Abstract
We apply the algebraic reliability method to the analysis of several variants of multi-state k-out-of-n systems. We describe and use the reliability ideals of multi-state consecutive k-out-of-n systems with and without sparse, and show the results of computer experiments on these kinds of systems. We also give an algebraic analysis of weighted multi-state k-out-of-n systems and show that this provides an efficient algorithms for the computation of their reliability.
Highlights
The usual approach to system reliability assumes that the system and its components can only be in one of two states, failure and working
Multi-state versions of k-out-of-n systems have been proposed in the literature and several methods are used for their reliability analysis
Connected homogeneous multi-state consecutive k-out-of-n:G systems were proposed in [10] as a generalization of the binary sparse k-out-of-n systems proposed by Zhao et al in [32], which were themselves conceived as an extension of the consecutive k-out-of-n model
Summary
The usual approach to system reliability assumes that the system and its components can only be in one of two states, failure and working. In case that the structure function does not have an easy to describe pattern, like in general networks, the algebraic method based on monomial ideals is an approach that produces efficient algorithms [12,13,14,15] This latter method has been used to analyze k-out-of-n systems and variants in the binary case [13,16] and the generalized multi-state version [17]. We take advantage of the versatility of the algebraic method based on monomial ideals and apply it to the analysis of the reliability of recently proposed variants of multi-state k-out-of-n systems.
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