Optimality of k-out-of-n Structures for Condition Monitoring Maintenance Using Dependent Information

Abstract

A maintenance monitoring system is considered that is subject to two types of contradictory failures, “false alarm” and “failure to alarm”. It is shown that, for a monitoring system with dependent observations, the optimal decision procedure is given by a k-out-of-n structure under a weaker condition than that used in previous research. The condition is that the ratios of the same size elements of the conditional probabilities for the observational matrix of the monitors given the true state of the observed system are the same besides the probability matrix having a weak-MLR (weak-multivariate monotone likelihood ratio) property. If the optimal procedure is given by a k-out-of-n structure, the amount of calculation time needed to identify an optimal decision procedure can be greatly reduced. This enables an optimal action to be found quickly.