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Reliability Analysis of Binary-Imaged Generalized Multi-State k-out-of-n Systems


Ali Muhammad Rushdi, Shakir Ahmed AlHuthali, Nawaf Ali AlZahrani, AbdulGhani Bakur Alsayegh


Vol. 20  No. 9  pp. 251-264


A celebrated reliability model is the binary k-out of-n system, which is a dichotomous system that is successful if and only if at least k out of its n components are successful. In contrast to general reliability systems whose handling entails exponential complexity, this system possesses an elegant quadratic-time algorithm for evaluating its reliability. The aim of this paper is to extend the utility of this algorithm to the reliability analysis of a homogeneous binary-imaged multi-state coherent generalized k-out-of-n system, which is still described as a non-repairable system with independent non-identical components. The paper characterizes such a system via switching-algebraic expressions of either system success or system failure at each non-zero level, or equivalently, via, minimal upper vectors or maximal lower vectors. We also adapt the afore-mentioned quadratic-time algorithm to compute the reliability and unreliability at each non-zero system level. We point to the inconvenience of using fixed-point reliability values for systems with good components, and recommend using floating-point unreliability values in this case.


System reliability, Multi-state system, k-out-of-n system, Minimal upper vector, Maximal lower vector. Quadratic-time algorithm..