First hitting time distribution and cost assessment in a two-unit system with dependent degradation processes subject to imperfect maintenance

Lucía Bautista, Inma T. Castro, Christophe Bérenguer, Olivier Gaudoin and Laurent Doyen

Journal of Risk and Reliability, 2025, vol. 239, issue 1, 182-206

Abstract: This paper proposes a degradation model for a two-unit series system, where the components exhibit dependence and are subject to imperfect maintenance. The interdependence between both components is captured using the trivariate reduction method. The system failure occurs when the degradation level of either component exceeds a predetermined threshold. The main motivation of this work is to develop a preventive maintenance strategy for this system, incorporating periodic imperfect maintenance actions in order to extend its useful lifetime. These actions aim to reduce the accumulated degradation level of each component from its installation in a fixed percentage, following the Arithmetic Reduction of Degradation model of infinite order. Another goal is to derive the distribution of time to the system failure, which provides crucial insights into the system’s reliability and performance, especially in the case of bivariate degradation. Additionally, a cost model for this maintenance strategy is developed and several numerical examples are presented to illustrate the practical implications. The maintenance decision variables are optimized in order to obtain the minimal expected cost rate within a finite time horizon.

Keywords: Bivariate degradation; imperfect repairs; first hitting time; Wiener process; gamma process (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://journals.sagepub.com/doi/10.1177/1748006X231211378 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:risrel:v:239:y:2025:i:1:p:182-206

DOI: 10.1177/1748006X231211378

Access Statistics for this article

More articles in Journal of Risk and Reliability
Bibliographic data for series maintained by SAGE Publications ().