Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P. O. Box 80204, Jeddah, 21589, Saudi Arabia.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.2-025

  ;

Abstract

Symmetric switching functions (SSFs) play a prominent role in the reliability analysis of a binary k-out-of-n: G system, which is a dichotomous system that is successful if and only if at least k out of its n components are successful. The aim of this paper is to extend the utility of SSFs to the reliability analysis of a multi-state k-out-of-n: G system, which is a multi-state system whose multi-valued success is greater than or equal to a certain value j (lying between 1 (the lowest output level) and M (the highest output level)) whenever at least km components are in state m or above for all m such that 1 ≤ m ≤ j. This paper is devoted to the analysis of non-repairable multi-state k-out-of-n: G systems with independent non-identical components. The paper utilizes algebraic techniques of multiple-valued logic (together with known properties of SSFs) to evaluate each of the multiple levels of the system output as an individual binary or propositional function of the system multi-valued inputs. The formula of each of these levels is then written as a probability–ready expression, thereby allowing its immediate conversion, on a one-to-one basis, into a probability or expected value. The symbolic reliability analysis of a commodity-supply system (which serves as a standard gold example of a multi-state k-out-of-n: G system) is completed successfully herein, yielding results that have been checked symbolically, and also were shown to agree numerically with those obtained earlier.

Keywords- System reliability, Probability-ready expression, k-out-of-n system, Multi-state system, Multiple-valued logic, Boolean quotient, Checking symbolic reliability, Variable-entered Karnaugh map.

Citation

Rushdi, A. M. A. (2019). Utilization of Symmetric Switching Functions in the Symbolic Reliability Analysis of Multi-State k-out-of-n Systems. International Journal of Mathematical, Engineering and Management Sciences, 4(2), 306-326. https://dx.doi.org/10.33889/IJMEMS.2019.4.2-025.