Reliability data analysis of systems in the wear-out phase using a (corrected) q-Exponential likelihood

Negreiros, Ana Cláudia Souza Vidal de, Isis Didier Lins, Moura, Márcio José das Chagas and Droguett, Enrique López

Reliability Engineering and System Safety, 2020, vol. 197, issue C

Abstract: Maintenance-related decisions are often based on the expected number of interventions during a specified period of time. The proper estimation of this quantity relies on the choice of the probabilistic model that best fits reliability-related data. In this context, the q-Exponential probability distribution has emerged as a promising alternative. It can model each of the three phases of the bathtub curve; however, for the wear-out phase, its usage may become difficult due to the “monotone likelihood problem†. Two correction methods (Firth's and resample-based) are considered and have their performances evaluated through numerical experiments. To aid the reliability analyst in applying the q-Exponential model, we devise a methodology involving original and corrected functions for point and interval estimates for the q-Exponential parameters and validation of the estimated models using the expected number of failures via Monte Carlo simulation and the bootstrapped Kolmogorov-Smirnov test. Two examples with failure data presenting increasing hazard rates are provided. The performances of the estimated q-Exponential, Weibull, q-Weibull and modified extended Weibull (MEW) models are compared. In both examples, the q-Exponential presented superior results, despite the increased flexibility of the q-Weibull and MEW distributions in modeling non-monotone hazard rates (e.g., bathtub-shaped).

Keywords: q-Exponential distribution; Wear-out phase; Monotone likelihood; Firth's correction; Resample correction (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:197:y:2020:i:c:s0951832018314868

DOI: 10.1016/j.ress.2019.106787

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