On optimal joint replacement policy for deteriorating series systems

摘要

In this paper, a general repair-replacement model for a k-component series system is proposed. Components of the system may break down randomly and can be repaired immediately. Due to the imperfect repair, the successive operating times decrease stochastically while the consecutive repair times increase stochastically. A joint replacement policy is adopted based on the failure number of each component. The explicit expression of the long-run average cost rate is derived. Furthermore, we investigate the optimal policies of series system and single-component system respectively, the explicit relationship between them is determined in the form of a theorem for the first time. It shows that the optimal replacement policy of a component in a series system is not less than that when it forms a single-component system, and the former is non-decreasing with the number of components. Some other analytical results are also obtained. Based on these useful results, an efficient algorithm is devised to search the optimal joint policy which leads to an elegant, mathematical appealing analysis that is easy to use in practice. Finally, illustrative examples are provided to demonstrate the proposed model and the method.