Bayesian Reliability Analysis with Imprecise Prior Probabilities

摘要

The Bayesian framework for statistical inference offers the possibility of takingexpert opinions into account, and is therefore attractive in practical problems concerning reliability of technical systems. Probability is the only language in which uncertainty can be consistently expressed, and this requires the use of prior distributions for reporting expert opinions. In the paper an extension of the standard Bayesian approach based on the theory of imprecise probabilities and intervals of measures is developed. It is shown that this is necessary to take the nature of experts knowledge into account. The application of the approach in reliability theory is outlined. The concept of imprecise probabilities allows one to accept a range of possible probabilities from an expert for events of interest and thus makes the elicitation of prior information simpler and clearer. The method also provides a consistent way for combining the opinions of several experts.