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Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring

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  • Abdel-Hamid, Alaa H.
  • AL-Hussaini, Essam K.

Abstract

The step-stress accelerated life tests allow the experimenter to increase the stress levels at fixed times during the experiment. The lifetime of a product at any level of stress is assumed to have an exponentiated distribution, whose baseline distribution is a general class of distributions which includes, among others, Weibull, compound Weibull, Pareto, Gompertz, normal and logistic distributions. The scale parameter of the baseline distribution is assumed to be a log-linear function of the stress and a cumulative exposure model holds. Special attention is paid to an exponentiated exponential distribution. Based on type-I censoring, the maximum likelihood estimates of the parameters under consideration are obtained. A Monte Carlo simulation study is carried out to investigate the precision of the maximum likelihood estimates and to obtain the coverage probabilities of the bootstrap confidence intervals for the parameters involved. Finally, an example is presented to illustrate the two discussed methods of bootstrap confidence intervals.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1328-1338
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    1. Gupta, Rameshwar D. & Kundu, Debasis, 2003. "Discriminating between Weibull and generalized exponential distributions," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 179-196, June.
    2. 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. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    2. Samanta, Debashis & Kundu, Debasis, 2018. "Order restricted inference of a multiple step-stress model," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 62-75.
    3. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
    4. Alaa H. Abdel-Hamid & Atef F. Hashem, 2021. "Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function," Mathematics, MDPI, vol. 9(13), pages 1-28, June.
    5. Heba S. Mohammed & Saieed F. Ateya & Essam K. AL-Hussaini, 2017. "Estimation based on progressive first-failure censoring from exponentiated exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1479-1494, June.
    6. Atef F. Hashem & Salem A. Alyami & Alaa H. Abdel-Hamid, 2022. "Inference for a Progressive-Stress Model Based on Ordered Ranked Set Sampling under Type-II Censoring," Mathematics, MDPI, vol. 10(15), pages 1-23, August.
    7. Kateri, Maria & Kamps, Udo & Balakrishnan, Narayanaswamy, 2011. "Optimal allocation of change points in simple step-stress experiments under Type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 236-247, January.
    8. 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.
    9. David Han & Debasis Kundu, 2013. "Inference for a step-stress model with competing risks from the GE distribution under Type-I censoring," Working Papers 0181mss, College of Business, University of Texas at San Antonio.
    10. 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.
    11. Debashis Samanta & Debasis Kundu & Ayon Ganguly, 2018. "Order Restricted Bayesian Analysis of a Simple Step Stress Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-221, November.
    12. Korkmaz Mustafa Ç. & Yousof Haitham M., 2017. "The One-Parameter Odd Lindley Exponential Model: Mathematical Properties and Applications," Stochastics and Quality Control, De Gruyter, vol. 32(1), pages 25-35, June.
    13. Essam AL-Hussaini & Alaa Abdel-Hamid & Atef Hashem, 2015. "One-sample Bayesian prediction intervals based on progressively type-II censored data from the half-logistic distribution under progressive stress model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 771-783, October.

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