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This paper considers a preventive maintenance model for an operating system that works for jobs at random times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of two types minimal repair and type II (non-repairable) failure is removed by a corrective replacement. A modified random and age replacement model is considered in which the system is replaced at a planned time T or at a random working time the total expected cost and optimal schedule of preventive replacement time which minimizes it are presented analytically and discussed numerically. It random working time is small enough, the system can be operating for a longer time and avoid unnecessary replacements when replacement last is done. Finally, the proposed model extends some existing results.

Optimal preventive replacement model for a system subject to two types of failure