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

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

Suggested Citation

  • Negreiros, Ana Cláudia Souza Vidal de & Lins, Isis Didier & Moura, Márcio José das Chagas & Droguett, Enrique López, 2020. "Reliability data analysis of systems in the wear-out phase using a (corrected) q-Exponential likelihood," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:reensy:v:197:y:2020:i:c:s0951832018314868
    DOI: 10.1016/j.ress.2019.106787
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    1. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
    2. He, Bo & Cui, Weimin & Du, Xiaofeng, 2016. "An additive modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 28-37.
    3. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    4. Zeng, Hongtao & Lan, Tian & Chen, Qiming, 2016. "Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 307-315.
    5. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
    6. Georg Heinze & Michael Schemper, 2001. "A Solution to the Problem of Monotone Likelihood in Cox Regression," Biometrics, The International Biometric Society, vol. 57(1), pages 114-119, March.
    7. Cribari-Neto, Francisco & Frery, Alejandro C. & Silva, Michel F., 2002. "Improved estimation of clutter properties in speckled imagery," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 801-824, October.
    8. Gupta, Ashutosh & Mukherjee, Bhaswati & Upadhyay, S.K., 2008. "Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1434-1443.
    9. Xu, Meng & Droguett, Enrique López & Lins, Isis Didier & das Chagas Moura, Márcio, 2017. "On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 93-105.
    10. Lins, Isis Didier & Droguett, Enrique López & Moura, Márcio das Chagas & Zio, Enrico & Jacinto, Carlos Magno, 2015. "Computing confidence and prediction intervals of industrial equipment degradation by bootstrapped support vector regression," Reliability Engineering and System Safety, Elsevier, vol. 137(C), pages 120-128.
    11. Pianto, Donald M. & Cribari-Neto, Francisco, 2011. "Dealing with monotone likelihood in a model for speckled data," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1394-1409, March.
    12. Baker, Rose, 2019. "New survival distributions that quantify the gain from eliminating flawed components," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 493-501.
    13. Jiang, R., 2013. "A new bathtub curve model with a finite support," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 44-51.
    14. Haghighi, Firoozeh, 2014. "Optimal design of accelerated life tests for an extension of the exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 251-256.
    15. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    16. Kristan Alexander Schneider, 2018. "Large and finite sample properties of a maximum-likelihood estimator for multiplicity of infection," PLOS ONE, Public Library of Science, vol. 13(4), pages 1-21, April.
    17. Zhang, Fode & Shi, Yimin & Wang, Ruibing, 2017. "Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 552-565.
    18. Fonseca, Rodney V. & Cribari-Neto, Francisco, 2018. "Inference in a bimodal Birnbaum–Saunders model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 134-159.
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    1. Du, Yi-Mu & Sun, C.P., 2022. "A novel interpretable model of bathtub hazard rate based on system hierarchy," Reliability Engineering and System Safety, Elsevier, vol. 228(C).

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