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On the upper truncated Weibull distribution and its reliability implications

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  • Zhang, Tieling
  • Xie, Min

Abstract

The characteristics and application of the truncated Weibull distribution are studied in this paper. This distribution is applicable to the situation where the test data are bounded in an interval because of test conditions, cost and other restrictions. An important property of the truncated Weibull distribution is that it can have bathtub-shaped failure rate function. In this paper, the parametric analysis and parameter estimation methods of the distribution are investigated. Both the graphical approach and the maximum likelihood estimation are considered. The applicability of this distribution to modeling lifetime data is illustrated by an example and the results of comparisons to other competitive models in modeling the given data are also presented. Moreover, the possible application of the distribution to modeling component or system failure is discussed.

Suggested Citation

  • Zhang, Tieling & Xie, Min, 2011. "On the upper truncated Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 194-200.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:1:p:194-200
    DOI: 10.1016/j.ress.2010.09.004
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    References listed on IDEAS

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    1. Martínez, Servet & Quintana, Fernando, 1991. "On a test for generalized upper truncated Weibull distributions," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 273-279, October.
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    Cited by:

    1. 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.
    2. Sidibe, I.B. & Khatab, A. & Diallo, C. & Kassambara, A., 2017. "Preventive maintenance optimization for a stochastically degrading system with a random initial age," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 255-263.
    3. Ranjan, Rakesh & Sen, Rijji & Upadhyay, Satyanshu K., 2021. "Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    4. Marseguerra, M., 2013. "A MC-PSO approach to the failure probability evaluation of risky plant components: The maintenance design," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 1-8.
    5. Almalki, Saad J. & Yuan, Jingsong, 2013. "A new modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 164-170.
    6. C. Satheesh Kumar & Subha R. Nair, 2021. "A generalization to the log-inverse Weibull distribution and its applications in cancer research," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-30, December.
    7. Hassan M. Okasha & Heba S. Mohammed & Yuhlong Lio, 2021. "E-Bayesian Estimation of Reliability Characteristics of a Weibull Distribution with Applications," Mathematics, MDPI, vol. 9(11), pages 1-19, May.
    8. He, Bo & Cui, Weimin & Du, Xiaofeng, 2016. "An additive modified Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 28-37.
    9. Shakhatreh, Mohammed K. & Lemonte, Artur J. & Moreno–Arenas, Germán, 2019. "The log-normal modified Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 6-22.
    10. Abba, Badamasi & Wang, Hong & Bakouch, Hassan S., 2022. "A reliability and survival model for one and two failure modes system with applications to complete and censored datasets," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    11. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    12. Sanku Dey & Vikas Kumar Sharma & Mhamed Mesfioui, 2017. "A New Extension of Weibull Distribution with Application to Lifetime Data," Annals of Data Science, Springer, vol. 4(1), pages 31-61, March.
    13. Abhimanyu Singh Yadav & Shivanshi Shukla & Amrita Kumari, 2022. "Statistical Inference for Truncated Inverse Lomax Distribution and its Application to Survival Data," Annals of Data Science, Springer, vol. 9(4), pages 829-845, August.
    14. Jiang, R., 2013. "A new bathtub curve model with a finite support," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 44-51.
    15. Zhu, Tiefeng, 2020. "Reliability estimation for two-parameter Weibull distribution under block censoring," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    16. Farha Sultana & Yogesh Mani Tripathi & Shuo-Jye Wu & Tanmay Sen, 2022. "Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 9(6), pages 1283-1307, December.
    17. Jiang, R. & Murthy, D.N.P., 2011. "A study of Weibull shape parameter: Properties and significance," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1619-1626.
    18. Ahtasham Gul & Muhammad Mohsin & Muhammad Adil & Mansoor Ali, 2021. "A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-24, April.

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