Bayesian Weibull reliability estimation

The Weibull distribution is widely used as a failure model, particularly for mechanical components. This distribution is rich in shape and requires a fairly large sample size to produce accurate statistical estimators, particularly for the lower percentiles, as is usually required for a reliability analysis. In practice, sample sizes are almost always small and subjective judgement is applied, aided by a Weibull plot of the test data to determine the adequacy of the component design to meet reliability goals. The procedure is somewhat ad hoc, but apparently reasonably good results are obtained based on our experience with many past design and development programs and by comparison with actual field performance. We conjecture that the reason this procedure is successful is that test programs and methodology are standardized and quite well documented, from the standpoint of the physical test parameters. Test personnel have a wealth of experience in testing components, from one program to the next, and reliability judgements are made with regard to well-known points in the product's life. All of these factors tend to promote correct outcomes from the decision process even though sample sizes are small. The Bayesian approach provides some structure for the application of subjective judgement to this decision process. To apply this approach, several complex decisions must be made. In this article, we have provided a structure for this decision process. © 1995 IIE.