Test every second looking for a sample every 6 minutes on average

test.js

var hard_min = 60
var target = 360
var hard_max = target*2
var samples = 1e7

function test(multiplier) {
  var data = []
  var period = target * multiplier
  var min = hard_max
  var max = hard_min
  var i = hard_min
  while (data.length < samples) {
    i += 1
    if (Math.random() < i/period) {
      data.push(i)
      if (i < min) {
        min = i
      }
      if (i > max) {
        max = i
      }
      i = 0
    } else if (i === hard_max) {
      data.push(i)
      i = 0
    }
  }
  var total = data.reduce(function (a, b) {
    return a + b
  }, 0)
  console.log(min, max, data.slice(0,20))
  return total/data.length
}

var last = 0
var i = 235
var interval = 0.1
while (last < 361) {
  last = test(i)
  console.log(i, last)
  i += interval
}