 , 92.9950941083 )\n( 6345 , 93.0031991485 )\n( 6346 , 93.0112970582 )\n( 6347 , 93.0193878408 )\n( 6348 , 93.0274714995 )\n( 6349 , 93.0355480376 )\n( 6350 , 93.0436174586 )\n( 6351 , 93.0516797657 )\n( 6352 , 93.0597349622 )\n( 6353 , 93.0677830515 )\n( 6354 , 93.0758240369 )\n( 6355 , 93.0838579218 )\n( 6356 , 93.0918847094 )\n( 6357 , 93.0999044032 )\n( 6358 , 93.1079170064 )\n( 6359 , 93.1159225224 )\n( 6360 , 93.1239209545 )\n( 6361 , 93.1319123062 )\n( 6362 , 93.1398965806 )\n( 6363 , 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93.4457990036 )\n( 6402 , 93.4535029591 )\n( 6403 , 93.4611999764 )\n( 6404 , 93.4688900589 )\n( 6405 , 93.47657321 )\n( 6406 , 93.4842494332 )\n( 6407 , 93.4919187319 )\n( 6408 , 93.4995811094 )\n( 6409 , 93.5072365694 )\n( 6410 , 93.5148851151 )\n( 6411 , 93.5225267501 )\n( 6412 , 93.5301614778 )\n( 6413 , 93.5377893016 )\n( 6414 , 93.5454102249 )\n( 6415 , 93.5530242513 )\n( 6416 , 93.5606313841 )\n( 6417 , 93.5682316269 )\n( 6418 , 93.5758249831 )\n( 6419 , 93.583411456 )\n( 6420 , 93.5909910493 )\n( 6421 , 93.5985637663 )\n( 6422 , 93.6061296105 )\n( 6423 , 93.6136885853 )\n( 6424 , 93.6212406943 )\n( 6425 , 93.6287859409 )\n( 6426 , 93.6363243285 )\n( 6427 , 93.6438558607 )\n( 6428 , 93.6513805408 )\n( 6429 , 93.6588983724 )\n( 6430 , 93.666409359 )\n( 6431 , 93.6739135039 )\n( 6432 , 93.6814108108 )\n( 6433 , 93.688901283 )\n( 6434 , 93.6963849241 )\n( 6435 , 93.7038617375 )\n( 6436 , 93.7113317267 )\n( 6437 , 93.7187948952 )\n( 6438 , 93.7262512465 )\n( 6439 , 93.7337007841 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99.8602305256 )\n( 8805 , 99.860518496 )\n( 8806 , 99.8608059305 )\n( 8807 , 99.86109283 )\n( 8808 , 99.8613791954 )\n( 8809 , 99.8616650276 )\n( 8810 , 99.8619503274 )\n( 8811 , 99.8622350957 )\n( 8812 , 99.8625193334 )\n( 8813 , 99.8628030413 )\n( 8814 , 99.8630862203 )\n( 8815 , 99.8633688713 )\n( 8816 , 99.8636509951 )\n( 8817 , 99.8639325925 )\n( 8818 , 99.8642136645 )\n( 8819 , 99.8644942119 )\n( 8820 , 99.8647742356 )\n( 8821 , 99.8650537363 )\n( 8822 , 99.8653327151 )\n( 8823 , 99.8656111726 )\n( 8824 , 99.8658891098 )\n( 8825 , 99.8661665276 )\n( 8826 , 99.8664434267 )\n( 8827 , 99.866719808 )\n( 8828 , 99.8669956724 )\n( 8829 , 99.8672710207 )\n( 8830 , 99.8675458538 )\n( 8831 , 99.8678201725 )\n( 8832 , 99.8680939776 )\n( 8833 , 99.86836727 )\n( 8834 , 99.8686400506 )\n( 8835 , 99.8689123201 )\n( 8836 , 99.8691840794 )\n( 8837 , 99.8694553294 )\n( 8838 , 99.8697260709 )\n( 8839 , 99.8699963047 )\n( 8840 , 99.8702660317 )\n( 8841 , 99.8705352526 )\n( 8842 , 99.8708039683 )\n( 8843 , 99.8710721798 )\n( 8844 , 99.8713398876 )\n( 8845 , 99.8716070928 )\n( 8846 , 99.8718737962 )\n( 8847 , 99.8721399985 )\n( 8848 , 99.8724057005 )\n( 8849 , 99.8726709032 )\n( 8850 , 99.8729356074 )\n( 8851 , 99.8731998138 )\n( 8852 , 99.8734635232 )\n( 8853 , 99.8737267366 )\n( 8854 , 99.8739894547 )\n( 8855 , 99.8742516783 )\n( 8856 , 99.8745134082 )\n( 8857 , 99.8747746454 )\n( 8858 , 99.8750353905 )\n( 8859 , 99.8752956444 )\n( 8860 , 99.8755554079 )\n( 8861 , 99.8758146818 )\n( 8862 , 99.8760734669 )\n( 8863 , 99.8763317641 )\n( 8864 , 99.8765895741 )\n( 8865 , 99.8768468977 )\n( 8866 , 99.8771037358 )\n( 8867 , 99.8773600892 )\n( 8868 , 99.8776159586 )\n( 8869 , 99.8778713449 )\n( 8870 , 99.8781262488 )\n( 8871 , 99.8783806712 )\n( 8872 , 99.8786346128 )\n( 8873 , 99.8788880746 )\n( 8874 , 99.8791410571 )\n( 8875 , 99.8793935613 )\n( 8876 , 99.879645588 )\n( 8877 , 99.8798971379 )\n( 8878 , 99.8801482118 )\n( 8879 , 99.8803988105 )\n( 8880 , 99.8806489348 )\n( 8881 , 99.8808985856 )\n( 8882 , 99.8811477635 )\n( 8883 , 99.8813964694 )\n( 8884 , 99.881644704 )\n( 8885 , 99.8818924682 )\n( 8886 , 99.8821397627 )\n( 8887 , 99.8823865883 )\n( 8888 , 99.8826329458 )\n( 8889 , 99.882878836 )\n( 8890 , 99.8831242596 )\n( 8891 , 99.8833692175 )\n( 8892 , 99.8836137103 )\n( 8893 , 99.8838577389 )\n( 8894 , 99.8841013041 )\n( 8895 , 99.8843444066 )\n( 8896 , 99.8845870472 )\n( 8897 , 99.8848292267 )\n( 8898 , 99.8850709458 )\n( 8899 , 99.8853122053 )\n( 8900 , 99.885553006 )\n( 8901 , 99.8857933486 )\n( 8902 , 99.8860332339 )\n( 8903 , 99.8862726627 )\n( 8904 , 99.8865116358 )\n( 8905 , 99.8867501539 )\n( 8906 , 99.8869882177 )\n( 8907 , 99.887225828 )\n( 8908 , 99.8874629857 )\n( 8909 , 99.8876996914 )\n( 8910 , 99.8879359458 )\n( 8911 , 99.8881717499 )\n( 8912 , 99.8884071042 )\n( 8913 , 99.8886420096 )\n( 8914 , 99.8888764669 )\n( 8915 , 99.8891104767 )\n( 8916 , 99.8893440398 )\n( 8917 , 99.8895771571 )\n( 8918 , 99.8898098291 )\n( 8919 , 99.8900420567 )\n( 8920 , 99.8902738406 )\n( 8921 , 99.8905051816 )\n( 8922 , 99.8907360804 )\n( 8923 , 99.8909665378 )\n( 8924 , 99.8911965545 )\n( 8925 , 99.8914261312 )\n( 8926 , 99.8916552687 )\n( 8927 , 99.8918839677 )\n( 8928 , 99.8921122289 )\n( 8929 , 99.8923400532 )\n( 8930 , 99.8925674412 )\n( 8931 , 99.8927943937 )\n( 8932 , 99.8930209113 )\n( 8933 , 99.8932469949 )\n( 8934 , 99.8934726452 )\n( 8935 , 99.8936978629 )\n( 8936 , 99.8939226487 )\n( 8937 , 99.8941470034 )\n( 8938 , 99.8943709277 )\n( 8939 , 99.8945944223 )\n( 8940 , 99.8948174879 )\n( 8941 , 99.8950401253 )\n( 8942 , 99.8952623352 )\n( 8943 , 99.8954841183 )\n( 8944 , 99.8957054753 )\n( 8945 , 99.8959264071 )\n( 8946 , 99.8961469142 )\n( 8947 , 99.8963669974 )\n( 8948 , 99.8965866574 )\n( 8949 , 99.8968058949 )\n( 8950 , 99.8970247107 )\n( 8951 , 99.8972431055 )\n( 8952 , 99.89746108 )\n( 8953 , 99.8976786348 )\n( 8954 , 99.8978957708 )\n( 8955 , 99.8981124886 )\n( 8956 , 99.8983287889 )\n( 8957 , 99.8985446724 )\n( 8958 , 99.8987601399 )\n( 8959 , 99.8989751921 )\n( 8960 , 99.8991898296 )\n( 8961 , 99.8994040531 )\n( 8962 , 99.8996178635 )\n( 8963 , 99.8998312613 )\n( 8964 , 99.9000442473 )\n( 8965 , 99.9002568222 )\n( 8966 , 99.9004689866 )\n( 8967 , 99.9006807413 )\n( 8968 , 99.900892087 )\n( 8969 , 99.9011030244 )\n( 8970 , 99.9013135541 )\n( 8971 , 99.9015236769 )\n( 8972 , 99.9017333934 )\n( 8973 , 99.9019427044 )\n( 8974 , 99.9021516105 )\n( 8975 , 99.9023601125 )\n( 8976 , 99.902568211 )\n( 8977 , 99.9027759067 )\n( 8978 , 99.9029832003 )\n( 8979 , 99.9031900924 )\n( 8980 , 99.9033965839 )\n( 8981 , 99.9036026753 )\n( 8982 , 99.9038083674 )\n( 8983 , 99.9040136607 )\n( 8984 , 99.9042185561 )\n( 8985 , 99.9044230542 )\n( 8986 , 99.9046271557 )\n( 8987 , 99.9048308612 )\n( 8988 , 99.9050341714 )\n( 8989 , 99.905237087 )\n( 8990 , 99.9054396088 )\n( 8991 , 99.9056417372 )\n( 8992 , 99.9058434732 )\n( 8993 , 99.9060448172 )\n( 8994 , 99.90624577 )\n( 8995 , 99.9064463322 )\n( 8996 , 99.9066465046 )\n( 8997 , 99.9068462877 )\n( 8998 , 99.9070456823 )\n( 8999 , 99.9072446891 )\n"
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "This IPython notebook Weibull analysis was made possible based on reference material from the <a href=\"http://www.weibull.nl/weibullstatistics.htm\">weibull.nl</a> website and also from <a href=\"http://www.qualitydigest.com/jan99/html/body_weibull.html\">this</a> example of doing Weibull analysis using Excel."
    }
   ],
   "metadata": {}
  }
 ]
}