Purpose: Estimate the maintenance efficiency in the Brown-Proschan model with the bathtub failure intensity.

Design/methodology/approach: Empirical research through which we propose a framework to establish the characteristics of failure process and its influence on maintenance process.

Findings: The main contribution of the present study is the reformulation of the Brown and Proschan model using the bathtub failure intensity

Practical implications: Our model is defined by BP reformulation one using bathtub failure intensity. This form of intensity is presented like superposition of two NHPP and Homogeneous Poisson one.

Originality/value: This is the follow on research on the study that employed the power-law-process type of failure intensity.

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Repairable systems are submitted to corrective maintenance and condition-based preventive maintenance actions. Condition-based preventive maintenance occurs at times which are determined according to the results of inspections and degradation or operation controls. The generalization of the models suggested makes it possible to integrate the dependence between corrective and preventive maintenances. In order to take into account this dependency and the possibility of imperfect maintenances, generalized competing risks models have been presented in Doyen and Gaudoin (2006). In this study, we revise the general case in which the potential times to next corrective and preventive maintenance are independent conditionally to the past of the maintenance process. We address the identifiability issue and we find a result similar to that of Zhou, Lu, Shi and Cheng (2018) for usual competing risks. We propose realistic models with exponential risks and derive their likelihood functions.

The aim of this paper is to study the asymptotic behavior of the Arithmetic Reduction of Intensity (ARI) and Arithmetic Reduction of Age (ARA) models as two imperfect maintenance models. These models have been proposed by Doyen & Gaudoin (2011), the failure process with bathtub failure intensity. The maintenance effect is characterized by the change induced by the failure intensity before and after a failure during the degradation period. To simplify the study, the asymptotic properties of the failure process are derived. Then, the asymptotic normality of several maintenance efficiency estimators can be proved in the case where the failure process without maintenance is known. Practically, the coverage rate of the asymptotic confidence intervals issued from those estimators is studied.

No abstract