Analysis of a deteriorating system with delayed repair and unreliable repair equipment

Abstract

Abstract In this article, we mainly consider a repairable degradation system consisting of a single component, a repairman, and repair equipment. Suppose that the system cannot be repaired immediately after failure and cannot be repaired “as good as new.” Herein, the repair equipment may fail during repair and the system will replace a new one after failures. In particular, the repair time follows the general distribution. Under the above assumptions, a partial differential equation model is established through the geometric process and supplementary variable technique. By Laplace transform, we obtain the availability of the system, and from the expression one can see that the availability of the system will tend to zero after running for a long time. Therefore, we further study a replacement policy N N based on the failed times of the system. We give the explicit expression of the system average cost C ( N ) C\left(N) and obtain the optimal replacement policy N ∗ {N}^{\ast } by minimizing the average cost rate C ( N ∗ ) C\left({N}^{\ast }) . That is, the system will be replaced when the failure number of the system reaches N ∗ {N}^{\ast } . Furthermore, the extended degenerate system is proposed by assuming that the system is not always successive degenerative after repair, and then the optimal replacement policy is studied. Finally, the numerical analysis is given to illustrate the theoretical results.