Reliability evaluation of multi-component cold-standby redundant systems

A new methodology for the reliability evaluation of an l-dissimilar-unit non-repairable cold-standby redundant system is introduced in this paper. Each unit is composed of a number of independent components with generalized Erlang distributions of lifetimes, arranged in any general configuration. We also extend the proposed model to the general types of non-constant hazard functions. To evaluate the system reliability, we construct a directed stochastic network with exponentially distributed arc lengths, in which each path of this network corresponds with a particular minimal cut of the reliability graph of system. Then, we present an analytical method to solve the resulting system of differential equations and to obtain the reliability function of the standby system. The time complexity of the proposed algorithm is O(2n), which is much less than the standard state-space method with the complexity of O(3n2). Finally, we generalize the proposed methodology, in which the failure mechanisms of the components are different.