IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i4p1328-1338.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00546-X
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Zoran Vidović, 2019. "Bayesian Prediction of Order Statistics Based on k -Record Values from a Generalized Exponential Distribution," Stats, MDPI, vol. 2(4), pages 1-10, November.
    3. Amel Abd-El-Monem & Mohamed S. Eliwa & Mahmoud El-Morshedy & Afrah Al-Bossly & Rashad M. EL-Sagheer, 2023. "Statistical Analysis and Theoretical Framework for a Partially Accelerated Life Test Model with Progressive First Failure Censoring Utilizing a Power Hazard Distribution," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    4. Chansoo Kim & Seongho Song, 2010. "Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples," Statistical Papers, Springer, vol. 51(3), pages 583-597, September.
    5. 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.
    6. 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.
    7. Shovan Chowdhury, 2019. "Selection between Exponential and Lindley distributions," Working papers 316, Indian Institute of Management Kozhikode.
    8. Saieed Ateya, 2014. "Maximum likelihood estimation under a finite mixture of generalized exponential distributions based on censored data," Statistical Papers, Springer, vol. 55(2), pages 311-325, May.
    9. Chen, D.G. & Lio, Y.L., 2010. "Parameter estimations for generalized exponential distribution under progressive type-I interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1581-1591, June.
    10. Kim, Jin Seon & Yum, Bong-Jin, 2008. "Selection between Weibull and lognormal distributions: A comparative simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 477-485, December.
    11. 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.
    12. Debasis Kundu & Anubhav Manglick, 2004. "Discriminating between the Weibull and log‐normal distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(6), pages 893-905, September.
    13. Kundu, Debasis & Gupta, Rameshwar D., 2007. "A convenient way of generating gamma random variables using generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2796-2802, March.
    14. 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.
    15. Nandi, Swagata & Dewan, Isha, 2010. "An EM algorithm for estimating the parameters of bivariate Weibull distribution under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1559-1569, June.
    16. Nadarajah, Saralees & Kotz, Samuel, 2006. "The beta exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 689-697.
    17. Ruizheng Niu & Weizhong Tian & Yunchu Zhang, 2023. "Discriminating among Generalized Exponential, Weighted Exponential and Weibull Distributions," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    18. Yu-Jau Lin & Y. L. Lio, 2012. "Bayesian inference under progressive type-I interval censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1811-1824, April.
    19. 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.
    20. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1328-1338. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.