Int J Performability Eng ›› 2012, Vol. 8 ›› Issue (4): 417-425.doi: 10.23940/ijpe.12.4.p417.mag

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


  1. Parametric Technology Corporation, Greensburg, PA 15601 USA


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.

Received on September 8, 2011, revised on May 21, 2012
References: 14