A two-unit system subject to a partial-failure mode and gamma repair-time distribution

Abstract

This paper deals with the profit analysis of a single-server, two-unit cold standby system under the assumption that each unit has three different modes—normal, partial failure and total failure. The distributions of times to failure and the distribution of the time to repair of a partially failed unit are negative exponential, whereas the time to repair a totally failed unit follows gamma distribution. Breakdown of the system occurs when both the units are in a total failure mode. By identifying the system at suitable regenerative epochs, the integral equations are set up for the probabilities of system being in “up” or “failed state”. The Laplace transform technique is adopted to solve these equations.