BAYESIAN RELIABILITY-ANALYSIS WITH IMPRECISE PRIOR PROBABILITIES

The Bayesian framework for statistical inference offers the possibilit y of taking expert opinions into account, and is therefore attractive in practical problems concerning the reliability of technical systems. Probability is the only language in which uncertainty can be consiste ntly expressed, and this requires the use of prior distributions for r eporting expert opinions. In this paper an extension of the standard B ayesian approach based on the theory of imprecise probabilities and in tervals of measures is developed. It is shown that this is necessary t o take the nature of experts' knowledge into account. The application of this approach in reliability theory is outlined. The concept of imp recise probabilities allows us to accept a range of possible probabili ties from an expert for events of interest and thus makes the elicitat ion of prior information simpler and clearer. The method also provides a consistent way for combining the opinions of several experts.