USING EXPERT OPINIONS IN BAYESIAN PREDICTION OF COMPONENT LIFETIMES IN A SHOCK MODEL

This paper is concerned with the combination of k expert opinions abou t the lifetimes of n components of a binary system. This problem has b een treated in the single component case by Huseby (1986, 1988). Since the experts often share data, he argues that their assessments will t ypically be dependent and that this difficulty cannot be handled witho ut making judgements concerning the underlying sources of information and to what extent these are available to each of the experts. The inf ormation available to the experts is modeled as a set of observations Y-i,.... Y-m. These observations are then reconstructed as far as poss ible from the information provided by the experts and used as a basis for the combined judgement. This is called the retrospective approach. Huseby (1988) treats a predictive case where the uncertain quantity i s modeled as a future observation Y, from the same distribution as the Y-i's. For the case n > 1, where each expert is giving opinions about more than one component, additional dependencies between the reliabil ities of the components come into play. This is for instance true if t wo or more components are of similar type, are sharing a common enviro nment or are exposed to common cause failures. For the case n = 2, the retrospective approach and, in particular, the predictive case are tr eated in Natvig (1993). In the present paper, the predictive case is c onsidered for an arbitrary n and for an arbitrary overlapping of the o bservation sets from the different experts. The component lifetimes ar e assumed to have a multivariate exponential distribution of the Marsh all-Olkin type. At the end of the paper, it is shown how the joint dis tribution of the lifetimes of the n components can easily be updated i n the case of getting real data.