Probabilistic analysis of a n-unit cold-standby system with general failure and repair time distributions

Abstract

In this paper, a n-unit cold-standby system with a single repair facility is analysed under the assumption that the failure and repair times are arbitrarily distributed. A mathematical model is developed using semi-regenerative processes. Systems of integral equations satisfied by various states probabilities corresponding to different initial conditions are obtained. Explicit expressions for the availability, reliability and the expected busy period of the service facility are obtained. Two special cases when either the failure or repair rate is constant are discussed. A particular case with three units is analysed numerically by assuming Weibull distribution for failure time and normal distribution for repair time.