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A system subject to degradation is considered. The degradation is modelled by a gamma process. A condition-based maintenance policy with perfect corrective and an imperfect preventive actions is proposed. The maintenance cost is derived considering a Markov-renewal process. The statistical inference of the degradation and maintenance parameters by the maximum likelihood method is investigated. A sensibility analysis to different parameters is carried out and the perspectives are detailed.

In this paper, the maintenance optimization problem of multi-component system is considered. It is assumed that the exact cause of system failure might be masked. That is, the exact cause of failure is unknown, and we only know that it belongs to a set called mask set. Both opportunistic perfect preventive maintenance (OPPM) and perfect corrective maintenance are considered. Threshold of OPPM and inter-inspection interval are considered as decision parameters which are optimized using long-run cost rate criteria. The applicability of the proposed maintenance policy is investigated using an illustrative example.

This article develops the warranty cost analysis of a two-component in-series system with stochastic dependence. From the perspectives of both the manufacturer and the consumer, the short-run total profits and costs under the non-renewing free replacement (non-renewing free replacement warranty) policy and the renewing free replacement warranty policy are derived, respectively. Numerical examples are given showing the impact of the failure dependence to both the consumer and the manufacturer.

The aim of this paper is to discuss the modelling and optimisation of condition-based maintenance policies for systems submitted to usage profile changes. The considered system undergoes a monotone deterioration (gamma process) and is impacted by the usage conditions (covariates) via the proportional hazards model. Four different policies are proposed and the optimal maintenance parameters minimising the long-run average maintenance cost are derived. The different maintenance policies are numerically compared using Monte Carlo simulations.

The paper treats the problem of the maintenance of controlled systems. The actuator of the system is subject to deterioration due to wear and to shocks caused by environmental changes. This latter is modeled by random variables called covariates. The deterioration of the actuator impact the control system and requires more effort to balance the deterioration impact and the controlled out put of the system. The main purpose of this paper is to propose a maintenance policy based on the residual lifetime of the system regulated by a Markovien command by taking into account the deterioration of the actuator. The originality of the paper is in one hand due to the consideration of a random deterioration of the actuator in the framework of a controlled system, and on the other hand the consideration of the remaining useful lifetime in the maintenance decision rule.

This paper considers a two component load-sharing system. The load and components failure rate are time dependent. It proposes a maintenance policy considering minimal repairs, imperfect maintenance and replacements. The existence of the optimal cost rate in the long run is proved. The optimal maintenance results are derived from the theoretical propositions and the sensitivity of the system parameters to the maintenance policy optimization criteria is pointed out.

The paper presents a Bayesian approach of the Brown–Proschan imperfect maintenance model. The initial failure rate is assumed to follow a Weibull distribution. A discussion of the choice of informative and non-informative prior distributions is provided. The implementation of the posterior distributions requires the Metropolis-within-Gibbs algorithm. A study on the quality of the estimators of the model obtained from Bayesian and frequentist inference is proposed. An application to real data is finally developed.

The aim of this article is double: propose a methodology for a probabilistic prognosis, and examine how the prognosis result impacts the maintenance process. First, the prognosis problem is mathematically defined: it consists in computing the distribution of the remaining useful life of the system conditionally to on-line available information. Considering on-line information allows to provide a specific prognosis for each system according to its life. Second, a global methodology is proposed when the state of the system and its degradations are modeled using a Markov process. This method is basically a two-step technique. On one hand, it requires the computation of the conditional law of the system regarding the available observations. On the other hand, it involves the computation of the reliability of the system. Some reliability computation techniques are proposed when the Markov process is a piecewise deterministic Markov process. The method is illustrated on an aeronautic example: a pneumatic valve within the bleed air system, used to provide regulated air (pressure, temperature) in the cabin. Eventually, the prognosis result is used to help maintenance optimization on an illustrative example. It highlights that the prognosis mainly improves the maintenance decision if the on-line available information is accurate enough.

A non-observable monotonically deteriorating system is considered. The observed data are the maintenance times and the kinds of maintenance performed. The aim of this paper is to propose a model of the dependency between all kinds of maintenance by considering imperfect maintenance efficiency. Furthermore, we present an additional planned preventive maintenance policy that reduces a finite horizon average total maintenance cost. To deal with such a problem a competing risks model is considered. A general class of models, denoted generalized proportional hazards, is presented and a particular model is derived. An estimation method is detailed for the proposed model. Finally, by numerical implementation, a maintenance policy that leads to the lowest finite horizon average total maintenance cost is proposed.

The goal of this paper is to propose an optimal statistical tool to detect a fault in a linear stochastic (dynamical) system with uncertainties (nuisance parameters). It is supposed that the nuisance parameters are unknown but non random; practically, this means that the nuisance can be intentionally chosen to maximize its negative impact on the monitored system (for instance, to mask a fault). An example of GPS integrity monitoring illustrates the proposed method.