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On the extension of signature-based representations for coherent systems with dependent non-exchangeable components

Part of: Distribution theory - Probability Design of experiments Operations research and management science

Published online by Cambridge University Press:  16 July 2020

Jorge Navarro  and
Juan Fernández-Sánchez
Jorge Navarro*
Affiliation:
Universidad de Murcia
Juan Fernández-Sánchez*
Affiliation:
Universidad de Almería
*
*Postal address: Facultad de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain. Email: jorgenav@um.es
**Postal address: Grupo de Investigación de Análisis Matemático, Universidad de Almería, 04120 Almería, Spain. Emails: juanfernandez@ual.es, jfsjufesa2@gmail.com
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Abstract

The signature representation shows that the reliability of the system is a mixture of the reliability functions of the k-out-of-n systems. The first representation was obtained for systems with independent and identically distributed (IID) components and after it was extended to exchangeable (EXC) components. The purpose of the present paper is to extend it to the class of systems with identically distributed (ID) components which have a diagonal-dependent copula. We prove that this class is much larger than the class with EXC components. This extension is used to compare systems with non-EXC components.

Keywords

Signaturecopulastochastic ordersk-out-of-n systems

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62K10: Block designs
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 57 , Issue 2 , June 2020 , pp. 429 - 440
Copyright
© Applied Probability Trust 2020

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