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Equivalency of multi-state survival signatures of multi-state systems of different sizes and its use in the comparison of systems

Published online by Cambridge University Press:  10 June 2022

He Yi
Affiliation:
School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China. E-mail: yihe@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-mail: lixiang@mail.buct.edu.cn

Abstract

In this paper, the multi-state survival signature is first redefined for multi-state coherent or mixed systems with independent and identically distributed (i.i.d.) multi-state components. With the assumption of independence of component lifetimes at different state levels, transformation formulas of multi-state survival signatures of different sizes are established through the use of equivalent systems and a generalized triangle rule for order statistics from several independent and non-identical distributions. The results obtained facilitate stochastic comparisons of multi-state coherent or mixed systems with different numbers of i.i.d. multi-state components. Specific examples are finally presented to illustrate the transformation formulas established here, and also their use in comparing systems of different sizes.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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