Reliability-based measure for a system with standbys subjected to switching failures

Purpose - The purpose of this paper is to explore the reliability and sensitivity analysis of a system with M primary units, W standby units, and one repair facility when switching to primary units may fail. Design/methodology/approach - Failure times of primary and standby units are assumed to have exponential distributions, and repair times of the failed units are also assumed to have an exponential distribution. Different failure rates and switching failure probabilities are given depending on the readiness states of standby units, designated hot warm, or cold. The Laplace transform technique is used to transform a set of ordinary differential equations to a set of equations. After finding the solution, we can obtain the desired measures in the time domain by using the inverse Laplace transform. Findings - Expressions for system reliability and mean time to failure (MTTF) are derived. Sensitivity analysis of the system reliability and the MTTF with respect to system parameters are investigated. Originality/value - This paper presents the first time that a contour of the MTTF with respect to standby states has been obtained, which is quite useful for the decision makers.