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Joint reliability based design and periodic preventive maintenance policy for systems sold with warranty

M.N. Darghouth (Department of Mechanical Engineering, Laval University, Quebec, Canada)
Daoud Ait-Kadi (Department of Mechanical Engineering, Laval University, Quebec, Canada)
Anis Chelbi (Department of Mechanical Engineering, University of Tunis, Tunis, Tunisia AND Interuniversity Research Center on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Canada)

Journal of Quality in Maintenance Engineering

ISSN: 1355-2511

Article publication date: 14 March 2016




The authors consider a system which is a part of a complex equipment (e.g. aircraft, automobile, medical equipment, production machine, etc.), and which consists of N independent series subsystems. The purpose of this paper is to determine simultaneously the system design (reliability) and its preventive maintenance (PM) replacements periodicity which minimize the total average cost per time unit over the equipment useful life, taking into account a minimum required reliability level between consecutive replacements.


The problem is tackled in the context of reliability-based design (RBD) considering at the same time the burn-in of components, the warranty commitment and the maintenance strategy to be adopted. A mathematical model is developed to express the total average cost per time unit to be minimized under a reliability constraint. The total average cost includes the cost of acquiring and assembling components, the burn-in of each component, preventive and corrective replacements performed during the warranty and post-warranty periods. A numerical procedure is proposed to solve the problem.


For any given set of input data including components reliability, their cost and the costs of their preventive and corrective replacements, the system design (reliability) and the periodicity of preventive replacement during the post-warranty period is obtained such as the system’s total average cost per time unit is minimized. The obtained results clearly indicate that a decrease in the number of PM actions to be performed during the post-warranty period increases the number of components to be added at each subsystem at the design stage.

Research limitations/implications

Given that the objective function (cost rate function) to be minimized is non-linear and involves several integer variables, it has not been possible to derive the optimal solution. A numerical procedure based on a heuristic approach has been proposed to solve the problem finding a nearly optimal solution for a given set of input data.

Practical implications

This paper offers to manufacturers a comprehensive approach to look for the most economical combination of the reliability level to be given to their products at the design stage, on one hand, and the PM policy to be adopted, on the other hand, given the offered warranty and service for the products and reliability requirements during the life cycle.


While the RBD problem has been largely treated, most of the published works have focussed on the development or the improvement of solving techniques used to find the optimal configuration. In this paper the authors provide a more comprehensive approach that considers simultaneously RBD, the burn-in and warranty periods, along with the maintenance policy to be adopted. The authors also consider the context of products whose component failures cannot be rectified through repair actions. They can only be fixed by replacement.



Darghouth, M.N., Ait-Kadi, D. and Chelbi, A. (2016), "Joint reliability based design and periodic preventive maintenance policy for systems sold with warranty", Journal of Quality in Maintenance Engineering, Vol. 22 No. 1, pp. 2-17.



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Copyright © 2016, Emerald Group Publishing Limited

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