An Adaptive Bayesian Scheme for Estimating Reliability Growth under Exponential Failure Times

摘要

In this paper we consider an adaptive approach for estimating reliability growth, based on prior information which is motivated from practical considerations. We discuss two situations: in the first one, both the prior distribution and the posterior distributions of the mean time to failure of an exponential distribution are stochastically ordered; in the second situation, the prior distribution is stochastically ordered with respect to the last posterior distribution. The former situation leads us to a procedure which is not fully Bayesian, and is therefore termed by us as 'pseudo-Bayesian.' Since we do not know the properties of this pseudo Bayesian approach, we can best describe our work here as being a 'pseudo-Bayesian scheme.' The second situation leads us to an approach which is fully Bayesian under certain assumptions. Our work in this general area of reliability growth is still in progress, and we invite the attention of other researchers to look into some of the problems that we have posed, and the questions that we have raised. (Author)