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Inference on the reliability of Weibull distribution with multiply Type-I censored data

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  • Jia, Xiang
  • Wang, Dong
  • Jiang, Ping
  • Guo, Bo

Abstract

In this paper, we focus on the reliability of Weibull distribution under multiply Type-I censoring, which is a general form of Type-I censoring. In multiply Type-I censoring in this study, all units in the life testing experiment are terminated at different times. Reliability estimation with the maximum likelihood estimate of Weibull parameters is conducted. With the delta method and Fisher information, we propose a confidence interval for reliability and compare it with the bias-corrected and accelerated bootstrap confidence interval. Furthermore, a scenario involving a few expert judgments of reliability is considered. A method is developed to generate extended estimations of reliability according to the original judgments and transform them to estimations of Weibull parameters. With Bayes theory and the Monte Carlo Markov Chain method, a posterior sample is obtained to compute the Bayes estimate and credible interval for reliability. Monte Carlo simulation demonstrates that the proposed confidence interval outperforms the bootstrap one. The Bayes estimate and credible interval for reliability are both satisfactory. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Suggested Citation

  • Jia, Xiang & Wang, Dong & Jiang, Ping & Guo, Bo, 2016. "Inference on the reliability of Weibull distribution with multiply Type-I censored data," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 171-181.
    • Handle: RePEc:eee:reensy:v:150:y:2016:i:c:p:171-181
    DOI: 10.1016/j.ress.2016.01.025
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    Cited by:

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    2. Saralees Nadarajah & Xiang Jia, 2017. "Estimation of $$P(Y > X)$$ P ( Y > X ) for the Weibull distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1762-1774, November.
    3. Starling, James K. & Mastrangelo, Christina & Choe, Youngjun, 2021. "Improving Weibull distribution estimation for generalized Type I censored data using modified SMOTE," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    4. Jia, Xiang & Guo, Bo, 2022. "Reliability analysis for complex system with multi-source data integration and multi-level data transmission," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    5. Zhu, Tiefeng, 2020. "Reliability estimation for two-parameter Weibull distribution under block censoring," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    6. E. M. Almetwally & H. M. Almongy & M. K. Rastogi & M. Ibrahim, 2020. "Maximum Product Spacing Estimation of Weibull Distribution Under Adaptive Type-II Progressive Censoring Schemes," Annals of Data Science, Springer, vol. 7(2), pages 257-279, June.
    7. Yolanda M. Gómez & Diego I. Gallardo & Carolina Marchant & Luis Sánchez & Marcelo Bourguignon, 2023. "An In-Depth Review of the Weibull Model with a Focus on Various Parameterizations," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    8. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.
    9. Mason, Paolo, 2017. "A Bayesian analysis of component life expectancy and its implications on the inspection schedule," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 87-94.
    10. Renyan Jiang, 2022. "A novel parameter estimation method for the Weibull distribution on heavily censored data," Journal of Risk and Reliability, , vol. 236(2), pages 307-316, April.
    11. Acitas, Sukru & Aladag, Cagdas Hakan & Senoglu, Birdal, 2019. "A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 116-127.
    12. Jia, Xiang & Cheng, Zhijun & Guo, Bo, 2022. "Reliability analysis for system by transmitting, pooling and integrating multi-source data," Reliability Engineering and System Safety, Elsevier, vol. 224(C).

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