NDLI: A Fast and Robust Reliability Evaluation Algorithm for Generalized Multi-State <formula formulatype=inline><tex Notation=TeX>$k$</tex> </formula>-out-of-<formula formulatype=inline><tex Notation=TeX>$n$</tex> </formula> Systems

Content Provider	IEEE Xplore Digital Library
Author	Amari, S.V. Zuo, M.J. Dill, G.
Copyright Year	1963
Abstract	The generalized multi-state k -out-of-n system model proposed recently provides more flexibility in describing practical systems. In this model, there are n components in the system where each component, as well as the system, can be in one of M+1 possible states: 0, 1,hellip, m. The system is in state j or above if there exists an integer value l(j les l les M) such that at least kl components are in state l or above. Although the model has several practical applications, existing methods for computing either the exact, or approximate reliability of these systems are computationally inefficient, and limited to very small systems. In this paper, we propose an efficient method, and a detailed algorithm to compute the exact reliability of multi-state k -out-of-n systems. The method is based on conditional probabilities, and is applicable to all cases of multi-state k-out-of-n systems: 1) constant, 2) decreasing, 3) increasing, and 4) non-monotone k values. The proposed algorithm is fast, and robust. The computational time complexity of the algorithm is O(knM), and the space complexity is O(n+M) where k=mean{k _i}. Using this algorithm, the reliability of very large multi-state k-out-of-n systems can be computed in a short time. For example, the exact reliability of a system with 500 components with 200 possible states can be computed in less than one second. Several numerical examples, including the published examples, are considered to illustrate the effectiveness, and efficiency of the proposed method. In addition to the detailed algorithm, and theoretical background, we also provide the complete listing of the MATLAB code used in the calculations.
Sponsorship	IEEE Reliability Society
Starting Page	88
Ending Page	97
Page Count	10
File Size	243712
File Format	PDF
ISSN	00189529
Volume Number	58
Issue Number	1
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Robustness Mathematical model MATLAB Mechanical engineering Reliability robust algorithm Generalized multi-state $k$-out-of-$n$ system performance measures reliability evaluation
Content Type	Text
Resource Type	Article
Subject	Safety, Risk, Reliability and Quality Electrical and Electronic Engineering

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