Life Testing from a B ayesian Perspective

Abstract

Abstract Life testing provides to the Bayesian analyst new information, which may lead to the revision of a belief held prior to observing the experimental data ( learning from experience ). The revised belief, expressed in terms of a posterior probability, constitutes the inferential result. Clearly, in a decision‐making approach, revising belief leads the expert to confirm or change the choice that would have been made among alternative courses of action on the basis of prior belief only. The way in which the observed data modify the current belief is formalized by Bayes theorem. As newer data is observed, today's posterior information becomes tomorrow's prior information, so that each time new observed data come in the current belief can be revised. Clearly, the effect of life testing in updating expert belief depends on the size of the observed sample and on the manner in which the data have been collected, i.e. on the design of life testing . In a Bayesian perspective the choice of life testing design is made by optimizing the design with respect to a given overall loss function, which is the sum of a decision loss , associated with the need of making a decision under uncertainty, and a sampling cost , representing the cost of collecting life testing data. Simple examples illustrate the Bayesian learning process and design optimization.