Performance prediction of machine repair problem with spares and two modes of failure

Abstract

This investigation is concerned with the transient analysis of machine repair problem with M operating units and multi types of warm spares. In case when all spares are being used, the failure of units occurs in degraded fashion. Each unit is assumed to fail in two modes. When all permanent repairmen are busy, the caretaker who brings the failed units for repair departs from the system after waiting for sometime in the queue due to impatience. For transient state, Chapman–Kolmogorov equations governing the model are constructed. Various performance measures such as expected number of failed units in each mode, average number of operating units in the system, average number of idle and busy repairmen in the system, operative utilisation factor, etc., are obtained. The cost minimisation problem to determine the optimum number of spares in terms of various cost elements has been formulated. We used Runge–Kutta technique to find the numerical solution for the transient model. The sensitivity analysis is performed to observe the effect of different parameters on various performance indices.