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This paper deals with the joint analysis of the optimal production and maintenance planning problems for a manufacturing system subject to random failures and repairs. When a machine fails down, an imperfect repair is undertaken. The objective of this study is to minimize a discounted overall cost consisting of preventive and corrective maintenance costs, inventory holding cost and backlog cost. A two-level hierarchical decision making approach, based on the determination of the mean time between failures (first level) and the statement of a joint optimization of production, preventive and corrective maintenance policies (second level) is proposed. Hence the production, preventive and corrective maintenance rates are determined in level 2 given the failure rates obtained from level 1. In the proposed model, the failure rate of the machine depends on the number of failures; hence, the control policies of the considered planning problem depend on the number of failures. A numerical example and a sensitivity analysis will illustrate the structure of the optimal control policies and the usefulness on the proposed approach. Keywords: Imperfect repairs; Manufacturing Systems; Preventive and Corrective Maintenance. IntroductionThe reliability of a manufacturing system depends on the quality of its conception and the actions of the maintenance which are undertaken during its exploitation (production activities). This paper deals with the control problem of a stochastic manufacturing system consisting of one machine producing one part type. The stochastic nature of the system is due to the fact that the machine is subject to random breakdowns and repairs. Upon a failure of a component of the machine, an imperfect repair is undertaken. The machine dynamics is assumed herein to be described by a finite state semi-Markov chain. The decision variables are the production, the preventive and the corrective maintenance rates, which influence the availability of the system and the stock level. Many authors have contributed to the production planning problem of manufacturing systems (Boukas (1998)), without considering the failure rates depending on the number of failures and the production control in the same model. The aim of this paper is to propose a production control and maintenance (preventive and corrective) planning for a manufacturing system subject to imperfect repairs, when the failure rate increases with the number of failures. The proposed hierarchical approach consists in developing a model where at the first level; the parameters of the machine failure stochastic process are derived for each number of failures. At the second level, we determine the optimal production, preventive and corrective maintenance policies for a system that deteriorates with the number of failures. We obtain a

This paper deals with the production-dependent failure rates for a hybrid manufacturing/remanufacturing system subject to random failures and repairs. The failure rate of the manufacturing machine depends on its production rate, while the failure rate of the remanufacturing machine is constant. In the proposed model, the manufacturing machine is characterized by a higher production rate. The machines produce one type of final product and unmet demand is backlogged. At the expected end of their usage, products are collected from the market and kept in recoverable inventory for future remanufacturing, or disposed of. The objective of the system is to find the production rates of the manufacturing and the remanufacturing machines that would minimize a discounted overall cost consisting of serviceable inventory cost, backlog cost and holding cost for returns. A computational algorithm, based on numerical methods, is used for solving the optimality conditions obtained from the application of the stochastic dynamic pro-gramming approach. Finally, a numerical example and sensitivity analyses are presented to illustrate the usefulness of the proposed approach. Our results clearly show that the optimal control policy of the system is obtained when the failure rates of the machine depend on its production rate.

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