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A new bathtub curve model with a finite support

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  • Jiang, R.

Abstract

The failure rate with a bathtub shape usually increases very fast in the wear-out phase. In this case, the bathtub curve model with a finite support can better adapt the sharp change in failure rate. There are few models with the finite support. This paper presents such a model. However, the maximum likelihood estimator of the location parameter of such models sometimes converges to the largest observation of a dataset. An extended maximum spacing method is developed to estimate the parameters for the case where the maximum likelihood method fails. Three examples are included to illustrate the appropriateness of the proposed model and estimation method.

Suggested Citation

  • Jiang, R., 2013. "A new bathtub curve model with a finite support," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 44-51.
    • Handle: RePEc:eee:reensy:v:119:y:2013:i:c:p:44-51
    DOI: 10.1016/j.ress.2013.05.019
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    References listed on IDEAS

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    1. 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.
    2. Sarhan, Ammar M. & Apaloo, Joseph, 2013. "Exponentiated modified Weibull extension distribution," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 137-144.
    3. 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.
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    1. 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).
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    5. 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.
    6. 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).
    7. Jiang, R., 2014. "A drawback and an improvement of the classical Weibull probability plot," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 135-142.
    8. Zihui Zhang & Wenhao Gui, 2022. "Statistical Analysis of the Lifetime Distribution with Bathtub-Shaped Hazard Function under Lagged-Effect Step-Stress Model," Mathematics, MDPI, vol. 10(5), pages 1-23, February.
    9. Ahmad, Abd EL-Baset A. & Ghazal, M.G.M., 2020. "Exponentiated additive Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
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    13. Dey Sanku & Waymyers Sophia & Kumar Devendra, 2020. "The Reflected-Shifted-Truncated Lindley Distribution with Applications," Stochastics and Quality Control, De Gruyter, vol. 35(2), pages 67-77, December.
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