IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p670-d351363.html
   My bibliography  Save this article

Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring

Author

Listed:
  • Siyi Chen

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Wenhao Gui

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

In this paper, the estimation problem of two parameters of a lifetime distribution with a bathtub-shaped failure rate function based on adaptive progressive type-II censored data is discussed. This censoring scheme allows the experiment to be more efficient in the use of time and cost while ensuring the statistical inference efficiency based on the experimental results. Maximum likelihood estimators are proposed and the approximate confidence intervals for two parameters are computed using the asymptotic normality. Lindley approximation and Gibbs sampling are used to obtain Bayes point estimates and the latter is also used to generate Bayes two-sided credible intervals. Finally, the performance of various estimation methods is evaluated through simulation experiments, and the proposed estimation method is illustrated through the analysis of a real data set.

Suggested Citation

  • Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:670-:d:351363
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/670/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/670/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Vikas Kumar Sharma & Sanjay Kumar Singh & Umesh Singh & Faton Merovci, 2016. "The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5709-5729, October.
    2. Manoj Kumar Rastogi & Yogesh Mani Tripathi & Shuo-Jye Wu, 2012. "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2389-2411, July.
    3. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
    4. Hon Keung Tony Ng & Debasis Kundu & Ping Shing Chan, 2009. "Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 687-698, December.
    5. Shuo-Jye Wu, 2008. "Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1139-1150.
    6. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    7. Mohammad Z. Raqab & Omar M. Bdair & Fahad M. Al-Aboud, 2018. "Inference for the two-parameter bathtub-shaped distribution based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 229-253, April.
    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. Muqrin A. Almuqrin & Mukhtar M. Salah & Essam A. Ahmed, 2022. "Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications," Mathematics, MDPI, vol. 10(22), pages 1-38, November.
    2. Refah Alotaibi & Mazen Nassar & Ahmed Elshahhat, 2022. "Computational Analysis of XLindley Parameters Using Adaptive Type-II Progressive Hybrid Censoring with Applications in Chemical Engineering," Mathematics, MDPI, vol. 10(18), pages 1-24, September.

    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. Mohammad Z. Raqab & Omar M. Bdair & Fahad M. Al-Aboud, 2018. "Inference for the two-parameter bathtub-shaped distribution based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 229-253, April.
    2. Pramendra Singh Pundir & Puneet Kumar Gupta, 2018. "Reliability Estimation in Load-Sharing System Model with Application to Real Data," Annals of Data Science, Springer, vol. 5(1), pages 69-91, March.
    3. Ahmed Elshahhat & Mazen Nassar, 2021. "Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data," Computational Statistics, Springer, vol. 36(3), pages 1965-1990, September.
    4. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
    5. Wenjie Zhang & Wenhao Gui, 2022. "Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    6. Abdalla Abdel-Ghaly & Hanan Aly & Elham Abdel-Rahman, 2023. "Bayesian Inference Under Ramp Stress Accelerated Life Testing Using Stan," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 132-174, May.
    7. Manoj Kumar Rastogi & Yogesh Mani Tripathi & Shuo-Jye Wu, 2012. "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2389-2411, July.
    8. Kyeongjun Lee & Youngseuk Cho, 2017. "Bayesian and maximum likelihood estimations of the inverted exponentiated half logistic distribution under progressive Type II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 811-832, April.
    9. Zihui Zhang & Wenhao Gui, 2022. "Statistical Analysis of the Lifetime Distribution with Bathtub-Shaped Hazard Function under Lagged-Effect Step-Stress Model," Mathematics, MDPI, vol. 10(5), pages 1-23, February.
    10. Refah Alotaibi & Mazen Nassar & Ahmed Elshahhat, 2022. "Computational Analysis of XLindley Parameters Using Adaptive Type-II Progressive Hybrid Censoring with Applications in Chemical Engineering," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    11. Friday Ikechukwu Agu & Joseph Thomas Eghwerido, 2021. "Agu-Eghwerido distribution, regression model and applications," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 59-76, December.
    12. Nesreen M. Al-Olaimat & Husam A. Bayoud & Mohammad Z. Raqab, 2021. "Record data from Kies distribution and related statistical inferences," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 153-170, December.
    13. Manoj Chacko & Rakhi Mohan, 2019. "Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals," Computational Statistics, Springer, vol. 34(1), pages 233-252, March.
    14. Al-Olaimat Nesreen M. & Bayoud Husam A. & Raqab Mohammad Z., 2021. "Record data from Kies distribution and related statistical inferences," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 153-170, December.
    15. Gauss M. Cordeiro & Giovana O. Silva & Edwin M. M. Ortega, 2016. "An extended-G geometric family," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-16, December.
    16. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    17. Varun Agiwal, 2023. "Bayesian Estimation of Stress Strength Reliability from Inverse Chen Distribution with Application on Failure Time Data," Annals of Data Science, Springer, vol. 10(2), pages 317-347, April.
    18. Fiaz Ahmad Bhatti & G. G. Hamedani & Seyed Morteza Najibi & Munir Ahmad, 2021. "On the Extended Chen Distribution: Development, Properties, Characterizations and Applications," Annals of Data Science, Springer, vol. 8(1), pages 159-180, March.
    19. Barriga, Gladys D.C. & Louzada-Neto, Franscisco & Cancho, Vicente G., 2011. "The complementary exponential power lifetime model," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1250-1259, March.
    20. Gupta, Ashutosh & Mukherjee, Bhaswati & Upadhyay, S.K., 2008. "Weibull extension model: A Bayes study using Markov chain Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1434-1443.

    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:gam:jmathe:v:8:y:2020:i:5:p:670-:d:351363. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.