Reliability Analysis of k-out-of-n Cold Standby Systems with Erlang Distributions

Many fielded systems use cold standby redundancy as an effective system design strategy. However, methods for analyzing the reliability of k-out-of-n cold standby systems, particularly with components having age-dependent hazard rates, are limited. In this paper, using the concepts of counting processes, we propose an efficient method to evaluate the reliability of k-out-of-n cold standby systems. This proposed method considers Erlang distributions for component lives and the effects of switch failures on system reliability. The main advantage of this counting process-based method is that it reduces a complex problem involving multiple integrals into an equivalent simple problem involving one-dimensional convolution integrals. We consider the Erlang distribution for three reasons: (1) it can be used to model either constant or increasing hazard rates, (2) it can be used to approximate several component failure time distributions, and (3) it has well established closed-form expressions for calculating the convolutions that are used in the counting process-based method. We show that all steps involved in finding the reliability of k-out-of-n cold standby system using the proposed method are simple. We demonstrate the proposed method and its computational efficiency using a numerical example.