The Role of the Prior Distribution in Bayesian Decision Making for the Binomial Situation
In reliability work, the Bayes approach is often used to obtain point and interval estimates on components and/or systems. The results of using inappropriate prior distributions with these Bayes techniques can be a misdirection of decisions or a decision which is less effective than a decision based on the corresponding classical technique. However, there is often prior information available which is relevant to the decision to be made and failure to take it into account may also lead to a misdirected decision. In addition, the choice of a prior distribution when no prior information is available cannot be made from an arbitrary “feeling” of objectivity and is just as important to consider as the choice of the proper prior when prior information is available. This paper investigates the role of the prior distribution in affecting decisions based on point and interval estimates of component and system reliability. The effectiveness and robustness of the Bayes techniques are discussed and the Bayes techniques are compared to the classical techniques in both a Bayes and classical framework. Some guidance is given on the choice of reasonable prior distributions.