Stochastic modeling of a repairable warm standby system in the presence of repair machines

Abstract

Most of the researches done on repairable systems assumed that when the system failed, it is repaired by repairman or repairmen. Little literature is found in the use of repair machines to repair the failed unit. In this study, stochastic analysis of a repairable 2-out-of-4 system is presented. The system comprises of two subsystems A and B arranged in series. Subsystems A and B are two units warm standby. The system is attended by two repair machines assigned to each subsystem to repair any failed unit. Explicit expressions for mean time to system failure (MTSF), the steady-state availability, busy period of repair machines, and profit function of the system are analyzed stochastically using Kolmogorov’s forward equation method. Analytical and numerical results giving some particular values to the costs and other parameters have been obtained.