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BIRNBAUM CRITICALITY AND IMPORTANCE MEASURES FOR MULTISTATE SYSTEMS WITH REPAIRABLE COMPONENTS

Published online by Cambridge University Press:  01 June 2020

Arne Bang Huseby Open the ORCID record for Arne Bang Huseby [Opens in a new window] ,
Martyna Kalinowska  and
Tobias Abrahamsen
Arne Bang Huseby
Affiliation:
University of Oslo, Oslo, Norway E-mail: arne@math.uio.no
Martyna Kalinowska
Affiliation:
University of Oslo, Oslo, Norway E-mail: arne@math.uio.no
Tobias Abrahamsen
Affiliation:
University of Oslo, Oslo, Norway E-mail: arne@math.uio.no
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Abstract

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We suggest four new measures of importance for repairable multistate systems based on the classical Birnbaum measure. Periodic component life cycles and general semi-Markov processes are considered. Similar to the Birnbaum measure, the proposed measures are generic in the sense that they only depend on the probabilistic properties of the components and the system structure. The multistate system model encodes physical properties of the components and the system directly into the structure function. As a result, calculating importance is easy, especially in the asymptotic case. Moreover, the proposed measures are composite measures, combining importance for all component states into a unified quantity. This simplifies ranking of the components with respect to importance. The proposed measures can be characterized with respect to two features: forward-looking versus backward-looking and with respect to how criticality is measured. Forward-looking importance measures focus on the next component states, while backward-looking importance measures focus on the previous component states. Two approaches to measuring criticality are considered: probability of criticality versus expected impact. Examples show that the different importance measures may result in unequal rankings.

Keywords

Birnbaum importancecomponent criticalitymultistate systemsrepairable componentssemi-Markov processes
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 66 - 86
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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