Calculating Method for the System State Distributions of Generalized Multi-State k-out-of-n:F Systems

Hisashi YAMAMOTO  Tomoaki AKIBA  Hideki NAGATSUKA 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E92-A  No.7  pp.1593-1599
Publication Date: 2009/07/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Recent Advances in Technologies for Assessing System Reliability)
Category: 
Keyword: 
multi-state k-out-of-n:F system,  system state distribution,  non-i.i.d. component state distributions, 

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Summary: 
In this paper, first, we propose a new recursive algorithm for evaluating generalized multi-state k-out-of-n:F systems. This recursive algorithm can be applied to the systems even though the states of all components in the system are assumed to be non-i.i.d. random variables. Our algorithm is useful for any multi-state k-out-of-n:F system, including the decreasing, increasing and constant multi-state k-out-of-n:F system. Furthermore, our algorithm can evaluate the state distributions of the other non-monotonic multi-state k-out-of-n:F systems. Next, we calculate the order of computing time and memory capacity of the proposed algorithm. We perform numerical experiments in the non-i.i.d. case. The results show that the proposed algorithm is efficient for evaluating the system state distribution of multi-state k-out-of-n:F system when n is large and kl are small.