THE POSTERIOR DISTRIBUTION OF THE PARAMETERS OF COMPONENT LIFETIMES BASED ON AUTOPSY DATA IN A SHOCK MODEL

In this paper we consider a binary, monotone system whose component st ates are dependent through the possible occurrence of independent comm on shocks, i.e. shocks that destroy several components at once. The in dividual failure of a component is also thought of as a shock. Such sy stems can be used to model common cause failures in reliability analys is. The system may be a technological one, or a human being. It is obs erved until it fails or dies, At this instant, the set of failed compo nents and the failure time of the system are noted. The failure times of the components are not known. These are the so-called autopsy data of the system. For the case of independent components, i.e. no common shocks, Meilijson (1981), Nowik (1990), Antoine et al. (1993) and G (a ) over circle semyr (1998) discuss the corresponding identifiability p roblem, i.e, whether the component life distributions can be determine d from the distribution of the observed data. Assuming a model where a utopsy data is known to be enough for identifiability, Meilijson (1994 ) goes beyond the identifiability question and into maximum likelihood estimation of the parameters of the component lifetime distributions based on empirical autopsy data from a sample of several systems. He a lso considers life-monitoring of some components and conditional life- monitoring of some other. Here a corresponding Bayesian approach is pr esented for the shock model, Due to prior information one advantage of this approach is that the identifiability problem represents no obsta cle. The motivation for introducing the shock model is that the autops y model is of special importance when components can not be tested sep arately because it is difficult to reproduce the conditions prevailing in the functioning system. In G (a) over circle semyr & Natvig (1997) we treat the Bayesian approach to life-monitoring and conditional lif e-monitoring of components.