All the info I found online for estimating failure rate from the number of failures over a time period make reference to chi-squre, but without actually describing how it comes about. The most helpful explanation I found is http://www.weibull.com/hotwire/issue116/relbasics116.htm.
However, I'm missing some fundamental intuition behind the starting point (equation 5). It is assumed that we see r failures over a time period T. The probabilities for 0 to r failures are summed up and related to the confidence level. Why is this equation true? I mean, we do not see 0 to r failures, we only see r failures, so why so those lesser failure counts come into the picture at all?
Thanks if anyone can refer to an online explanation. If it is offline, I can probably get it eventually, but online would be so much more suitable for my timeframe.