In this article, a deteriorating simple repairable system with inspections, is studied. We assume that the system failure can only be detected by inspections and the repair of the system is not as good as new. Further assume that the successive working times of the system form a decreasing geometric process whereas the consecutive repair times form an increasing geometric process. Under these assumptions, we present a bivariate mixed policy (T, N), respectively, based on the time interval between two successive inspections and the failure-number of the system. Our aim is to determine an optimal mixed policy (T, N) Ã such that the long-run average cost per unit time (i.e. the average cost rate) is minimised. The explicit expression of the average cost rate is derived, and the corresponding optimal mixed policy can be determined numerically. Finally, we provide a numerical example to illustrate our model, and carry through some discussions and sensitivity analysis.
In this paper, we consider an unreliable production system consisting of two machines (M1 and M2) in which M1 produces a single product type to satisfy a constant and continuous demand of M2 and it is subjected to random failures. In order to palliate perturbations caused by failures, a buffer stock is built up to satisfy the demand during the production unavailability of M1. A traditional assumption made in the previous research is that repairs can restore the failed machines to as good as new state. To develop a more realistic mathematical model of the system, we relax this assumption by assuming that the working times of M1 after repairs are geometrically decreasing, which means M1 cannot be repaired as good as new. Undergoing a specified number of repairs, M1 will be replaced by an identical new one. A bivariate policy ðS, NÞ is considered, where S is the buffer stock level and N is the number of failures at which M1 is replaced. We derive the long-run average cost rate CðS, NÞ used as the basis for optimal determination of the bivariate policy. The optimal policies S Ã and N Ã are derived, respectively. Then, an algorithm is presented to find the optimal joint policy ðS, NÞ Ã. Finally, an illustrative example is given to validate the proposed model. Sensitivity analyses are also carried out to illustrate the effectiveness and robustness of the proposed methodology.
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