Maintenance of Repairable Systems

Abstract

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 1

A failure interaction model for multicomponent repairable systems

“…The widely used NHPP is power law process (PLP) which assumes minimal repair (“as bad as old”) and nonconstant failure intensity function for the components in the system. 22–25 In PLP, the failure intensity function takes the form λ ( t ) = β / θ ( t / θ ) β − 1 , β > 0 , θ > 0 , t > 0 . Let N ( t ) be the number of failures occurred by the time t , then the probability that a system experiences j failures in an interval ( t 1 , t 2 ) is given by the Poisson expression (1)…”

“…The widely used NHPP is power law process (PLP) which assumes minimal repair (''as bad as old'') and nonconstant failure intensity function for the components in the system. [22][23][24][25] In PLP, the failure intensity function takes the form l(t) = b=u(t=u) bÀ1 , b . 0, u .…”

Impact of Different Repair Assumptions on Repairable System Risk Assessment

“…The models mostly used to predict such assumptions are renewal processes including Homogeneous Poisson Process and Non Homogeneous Poisson Process. Such models were enough for simple system, but for complex repairable system there is a need of a more effective model (Lindqvist, 2008). Kijima and Sumita suggested a new approach called General Renewal Process (GRP) which is capable of covering all the three possible repair assumptions of repairable system (Muhammad et al, 2009).…”

Applying Forgotten Lessons in Field Reliability Data Analysis to Performance-Based Support Contracts

“…In the presence of a trend, it is recommended that a Non Homogeneous Poisson Process (NHPP) is employed (Walls and Bendell, 1986). More sophisticated theoretical models exist (Lindqvist, 2008). However, when it comes to fitting a Poisson process to empirical recurrence data the formulation known as power law NHPP (Crow, 1990) is a convenient option.…”