Bayesian Reliability & Availability - A Review

Reliability/availability estimation in the classical sense has been well developed and widely discussed. The parameters in the classical reliability/availability distributions are considered to be unknown constants to be determined. If there is information about these parameters, besides that from some current experiment, it can be used as the basis of Bayesian inference. This paper illustrates procedures for using the Bayesian approach for the study of reliability/availability problems. References on the subject are collected and classified. Specifically, included in this paper are: 1) the statement of the classical estimate and Bayesian estimate, 2) the structure of the prior distribution, 3) the reliability life testing, 4) the empirical Bayes approach in reliability, and 5) Bayesian availability. A Bayesian parameter estimate is generally independent of the sampling stopping rule and has smaller variability than the classical estimate; however, a Bayesian estimate is usually biased and associated with difficulties of choosing a prior. The empirical Bayes approach eliminates some of these difficulties, but frequently at the cost of mathematical tractability. The Bayesian approach to reliability/availability is part of the general trend toward using comprehensive probabilistic methods for dealing with the uncertainties associated with modern engineering problems. This trend should also move toward some system effectiveness measures other than simply reliability or availability. For a large system the Bayesian approach could apply, especially when the test data are scarce and the testing procedure is expensive.