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FURTHER RESULTS ON STOCHASTIC ORDERINGS AND AGING CLASSES IN SYSTEMS WITH AGE REPLACEMENT

Published online by Cambridge University Press:  05 February 2021

Josué Corujo Open the ORCID record for Josué Corujo [Opens in a new window]  and
José E. Valdés
Josué Corujo
Affiliation:
CEREMADE, Université Paris-Dauphine, Université PSL, CNRS, 75016 Paris, France Institut de Mathématiques de Toulouse, Institut National des Sciences Appliquées, 31077 Toulouse, France E-mail: jcorujo@insa-toulouse.fr
José E. Valdés
Affiliation:
Facultad de Matématica y Computación, Universidad de La Habana, 10400 Habana, Cuba E-mail: vcastro@matcom.uh.cu
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Abstract

Reliability properties associated with the classic models of systems with age replacement have been a usual topic of research. Most previous works have checked the aging properties of the lifetime of the working units using stochastic comparisons among the systems with age replacement at different times. However, from a practical point of view, it would also be interesting to deduce to which aging classes the lifetime of the system belongs, making use of the aging properties of the lifetime of its working units. The first part of this article deals with this problem. Further along, stochastic orderings are established between the systems with replacement at the same time using several stochastic comparisons among the lifetimes of their working units. In addition, the lifetimes of two systems with age replacement are compared as well. This is performed assuming stochastic orderings between the number of replacement until failure, and the lifetimes of their working units conditioned to be less or equal than the replacement time. Similar comparisons are accomplished considering two systems with age replacement where the replacements occur at a random time. Illustrative examples are presented throughout the paper.

Keywords

age replacementaging classesparallel systemsrandom time replacementstationary pointwise availabilitystochastic orders
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 660 - 689
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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