A STOCHASTIC REGIME SWITCHING MODEL FOR THE FAILURE PROCESS OF A REPAIRABLE SYSTEM

This paper presents a stochastic model and estimation procedure for an alyzing the failure process of a repairable system. We consider repair able systems whose successive interfailure times reveal a significant dependence while showing an insignificant trend, Neither the renewal p rocess nor the non-homogeneous Poisson process are adequate for modeli ng such failure processes. Especially when the interfailure times show a cyclic pattern, we may consider a switching of the regimes Estates) governing the lifetime distribution of the system. We propose a Marko v switching model describing the failure process for such a case. The model postulates that a finite number of states governs the distinct l ifetime distributions, and the state makes transitions according to a discrete-time Markov chain. Each of the distinct lifetime distribution s represents a failure type that may change after successive repairs. Our model generalizes the mixture model by allowing the mixture probab ilities to change during the transient period of the system. The model can capture the transient behavior of the system. The interfailure ti mes constitute a set of incomplete data because the states are not exp licitly identified. For the incomplete data, we propose a procedure fo r finding the maximum likelihood estimates of the model parameters by adopting the expectation and maximization principle. We also suggest a statistical method to determine the number of significant states. A M onte Carlo study is performed with two-parameter Weibull lifetime dist ributions. The results show consistency and good properties of the est imates. Some sets of Proschan's air conditioning unit data [Technometr ics, 1963, 5' 375-383] are also analyzed and the results are discussed with respect to the number of significant states and the performance of the prediction. (C) 1998 Elsevier Science Limited.