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On Crevecoeur’s bathtub-shaped failure rate model


  • Liu, Junfeng
  • Wang, Yi


Crevecoeur (1993) developed a three-parameter bathtub-shaped failure rate model that enjoys nice mathematical properties and justification from engineering perspectives. In this paper, we derive the explicit formulas for the maximum likelihood estimation (MLE) of parameters for his model applied to both non-censored data and right-censored data. Meanwhile, explicit formulas for the MLE of parameters of Xie–Tang–Goh’s model (Xie et al., 2002) are given for both types of data in the paper. The results from using these two models are compared to some real data sets both in terms of AIC values and in terms of how well the intensity is fitted. We also investigate the MLE-based statistical inference including parameter confidence intervals and parameter significance test for both models. Finally, aiming at reliability-related decision-making and predicting the evolution behavior of a system, we report the relations of the reliability characteristics during the improvement phase to those of the steady service phase. A theory of system improvement limit is presented based on Crevecoeur’s failure rate model.

Suggested Citation

  • Liu, Junfeng & Wang, Yi, 2013. "On Crevecoeur’s bathtub-shaped failure rate model," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 645-660.
  • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:645-660
    DOI: 10.1016/j.csda.2012.08.002

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    References listed on IDEAS

    1. Cancho, Vicente G. & Louzada-Neto, Franscisco & Barriga, Gladys D.C., 2011. "The Poisson-exponential lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 677-686, January.
    2. Yu, Jun-Wu & Tian, Guo-Liang & Tang, Man-Lai, 2008. "Statistical inference and prediction for the Weibull process with incomplete observations," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1587-1603, January.
    3. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    4. 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.
    5. Silva, Rodrigo B. & Barreto-Souza, Wagner & Cordeiro, Gauss M., 2010. "A new distribution with decreasing, increasing and upside-down bathtub failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 935-944, April.
    6. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    7. Nandi, Swagata & Dewan, Isha, 2010. "An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1559-1569, June.
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