ON BAYESIAN RELIABILITY-ANALYSIS WITH INFORMATIVE PRIORS AND CENSORING

In the statistical literature many methods have been presented to deal with censored observations, both within the Bayesian and non-Bayesian frameworks, and such methods have been successfully applied to, e.g., reliability problems. Also, in reliability theory it is often emphasi zed that, through shortage of statistical data and possibilities for e xperiments, one often needs to rely heavily on judgements of engineers , or other experts, for which means Bayesian methods are attractive. I t is therefore important that such judgements can be elicited easily t o provide informative prior distributions that reflect the knowledge o f the engineers well. In this paper we focus on this aspect, especiall y on the situation that the judgements of the consulted engineers are based on experiences in environments where censoring has also been pre sent previously. We suggest the use of the attractive interpretation o f hyperparameters of conjugate prior distributions when these are avai lable for assumed parametric models for lifetimes, and we show how one may go beyond the standard conjugate priors, using similar interpreta tions of hyperparameters, to enable easier elicitation when censoring has been present in the past. This may even lead to more flexibility f or modelling prior knowledge than when using standard conjugate priors , whereas the disadvantage of more complicated calculations that may b e needed to determine posterior distributions play a minor role due to the advanced mathematical and statistical software that is widely ava ilable these days. (C) 1996 Elsevier Science Limited.