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Discrete competing risk model with application to modeling bus-motor failure data

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  • Jiang, R.

Abstract

Failure data are often modeled using continuous distributions. However, a discrete distribution can be appropriate for modeling interval or grouped data. When failure data come from a complex system, a simple discrete model can be inappropriate for modeling such data. This paper presents two types of discrete distributions. One is formed by exponentiating an underlying distribution, and the other is a two-fold competing risk model. The paper focuses on two special distributions: (a) exponentiated Poisson distribution and (b) competing risk model involving a geometric distribution and an exponentiated Poisson distribution. The competing risk model has a decreasing-followed-by-unimodal mass function and a bathtub-shaped failure rate. Five classical data sets on bus-motor failures can be simultaneously and appropriately fitted by a general 5-parameter competing risk model with the parameters being functions of the number of successive failures. The lifetime and aging characteristics of the fitted distribution are analyzed.

Suggested Citation

  • Jiang, R., 2010. "Discrete competing risk model with application to modeling bus-motor failure data," Reliability Engineering and System Safety, Elsevier, vol. 95(9), pages 981-988.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:9:p:981-988
    DOI: 10.1016/j.ress.2010.04.009
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    References listed on IDEAS

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    1. Best, D.J. & Rayner, J.C.W., 2007. "Chi-squared components for tests of fit and improved models for the grouped exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3946-3954, May.
    2. Kahadawala Cooray & Malwane Ananda, 2010. "Analyzing survival data with highly negatively skewed distribution: The Gompertz-sinh family," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 1-11.
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    Cited by:

    1. Bebbington, Mark & Lai, Chin-Diew & Wellington, Morgan & Zitikis, RiÄ ardas, 2012. "The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 37-44.
    2. Kasai, Naoya & Matsuhashi, Shigemi & Sekine, Kazuyoshi, 2013. "Accident occurrence model for the risk analysis of industrialfacilities," Reliability Engineering and System Safety, Elsevier, vol. 114(C), pages 71-74.
    3. Márcio das Chagas Moura & Enrique López Droguett & Paulo Renato Alves Firmino & Ricardo José Ferreira, 2014. "A competing risk model for dependent and imperfect condition–based preventive and corrective maintenances," Journal of Risk and Reliability, , vol. 228(6), pages 590-605, December.
    4. Coolen-Maturi, Tahani & Coolen, Frank P.A., 2014. "Nonparametric predictive inference for combined competing risks data," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 87-97.
    5. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.

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