Maintenance of Repairable Systems

A commonly used definition of a repairable system (Ascher and Feingold [3]) states that this is a system which, after failing to perform one or more of its functions satisfactorily, can be restored to fully satisfactory performance by any method other than replacement of the entire system. In order to cover more realistic applications, and to cover much recent literature on the subject, we need to extend this definition to include the possibility of additional maintenance actions which aim at servicing the system for better performance. This is referred to as preventive maintenance (PM), where one may further distinguish between condition based PM and planned PM. The former type of maintenance is due when the system exhibits inferior performance while the latter is performed at predetermined points in time. Traditionally, the literature on repairable systems is concerned with modelling of the failure times only, using point process theory. A classical reference here is Ascher and Feingold [3]. The most commonly used models for the failure process of a repairable system are renewal processes (RP), including the homogeneous Poisson processes (HPP), and nonhomogeneous Poisson processes (NHPP). While such models often are sufficient for simple reliability studies, the need for more complex models is clear. In this chapter we consider some generalizations and extensions of the basic models, with the aim to arrive at more realistic models which give better fit to data. First we consider the Trend Renewal Process (TRP) introduced and studied in Lindqvist, Elvebakk and Heggland [22]. The TRP includes NHPP and RP as special cases, and the main new feature is to allow a trend in processes of non-Poisson (renewal) type. As exemplified by some real data, in the case where several systems of the same kind are considered, there may be unobserved heterogeneity between the systems which, if overlooked, may lead to non-optimal or possibly completely wrong decisions. We will consider this in the framework of the TRP process, which in Lindqvist et al. [22] is extended to the so called HTRP model which includes the possibility of heterogeneity. Heterogeneity can be thought of as an effect of an unobserved covariate. Another extension of the basic models is to allow the systems to be preventively maintained. We review some recent research in this direction, where this