Asymptotic analysis and optimization of the reliability of two unit systems with quick

Abstract

A redundant system consisting of two dissimilar units and a single repair facility is considered. If the probability that the repair time is larger than the failure time tends to zero, then it is proved that the limiting distribution of the normalised system lifetime is exponential. The maximisation of the mean lifetime of the system with exponential repair times under the restriction that total service rate is fixed is investigated. Under the assumption that mean failure time of units is given it is proved that the mean of the system lifetime is maximised when the failure time of units is constant with probability one. Optimal starting order of units which maximises the mean of the system lifetime is analysed for special cases.