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Preservation properties of some reliability classes by lifetimes of coherent and mixed systems and their signatures

Published online by Cambridge University Press:  23 September 2022

Salman Izadkhah ,
Ebrahim Amini-Seresht Open the ORCID record for Ebrahim Amini-Seresht [Opens in a new window]  and
Narayanaswamy Balakrishnan
Salman Izadkhah
Affiliation:
Department of Statistics, Campus of Bijar, University of Kurdistan, Bijar, Iran
Ebrahim Amini-Seresht
Affiliation:
Department of Statistics, Bu-Ali Sina University, Hamedan, Iran. E-mail: e.amini64@yahoo.com
Narayanaswamy Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada
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Abstract

This paper examines the preservation of several aging classes of lifetime distributions in the formation of coherent and mixed systems with independent and identically distributed (i.i.d.) or identically distributed (i.d.) component lifetimes. The increasing mean inactivity time class and the decreasing mean time to failure class are developed for the lifetime of systems with possibly dependent and i.d. component lifetimes. The increasing likelihood ratio property is also discussed for the lifetime of a coherent system with i.i.d. component lifetimes. We present sufficient conditions satisfied by the signature of a coherent system with i.i.d. components with exponential distribution, under which the decreasing mean remaining lifetime, the increasing mean inactivity time, and the decreasing mean time to failure are all satisfied by the lifetime of the system. Illustrative examples are presented to support the established results.

Keywords

Aging classCoherent systemCopula functionExponential distributionResidual lifetimeSignaturesStochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 4 , October 2023 , pp. 943 - 960
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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