O(kn) Algorithms for Analyzing Repairable and Non-repairable k-out-of-n:G Systems

Abstract

The k-out-of-n:G system has a wide range of applications in reliability engineering. Several efficient algorithms are available for analyzing the reliability of non-repairable systems. However, such efficient algorithms are not readily available for computing other reliability indices such as the failure (hazard) rate, the probability density function, or the mean time to failure (MTTF). Similarly, the methods for computing the steady-state availability measures, such as failure frequency, mean up-time and mean down-time in a failure-repair cycle, and the mean time between failures (MTBF) of repairable k-out-ofn: G systems are limited. In this chapter, utilizing the concepts of failure frequency, we present efficient algorithms to compute various reliability and availability indices of k-out-of-n:G systems. The algorithms are applicable for arbitrary general failure and repair distributions. For repairable systems, we also consider a case where components are kept idle during a system failure (suspended animation). Whenever applicable, we also present simplified results for the exponential case. For the non-identical component case, all of these algorithms have at most O(kn) computational complexity. For the identical component case, the computational complexity reduces to O(n).