Use of Bayeslan Method in Reliability Estimation

Abstract

Since Bayes- theorem was published in 1763, the opinion as to the value of its use as a basis for statistical inference has swung between acceptance and rejection. More recently, however, the Bayesian method has been used more and more frequently as a tool for estimating the reliability parameters and for determining the uncertainty bounds on them. A very common situation one often encounters in the reliability estimation problem is as follows. There is an abundance of information regarding the reliability of a particular equipment coming from widely varying sources. Some of this information (such as generic reliability data from handbooks or from the manufacturer) is not specific to one's own equipment. Another part of the information (such as operating performance data on one-s own equipment) is much more relevant. Under such circumstances, the Bayesian method allows one to combine the much more abundant but not as relevant infromation with the less abundant but more relevant information in estimating the reliability. In this paper, a discussion is given on how the prior distribution may be obtained, and the Bayesian method is used to estimate the reliability parameters and the uncertainty bounds. Several examples will illustrate the methodology. The use of conjugate prior, the use of discretization as an approximation to a continuous prior distribution, and the use of numerical integration are compared. This paper demonstrates how easy it is to use the numerical integration approach, and thus deemphasizes the need to approximate a continuous prior distribution with discretization. Finally, the sensitivity of the posterior distribution to the amount of data is examined, and an indication is given as to why it is so important to be cautious in applying the Bayesian method.