Mohammadi, Fatemeh, Pascual-Ortigosa, Patricia, Sáenz-de-Cabezón, Eduardo and Wynn, Henry P. 
ORCID: 0000-0002-6448-1080
(2024)
Overview of the algebraic reliability of binary and multistate k-out-of-n and related systems.
In: Ram, Mangey, (ed.)
Developments in Reliability Engineering.
Advances in Reliability Science.
Elsevier, 687 - 730.
ISBN 9780443132414
Abstract
In this chapter, we present an algebraic method, based on monomial ideals, to compute the reliability of coherent systems. The first part of the chapter introduces the basics of the algebraic method and gives some examples of use. The rest of the chapter is devoted to the application of the algebraic method to binary and multistate k-out-of-n systems. We review the different definitions that binary and multistate k-out-of-n and their variant systems have received in the literature and present them in a unified way using the algebra of monomial ideals. We provide algorithms and formulas to compute the reliability of these systems and bounds for them. We include some computer experiments to evaluate the efficiency of the algebraic method showing its strengths and weaknesses.
| Item Type: | Book Section |
|---|---|
| Additional Information: | © 2024 Elsevier Inc. |
| Divisions: | Statistics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 15 Oct 2024 16:21 |
| Last Modified: | 12 Nov 2024 20:45 |
| URI: | http://eprints.lse.ac.uk/id/eprint/125774 |
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