Availability analysis of a repairable system with common-cause failure and one standby unit

Abstract

This paper investigates the mathematical model of a system consisting of two non-identical parallel redundant active units, with common-cause failure, and a cold standby unit. The failed units are repaired one at a time or are repaired together, if they fail due to common cause failure. All repair time distributions are arbitrary and different. The analysis is carried out under the assumption of having a single service facility for repair and replacement. Applying the supplementary variable technique, Laplace transforms of the various state probabilities are developed. Explicit expressions for the steady state probabilities and the steady state availability are derived. Some well known results are obtained as special cases. A numerical example is given to illustrate the effect of the repair policy on the steady state probabilities and the availability of the system.