Bayes' Equation, Reliability, and Multiple Hypothesis Testing

The rudiments of applying Bayes' Equation to hypotheses concerning reliability are introduced in a simple manner. The application is a means of obtaining posterior probabilities, for the reliability hypotheses, which are consistent with the prior beliefs and the available test results. The posterior distributions, from which decision theory could formally arrive at optimal estimates, are greatly dependent on the prior distributions. Thus, the discussion centers about the desired properties of a prior and its effects on the posterior for various data situations. Formulations for both continuous-conjugate and discrete representations of the prior beliefs are discussed and contrasted. The use of discrete priors offers many advantages over the use of continuous-conjugate priors.