EconPapers    
Economics at your fingertips  
 

A stochastic process for modeling failures of a system having a non-monotonic hazard rate function

Lucianne Varn, Stefanka Chukova and Richard Arnold

Journal of Risk and Reliability, 2019, vol. 233, issue 5, 731-746

Abstract: Reliability literature on modeling failures of repairable systems mostly deals with systems having monotonically increasing hazard/failure rates. When the hazard rate of a system is non-monotonic, models developed for monotonically increasing failure rates cannot be effectively applied without making assumptions on the types of repair performed following system failures. For instance, for systems having bathtub-shaped hazard rates, it is assumed that during the initial, decreasing hazard rate phase, all repairs are minimal. These assumptions on the type of general repair can be restrictive. In order to relax these assumptions, it has been suggested that general repairs in the initially decreasing phase can be modeled as “aging†the system. This approach however does not preserve the order of effectiveness of the types of general repair as defined in the literature. In this article, we develop a set of models to address these shortcomings. We propose a new stochastic process to model consecutive failures of repairable systems having non-monotonic, specifically bathtub-shaped, hazard rates, where the types of general repair are not restricted and the order of the effectiveness of the types of repair is preserved. The proposed models guarantee that a repaired system is at least as reliable as one that has not failed (or equivalently one that has been minimally repaired). To illustrate the models, we present multiple examples and simulate the failure-repair process and estimate the quantities of interest.

Keywords: General repair; non-monotonic failure rate; bathtub-shaped failure rate; stochastic failure process; point process simulation; failure intensity (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.sagepub.com/doi/10.1177/1748006X18818580 (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:233:y:2019:i:5:p:731-746

DOI: 10.1177/1748006X18818580

Access Statistics for this article

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

 
Page updated 2025-03-19
Handle: RePEc:sae:risrel:v:233:y:2019:i:5:p:731-746