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


Co-Author(s) Suprasad V. Amari; Aktar Kalam


Abstract 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 onedimensional convolution integrals using approximate closedform 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.


Keywords Cold standby redundancy, k-out-of-n systems, Rayleigh distribution, reliability analysis
    Article #:  1892
Proceedings of the 18th ISSAT International Conference on Reliability and Quality in Design
July 26-28, 2012 - Boston, Massachusetts, U.S.A.