Mathematical Modeling Approach to Analyzing Mean Time to System Failure of Two Unit Cold Standby System with A Supporting Device and Repairable Service Station

Abstract

This paper studies the mean time to system failure (MTSF) of two unit cold standby system operating with the help of a standby external supporting device. A repairable service station is set aside to repair any failed unit. The system is analyzed using first order linear differential equation to develop the explicit expression for mean time to system failure. Special cases such as the cold standby system with a supporting device and repairable standby repairable service stations, and the cold standby system with a supporting device and a repairable service station are treated. Some numerical experiments are conducted in order to illustrate the effects of failure and repair rates on mean time to system failure. Furthermore, we compare the mean time to system failure of the systems under study and found that the MTSF of two cold standby systems with standby supporting device and a repairable service station is better.