IDEAS home Printed from https://ideas.repec.org/a/wly/navlog/v26y1979i2p223-235.html
   My bibliography  Save this article

Bayesian estimation and optimal designs in partially accelerated life testing

Author

Listed:
  • Morris H. Degroot
  • Prem K. Goel

Abstract

A method of life testing is proposed which combines both ordinary and accelerated life‐testing procedures. It is assumed that an item can be tested either in a standard environment or under stress. The amount of stress is fixed in advance and is the same for all items to be tested However, the time x at which an item on lest is taken out of the standard environment and put under stress can be chosen by the experimenter subject to a given cost structure. When an item is put under stress its lifetime is changed by the factor α. Let the random variable T denote the lifetime of an item in the standard environment, and let γ denote its lifetime under the partially accelerated test procedure just described. Then Y = T if T ≦ x, and Y = x + α (T > x) if T > x. It is assumed that T has an exponential distribution with parameter θ. The estimation of θ and α and the optimal design of a partially accelerated life test are studied in the framework of Bayesian decision theory.

Suggested Citation

  • Morris H. Degroot & Prem K. Goel, 1979. "Bayesian estimation and optimal designs in partially accelerated life testing," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(2), pages 223-235, June.
  • Handle: RePEc:wly:navlog:v:26:y:1979:i:2:p:223-235
    DOI: 10.1002/nav.3800260204
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.3800260204
    Download Restriction: no

    File URL: https://libkey.io/10.1002/nav.3800260204?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Ling, M.H. & Hu, X.W., 2020. "Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. Intekhab Alam & Aquil Ahmed, 2023. "Parametric and Interval Estimation Under Step-Stress Partially Accelerated Life Tests Using Adaptive Type-II Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 10(2), pages 441-453, April.
    3. Refah Alotaibi & Ehab M. Almetwally & Qiuchen Hai & Hoda Rezk, 2022. "Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    4. Xiaojun Zhu & N. Balakrishnan & Yiliang Zhou, 2020. "Exact Likelihood-Ratio Tests for a Simple Step-Stress Cumulative Exposure Model with Censored Exponential Data," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 497-509, June.
    5. 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.
    6. 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.
    7. Insua, David Rios & Ruggeri, Fabrizio & Soyer, Refik & Wilson, Simon, 2020. "Advances in Bayesian decision making in reliability," European Journal of Operational Research, Elsevier, vol. 282(1), pages 1-18.
    8. Do Sun Bai & Myung Soo Kim, 1993. "Optimum simple step‐stress accelerated life tests for weibull distribution and type I censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 193-210, March.
    9. Benjamin Laumen & Erhard Cramer, 2019. "Stage life testing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 632-647, December.
    10. Showkat Ahmad Lone, 2023. "Simulating Fréchet Distribution Under Multiply Censored Partially Accelerated Life Testing," Annals of Data Science, Springer, vol. 10(6), pages 1447-1458, December.
    11. Hanan Haj Ahmad & Dina A. Ramadan & Ehab M. Almetwally, 2024. "Tampered Random Variable Analysis in Step-Stress Testing: Modeling, Inference, and Applications," Mathematics, MDPI, vol. 12(8), pages 1-25, April.
    12. Manoj Kumar & Anurag Pathak & Sukriti Soni, 2019. "Bayesian Inference for Rayleigh Distribution Under Step-Stress Partially Accelerated Test with Progressive Type-II Censoring with Binomial Removal," Annals of Data Science, Springer, vol. 6(1), pages 117-152, March.
    13. Julian Górny & Erhard Cramer, 2020. "On Exact Inferential Results for a Simple Step-Stress Model Under a Time Constraint," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 201-239, November.
    14. Ali A. Ismail, 2014. "Estimation under failure-censored step-stress life test for the generalized exponential distribution parameters," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(6), pages 1003-1015, December.
    15. Anurag Pathak & Manoj Kumar & Sanjay Kumar Singh & Umesh Singh & Manoj Kumar Tiwari & Sandeep Kumar, 2022. "Bayesian inference for Maxwell Boltzmann distribution on step-stress partially accelerated life test under progressive type-II censoring with binomial removals," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(4), pages 1976-2010, August.
    16. Zhang, Chunfang & Wang, Liang & Bai, Xuchao & Huang, Jianan, 2022. "Bayesian reliability analysis for copula based step-stress partially accelerated dependent competing risks model," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    17. 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.
    18. Ali A Ismail, 2013. "On designing step-stress partially accelerated life tests under failure-censoring scheme," Journal of Risk and Reliability, , vol. 227(6), pages 662-670, December.

    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:wly:navlog:v:26:y:1979:i:2:p:223-235. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1931-9193 .

    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.