A Bayesian hierarchical model for reliability analyses

Attribute tests are one sort of reliability experiments, in which only the information of success or failure of each test item is recorded. In the analyses of these kind of tests our goal is to estimate the success probability p. The classical methods for assessing this binomial proportion p do not adequately reflect the real world situation in more complex situations. Let us assume the test units come from different production locations, and thus have been manufactured under varying constraints such as environmental or operational conditions. Therefore it does not seem reasonable to model this situation with a single probability value p. Obviously, there is a need for a more sophisticated stochastic model, which is able to handle different probability values pi for the different production sites. We will introduce a hierarchical model, which governs the pis from a higher level, and has the capability to predict the success probability for a new production location.