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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.

In this article, we survey the developments with respect to generalized models of repairable systems during the 1990s, particularly for the last five years. In this field, we notice the sharp fundamental problem that voluminous and complicated models are proposed without sufficient evidence (or data) for justifying a success in tackling real engineering problems. Instead of following the myth of using simple models to face complicated reality, and based on our own research experiences, we select and review some practical models, in the quickly growing areas: age models, condition monitoring models, and shock and wear models, including the delay-time models. Further, we also notice that there is an attempt to develop synthetical models from a different point of view. Therefore, we comment the relevant developments with strong emphasis on stochastic processes reflecting the intrinsic nature of the actual physical dynamics of those repairable system models.

PurposeIntends to address a fundamental problem in maintenance engineering: how should the shutdown of a production system be scheduled? In this regard, intends to investigate a way to predict the next system failure time based on the system historical performances.Design/methodology/approachGM(1,1) model from the grey system theory and the fuzzy set statistics methodologies are used.FindingsIt was found out that the system next unexpected failure time can be predicted by grey system theory model as well as fuzzy set statistics methodology. Particularly, the grey modelling is more direct and less complicated in mathematical treatments.Research implicationsMany maintenance models have developed but most of them are seeking optimality from the viewpoint of probabilistic theory. A new filtering theory based on grey system theory is introduced so that any actual system functioning (failure) time can be effectively partitioned into system characteristic functioning times and repair improvement (damage) times.Practical implicationsIn today's highly competitive business world, the effectively address the production system's next failure time can guarantee the quality of the product and safely secure the delivery of product in schedule under contract. The grey filters have effectively addressed the next system failure time which is a function of chronological time of the production system, the system behaviour of near future is clearly shown so that management could utilize this state information for production and maintenance planning.Originality/valueProvides a viewpoint on system failure‐repair predictions.