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Inference for the Weibull distribution with progressive hybrid censoring

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  • Lin, Chien-Tai
  • Chou, Cheng-Chieh
  • Huang, Yen-Lung

Abstract

Recently, progressive hybrid censoring schemes have become quite popular in life-testing and reliability studies. In this paper, we investigate the maximum likelihood estimation and Bayesian estimation for a two-parameter Weibull distribution based on adaptive Type-I progressively hybrid censored data. The Bayes estimates of the unknown parameters are obtained by using the approximation forms of Lindley (1980) and Tierney and Kadane (1986) as well as two Markov Chain Monte Carlo methods under the assumption of gamma priors. Computational formulae for the expected number of failures is provided and it can be used to determine the optimal adaptive Type-I progressive hybrid censoring schemes under a pre-determined budget of experiment.

Suggested Citation

  • Lin, Chien-Tai & Chou, Cheng-Chieh & Huang, Yen-Lung, 2012. "Inference for the Weibull distribution with progressive hybrid censoring," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 451-467.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:451-467
    DOI: 10.1016/j.csda.2011.09.002
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    References listed on IDEAS

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    1. Balakrishnan, N. & Childs, A. & Chandrasekar, B., 2002. "An efficient computational method for moments of order statistics under progressive censoring," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 359-365, December.
    2. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    3. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    4. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
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    Cited by:

    1. 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.
    2. M. M. Mohie El-Din & M. Nagy & M. H. Abu-Moussa, 2019. "Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data," Annals of Data Science, Springer, vol. 6(4), pages 673-705, December.
    3. Tzong-Ru Tsai & Yuhlong Lio & Jyun-You Chiang & Yi-Jia Huang, 2022. "A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme," Mathematics, MDPI, vol. 10(21), pages 1-17, November.
    4. Kotb Mohammed S., 2018. "Bayesian Prediction Bounds for the Exponential-type Distribution Based on Generalized Progressive Hybrid Censoring Scheme," Stochastics and Quality Control, De Gruyter, vol. 33(2), pages 93-101, December.
    5. Subhankar Dutta & Suchandan Kayal, 2023. "Inference of a competing risks model with partially observed failure causes under improved adaptive type-II progressive censoring," Journal of Risk and Reliability, , vol. 237(4), pages 765-780, August.
    6. Ritwik Bhattacharya & Biswabrata Pradhan, 2017. "Computation of optimum Type-II progressively hybrid censoring schemes using variable neighborhood search algorithm," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 802-821, December.
    7. Mazen Nassar & Ahmed Elshahhat, 2023. "Statistical Analysis of Inverse Weibull Constant-Stress Partially Accelerated Life Tests with Adaptive Progressively Type I Censored Data," Mathematics, MDPI, vol. 11(2), pages 1-29, January.
    8. Rui Hua & Wenhao Gui, 2022. "Inference for copula-based dependent competing risks model with step-stress accelerated life test under generalized progressive hybrid censoring," Computational Statistics, Springer, vol. 37(5), pages 2399-2436, November.
    9. O. E. Abo-Kasem & Ehab M. Almetwally & Wael S. Abu El Azm, 2023. "Inferential Survival Analysis for Inverted NH Distribution Under Adaptive Progressive Hybrid Censoring with Application of Transformer Insulation," Annals of Data Science, Springer, vol. 10(5), pages 1237-1284, October.
    10. Ismail, Ali A., 2019. "Statistical analysis of Type-I progressively hybrid censored data under constant-stress life testing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 138-150.
    11. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2015. "Estimation for mixed exponential distributions under type-II progressively hybrid censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 85-96.

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