Geometric process repair model for an unreliable production system with an intermediate buffer

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 (S,N) 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 C(S,N) used as the basis for optimal determination of the bivariate policy. The optimal policies S* and N* are derived, respectively. Then, an algorithm is presented to find the optimal joint policy (S,N)*. 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.