@article{3e8e23399cce453880b737cb0da83567,
title = "Nonzero repair times dependent on the failure hazard",
abstract = "It is common in the literature on the reliability and maintenance of repairable systems to model the repair times as instantaneous. However, this is an unreasonable assumption for some complex systems, especially those requiring a high level of reliability, and such systems may spend a significant proportion of their lifetimes under maintenance and repair. We model the ageing of such a system with alternating stochastic processes. Operational times are generated at random and may have an increasing failure rate. Repair times are generated from a random process where the repair time is related to the hazard rate at failure. This yields lengthened repair times at late stages in a system subject to an increasing failure hazard rate but also accommodates long repair times at young ages in systems with a bathtub-shaped hazard rate function. We derive analytic results for a set of special cases of the model, show how simulation and inference can be carried out, and apply our method to real data from a large car manufacturer.",
keywords = "bathtub hazard rate, failure distributions, nonzero repair times, stochastic process, warranty analysis",
author = "Richard Arnold and Stefanka Chukova and Yu Hayakawa and Sarah Marshall",
note = "Funding Information: There are many systems for which the nonzero and nonconstant repair times can represent a significant variable cost for manufacturers issuing warranties. The model we present here introduces variable duration of repairs through a simple exponential distribution linked to the failure hazard rate through two extra parameters μ and β . The process can be readily simulated, and inference procedures for model selection and parameter estimation are straightforward and tractable. Nonparametric estimation of Likewise, there are many possible alternative specifications of the the failure and repair time distributions than the simple exponential we have presented here. In our two examples, we have shown how to fit commonly used parametric models to the underlying failure hazard rate λ ( t ) . More complex parametric formulations of λ ( t ) are of course possible, including ageing through shocks. λ ( t ) might be fruitful in situations where little is known about the true form of the hazard rate. found that most of the attention on nonzero repair to date has focussed on geometric and geometric‐like processes. The model we present here represents an alternative means of approaching the problem, and we expect the modelling of nonzero repair times will attract increasing attention in the literature through a broader class of models. An important extension of the work we present here would include the effect of good‐as‐new or partial repair, rather than the minimal repair assumption we have made here. The review by Arnold et al Our proposed model extends the class of available models for nonzero repair duration, motivated by the notion that the hazard rate is a proxy for the degree of deterioration in ageing systems. Thus (in some systems), the hazard rate may be a reasonable metric for the degree of complexity of the repairs that may be required after failure. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Waseda University, Grant for Special Research Projects (2018K‐383); JSPS KAKENHI Grant‐in‐Aid for Scientific Research (C), grant number 18K04621; Waseda Institute for Advanced Study Visiting Scholars 2018; FY2018Grant Program for Promotion of International Joint Research, Waseda University. Fulbright New Zealand: Fulbright Scholar Award 2018. Funding Information: There are many systems for which the nonzero and nonconstant repair times can represent a significant variable cost for manufacturers issuing warranties. The model we present here introduces variable duration of repairs through a simple exponential distribution linked to the failure hazard rate through two extra parameters ? and ?. The process can be readily simulated, and inference procedures for model selection and parameter estimation are straightforward and tractable. In our two examples, we have shown how to fit commonly used parametric models to the underlying failure hazard rate ?(t). More complex parametric formulations of ?(t) are of course possible, including ageing through shocks. Nonparametric estimation of ?(t) might be fruitful in situations where little is known about the true form of the hazard rate. Likewise, there are many possible alternative specifications of the the failure and repair time distributions than the simple exponential we have presented here. The review by Arnold et al found that most of the attention on nonzero repair to date has focussed on geometric and geometric-like processes. The model we present here represents an alternative means of approaching the problem, and we expect the modelling of nonzero repair times will attract increasing attention in the literature through a broader class of models. An important extension of the work we present here would include the effect of good-as-new or partial repair, rather than the minimal repair assumption we have made here. Our proposed model extends the class of available models for nonzero repair duration, motivated by the notion that the hazard rate is a proxy for the degree of deterioration in ageing systems. Thus (in some systems), the hazard rate may be a reasonable metric for the degree of complexity of the repairs that may be required after failure. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Waseda University, Grant for Special Research Projects (2018K-383); JSPS KAKENHI Grant-in-Aid for Scientific Research (C), grant number 18K04621; Waseda Institute for Advanced Study Visiting Scholars 2018; FY2018Grant Program for Promotion of International Joint Research, Waseda University. Fulbright New Zealand: Fulbright Scholar Award 2018. Publisher Copyright: {\textcopyright} 2019 John Wiley & Sons, Ltd.",
year = "2020",
month = apr,
day = "1",
doi = "10.1002/qre.2611",
language = "English",
volume = "36",
pages = "988--1004",
journal = "Quality and Reliability Engineering International",
issn = "0748-8017",
publisher = "John Wiley and Sons Ltd",
number = "3",
}