OPTIMAL STOPPING BY MEANS OF POINT PROCESS OBSERVATIONS WITH APPLICATIONS IN RELIABILITY

A problem in reliability is considered in which only partial informati on is available. Some technical system is assumed to work in one of N unobservable states. The changes of the states are driven by a Markov process with known characteristics. The system fails from time to time according to a point process with a failure rate (intensity) which de pends on the unobservable state. After failure a minimal repair is car ried out immediately which leaves the state of the system unchanged. I t is investigated under which conditions there exists an optimal time to stop operating the system with respect to some reward functional. T he only available information is given by the failure point process ob servations. An explicit solution to this optimal stopping problem with partial information is derived. The problem is solved in the martinga le framework. Results for monotone stopping problems are used and a ge neralization of the so-called monotone case is considered. The well-kn own disruption or disorder or detection problem is a special case (N = 2) and will be examined in the given context.