Markov Models for Periodically Tested Components 1

Simple Markov models for the failure mechanisms of periodically tested standby components were studied in Hokstad & Frrvig (1996). In this paper we reconsider and generalize their models, presenting a systematic and exible modeling approach. In addition we indicate how computer packages for symbolic mathematical computations, like Maple and Mathematica, are well suited for solving the models, yielding, for example, general expressions for interesting reliability measures. 1 INTRODUCTION Component failures can often be classiied into severity classes, for example critical or degraded failures. Simple Markov models for the failure mechanism of a component, suitable for making statistical inferences based on reliability data bases, were suggested and studied in Hokstad and Frrvig (1996). Their study involved dormant (hidden) failures of periodically tested standby components. In this paper we reconsider and generalize their models, presenting a systematic and exible modeling approach which enables easy computation of key gures like mean time between failures and mean fractional deadtime, here called critical safety unavailability. For simplicity we shall in the sequel refer to the paper Hokstad & Frrvig (1996) as HF. Our approach involves a continuous time Markov model for the component state when time runs between testing epochs, and in addition two discrete time Markov chains for the states of the component reported immediately before and after each test, respectively. As will be seen, the given framework also allows in an easy manner the potentially useful extension to modeling of incomplete repairs or maintenance actions. It will be brieey indicated how computer packages for symbolic mathematical computations, like Maple V (Waterloo Maple, Inc., Ontario) and