Reliability of k-out-of-n Cold Standby Systems with Rayleigh Distributions

摘要

Many fielded systems use cold standby redundancy as an effective design strategy for improving system reliability. However, methods for analyzing the reliability of k-out-of-n cold standby systems, particularly with components having age-dependent hazard (failure) rates, are limited. In this paper, using the concepts of counting processes, we propose an efficient approximate method to evaluate the reliability of k-out-of-n cold standby systems. This proposed method considers Rayleigh distributions for component life times 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 further eliminate the need for one-dimensional convolution integrals using approximate closed-form expressions for computing the distribution of sum of Rayleigh distributed random variables. Hence, we show that all steps involved in evaluating the reliability of k-out-of-n cold standby system with components having Rayleigh operational failure time distributions are simple and straightforward. We illustrate the proposed method and its computational efficiency and accuracy using a numerical example.