Assuming outages are totally unrelated and occur at a rate of every other month, what's the chance of seeing more than four in a given week? About one in seven million.

outages.R

# https://news.ycombinator.com/item?id=20356610
# chance of the cluster size being >5 when we can cluster events within a one-week period 
# and the rate of events is one every 2 months (debatable, but feels right to me)?

# My re-write:
# probability of more than four outages in a given week given a rate of every other month
# _assuming_: totally unrelated infra (none share AWS, etc.)
ppois(4, lambda = 1/2/4.5, lower.tail = FALSE) # ~ 1/7M chance.

# Given that we've observed five in one-week, 
# what could we guess about the weekly rate?
library(tidyverse)
tibble(possible_lambdas = seq(0.1, 2e1, 0.1)) %>%
  mutate(given_five_outages_chance_of_lambda = dpois(5, lambda = possible_lambdas)) %>%
  mutate(max_likelihood = possible_lambdas[given_five_outages_chance_of_lambda == max(given_five_outages_chance_of_lambda)]) %>%
  ggplot(aes(x = possible_lambdas, y = given_five_outages_chance_of_lambda)) +
  geom_line() +
  geom_vline(aes(xintercept = max_likelihood), color = "red") +
  ggtitle("Likelihood of unknown outage rate\ngiven one week with five outages.") +
  xlab("Possible unknown outage rate candidates") +
  ylab("Likelihood of candidate rate")