Partial monitoring of multistate systems

Abstract

For large multicomponent systems it is typically too costly to monitor the entire system constantly. In the presentpaper we consider a case where a component is unobserved in a time interval [0, T]. The time T is a stochasticvariable with a distribution which depends on the structure of the system and the lifetime distribution of theother components. Different systems will result in different distributions of T. The main focus is on how theunobserved period of time a ffects what we learn about the unobserved component during this period. Weanalyse this by considering one single component in three different cases. In the first case we consider both T aswell as the state of the unobserved component at time T as given. In the second case we allow the state of theunobserved component at time T to be stochastic, while in the third case both T and the state are treated asstochastic variables. In all cases we study the problem using preposterior analysis. That is, we investigate howmuch information we can expect to get by the end of the time interval [0, T]. The methodology is also illustratedon a more complex example.

Partial monitoring of multistate systems