The autopsy data of a coherent system is the pair (T, I), where T is the time to the failure of the system, and I is the set of components failed by that time. A basic question is under which conditions the distribution of the autopsy data determines the joint life distribution of the components. This problem has been studied under various distributional and structural assumptions (always under the assumption of independent component life distributions) by Meilijson (1981), Nowik (1990) and Antoine, Doss and Hollander (1993). In this paper we study the same problem in the situation when the autopsy data is supplemented with data from lifemonitoring and conditional lifemonitoring of some components, as introduced by Meilijson (1994).
