Abstract
In this article, we survey the developments in the generalised models of repairable systems reliability during 1990s, particularly the last five years. In this field, we notice the sharp fundamental problem that voluminous complex models were developed but there is an absence of sufficient data of interest for justifying the success in tackling the real engineering problems. Instead of following the myth of using simple models to face the complex reality, we select and review some practical models, particularly the stochastic processes behind them. The Models in three quick growth areas: age models, condition monitoring technique related models, say, proportional intensity and their extensions, and shock and wearing models, including the delay-time models are reviewed. With the belief that only those stochastic processes reflecting the instinct nature of the actual physical processes of repairable systems, without excessive assumptions, may have a better chance to meet the demands of engineers and managers.
Highlights
General speaking, a reasonable reliability model might be understood as a formalism which is flexible enough to capture up approximately the dynamic changes of a physical system during its functioning life time
The manner in which we reviewed those models is not exhaustive but tries to examine their underlying physical and engineering mechanism, i.e., the stochastic processes behind those general models, because operating / failure / maintenance processes are in nature stochastic processes
It is not as an advertising campaign that we listed our works before 1995, rather it is to emphasise our criticisms and suggestions in repairable system modelling are based on our own background and experience
Summary
A reasonable reliability model might be understood as a formalism which is flexible enough to capture up approximately the dynamic changes of a physical system during its functioning life time. Good-as-new and bad-as-old only apply to repair-improving systems but not to those improved in terms of non-stopping operation Without any doubts, those developments have enhanced the repairable system modelling literature greatly but the endless growth of mathematical models may partly reflect the demands of industry and business. One example to illustrate such state space changes to repairable system modelling is the work by Lawless and Thiagarajah [58], in which they considered a CIF (Conditional Intensity Function) of the form υ (t Αt ) = eθ ’z(t).
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