The new reliability notion describing the remaining lifetime is introduced for items with monotonically increasing degradation. We consider the remaining lifetime of an item (to be called, the predicted remaining lifetime) after its degradation reaches the predetermined level. The prediction is executed at inception of an item into operation. For the nonhomogeneous stochastic processes of degradation, this characteristic depends on the random first passage time of a degradation process. Some properties of the predicted remaining lifetime and the corresponding stochastic comparisons are discussed for items from homogeneous and heterogeneous populations, and a generalization to the case of the n-component coherent system is outlined. The problem of regime switching is described, and the new notion of the corresponding virtual age after the switching is proposed.

We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously.

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning; however, the corresponding additional assumptions are not obvious, which can be seen from the proofs of our theorems.

In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. A shock model which combines these two types is called a ‘combined shock model’. In this paper we study new classes of extreme shock models and, based on the obtained results and model interpretations, we extend these results to several specific combined shock models. For systems subject to nonhomogeneous Poisson processes of shocks, we derive the corresponding survival probabilities and discuss some meaningful interpretations and examples.

In extreme shock models, only the impact of the current, possibly fatal shock is usually taken into account, whereas in cumulative shock models, the impact of the preceding shocks is accumulated as well. In this paper we combine an extreme shock model with a specific cumulative shock model. It is shown that the proposed setting can also be interpreted as a generalization of the well-known Brown–Proschan model that describes repair actions for repairable systems. For a system subject to a specific process of shocks, we derive the survival probability and the corresponding failure rate function. Some meaningful interpretations and examples are discussed.

We consider ageing properties of a general repair process. Under certain assumptions we prove that the expectation of an age at the beginning of the next cycle in this process is smaller than the initial age of the previous cycle. Using this reasoning, we show that the sequence of random ages at the start (end) of consecutive cycles is stochastically increasing and is converging to a limiting distribution. We discuss possible applications and interpretations of our results.

In this paper we present a general framework for the modelling of the process of corrective and condition-based preventive maintenance actions for complex repairable systems. A new class of models is proposed, the generalized virtual age models. On the one hand, these models generalize Kijima's virtual age models to the case where both preventive and corrective maintenances are present. On the other hand, they generalize the usual competing risks models to imperfect maintenance actions which do not renew the system. A generalized virtual age model is defined by both a sequence of effective ages which characterizes the effects of both types of maintenance according to a classical virtual age model, and a usual competing risks model which characterizes the dependency between the two types of maintenance. Several particular cases of the general model are derived.