After n successes in n exchangeable trials, under a uniform prior the next is estimated to succeed with probability (n+1)/(n+2); never treat a finite run as certainty.
For exchangeable Bernoulli trials with a fixed unknown success probability and a uniform prior, n successes and no failures give a posterior predictive probability of (n+1)/(n+2). It is what makes "it has never failed" quantifiable: after 100 successes the estimated failure rate is about 1 in 102 rather than zero, provided those assumptions hold. Often mislabelled as a rule of Bayes.
In practice
- A supplier with forty consecutive on-time deliveries is not certain to deliver on time, and the honest estimate is about one failure in forty-two.
- A component with a four-year unblemished record has a quantifiable failure probability, and "it has never happened" is not the number.
- Standing
- Often mislabelled as a rule of Bayes.
- Further reading
- Wikipedia
- Subject
- Decision-making & Reasoning
- Essay
- The catalogue of predictable errors