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Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring

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  • Abdel-Hamid, Alaa H.

Abstract

Based on progressively type-II censored samples, constant-partially accelerated life tests (PALTs) when the lifetime of items under use condition follow the two-parameter Burr type-XII (Burr(c,k)) distribution are considered. The likelihood equations of the involved parameters are derived and then reduced to a single nonlinear equation to be solved numerically to obtain the maximum likelihood estimates (MLEs) of the parameters. The observed Fisher information matrix, as well as the asymptotic variance-covariance matrix of the MLEs are derived. Approximate confidence intervals (CIs) for the parameters, based on normal approximation to the asymptotic distribution of MLEs, studentized-t and percentile bootstrap CIs are derived. A Monte Carlo simulation study is carried out to investigate the precision of the MLEs and to compare the performance of the CIs considered. Finally, two examples presented to illustrate our results are followed by conclusions.

Suggested Citation

  • Abdel-Hamid, Alaa H., 2009. "Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2511-2523, May.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2511-2523
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    References listed on IDEAS

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    1. M. Mousa & Z. Jaheen, 2002. "Bayesian prediction for progressively censored data from the Burr model," Statistical Papers, Springer, vol. 43(4), pages 587-593, October.
    2. Abdel-Hamid, Alaa H. & AL-Hussaini, Essam K., 2009. "Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1328-1338, February.
    3. Burkschat, M. & Cramer, E. & Kamps, U., 2006. "On optimal schemes in progressive censoring," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1032-1036, May.
    4. Alaa Abdel-Hamid & Essam AL-Hussaini, 2007. "Progressive stress accelerated life tests under finite mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 213-231, September.
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    Cited by:

    1. M. Nassar & S. G. Nassr & S. Dey, 2017. "Analysis of Burr Type-XII Distribution Under Step Stress Partially Accelerated Life Tests with Type-I and Adaptive Type-II Progressively Hybrid Censoring Schemes," Annals of Data Science, Springer, vol. 4(2), pages 227-248, June.
    2. Hua Xin & Zhifang Liu & Yuhlong Lio & Tzong-Ru Tsai, 2020. "Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution," Mathematics, MDPI, vol. 8(2), pages 1-23, January.
    3. R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2014. "Improved confidence intervals for the scale parameter of Burr XII model based on record values," Computational Statistics, Springer, vol. 29(5), pages 1153-1173, October.
    4. R. Arabi Belaghi & M. Noori Asl, 2019. "Estimation based on progressively type-I hybrid censored data from the Burr XII distribution," Statistical Papers, Springer, vol. 60(3), pages 761-803, June.
    5. Amal S. Hassan & Said G. Nassr & Sukanta Pramanik & Sudhansu S. Maiti, 2020. "Estimation in Constant Stress Partially Accelerated Life Tests for Weibull Distribution Based on Censored Competing Risks Data," Annals of Data Science, Springer, vol. 7(1), pages 45-62, March.
    6. M. M. Mohie El-Din & A. M. Abd El-Raheem & S. O. Abd El-Azeem, 2021. "On Step-Stress Accelerated Life Testing for Power Generalized Weibull Distribution Under Progressive Type-II Censoring," Annals of Data Science, Springer, vol. 8(3), pages 629-644, September.
    7. M. M. Mohie El-Din & S. E. Abu-Youssef & Nahed S. A. Ali & A. M. Abd El-Raheem, 2016. "Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 253-273, August.

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