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Equivalency in joint signatures for binary/multi-state systems of different sizes

Published online by Cambridge University Press:  14 July 2021

He Yi Open the ORCID record for He Yi [Opens in a new window] ,
Narayanaswamy Balakrishnan  and
Xiang Li
He Yi
Affiliation:
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China. E-mails: yihe@mail.buct.edu.cn; lixiang@mail.buct.edu.cn
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton L8S 4K1, Ontario, Canada. E-mail: bala@mcmaster.ca
Xiang Li
Affiliation:
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China. E-mails: yihe@mail.buct.edu.cn; lixiang@mail.buct.edu.cn
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Abstract

The joint signatures of binary-state and multi-state (semi-coherent or mixed) systems with i.i.d. (independent and identically distributed) binary-state components are considered in this work. For the comparison of pairs of binary-state systems of different sizes, transformation formulas of their joint signatures are derived by using the concept of equivalent systems and a generalized triangle rule for order statistics. Similarly, for facilitating the comparison of pairs of multi-state systems of different sizes, transformation formulas of their multi-state joint signatures are also derived. Some examples are finally presented to illustrate and to verify the theoretical results established here.

Keywords

Binary-state systemEquivalent systemGeneralized triangle ruleJoint signatureMulti-state systemOrder statistics
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 4 , October 2022 , pp. 1027 - 1054
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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