ON IDENTIFIABILITY IN THE AUTOPSY MODEL OF RELIABILITY THEORY

A coherent system is observed until it fails. At the instant of system failure, the set of failed components and the failure time of the sys tem are noted. The failure times of the components are not known. We c onsider whether the component life distributions can be determined fro m the distributions of the observed data. Meilijson (1981) gave a cond ition on the structure of the system that was sufficient for the ident ifiability of the component distributions, under the assumption that t he component life distributions are continuous and have common essenti al extrema. Nowik (1990) gave necessary and sufficient conditions for identifiability under the more restrictive condition that the componen t distributions have atoms at their common essential infimum and are m utually absolutely continuous. We give a necessary condition for ident ifiability, which we show to be equivalent to Nowik's condition, under the assumption that the distributions are continuous and strictly inc reasing. We derive a sufficient condition for identifiability, more ge neral than Meilijson's, for the case in which the component distributi ons are assumed to be analytic, We also show that our necessary condit ion for identifiability is both necessary and sufficient when the comp onent life distributions are assumed to belong to certain parametric f amilies.