IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v66y2019i8p632-647.html
   My bibliography  Save this article

Stage life testing

Author

Listed:
  • Benjamin Laumen
  • Erhard Cramer

Abstract

In progressive censoring, items are removed at certain times during the life test. Commonly, it is assumed that the removed items are used for further testing. In order to take into account information about these additional testing in inferential procedures, we propose a two‐step model of stage life testing with one fixed stage‐change time which incorporates information about both the removed items (further tested under different conditions) and those remaining in the current life test. We show that some marginal distributions in our model correspond either to progressive censoring with a fixed censoring time or to a simple‐step stress model. Furthermore, assuming a cumulative exposure model, we establish exact inferential results for the distribution parameters when the lifetimes are exponentially distributed. An extension to Weibull distributed lifetimes is also discussed.

Suggested Citation

  • Benjamin Laumen & Erhard Cramer, 2019. "Stage life testing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 632-647, December.
    • Handle: RePEc:wly:navres:v:66:y:2019:i:8:p:632-647
    DOI: 10.1002/nav.21874
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21874
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21874?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    3. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    4. Balakrishnan, N. & Kateri, M., 2008. "On the maximum likelihood estimation of parameters of Weibull distribution based on complete and censored data," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2971-2975, December.
    5. Balakrishnan, N. & Burkschat, Marco & Cramer, Erhard & Hofmann, Glenn, 2008. "Fisher information based progressive censoring plans," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 366-380, December.
    6. 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.
    7. Iliopoulos, G. & Balakrishnan, N., 2009. "Conditional independence of blocked ordered data," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1008-1015, April.
    Full references (including those not matched with items on IDEAS)

    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. Ritwik Bhattacharya, 2020. "Implementation of compound optimal design strategy in censored life-testing experiment," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1029-1050, December.
    2. Park, Sangun & Ng, Hon Keung Tony & Chan, Ping Shing, 2015. "On the Fisher information and design of a flexible progressive censored experiment," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 142-149.
    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. Pareek, Bhuvanesh & Kundu, Debasis & Kumar, Sumit, 2009. "On progressively censored competing risks data for Weibull distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4083-4094, October.
    5. Elham Basiri & Jafar Ahmadi, 2013. "Nonparametric prediction intervals for progressive Type-II censored order statistics based on $$k$$ k -records," Computational Statistics, Springer, vol. 28(6), pages 2825-2848, December.
    6. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    7. 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.
    8. U. H. Salemi & S. Rezaei & Y. Si & S. Nadarajah, 2018. "On Optimal Progressive Censoring Schemes for Normal Distribution," Annals of Data Science, Springer, vol. 5(4), pages 637-658, December.
    9. M. Razmkhah & S. Simriz, 2018. "Statistical inferences based on INID progressively type II censored order statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 583-604, June.
    10. Ritwik Bhattacharya & Biswabrata Pradhan, 2017. "Computation of optimum Type-II progressively hybrid censoring schemes using variable neighborhood search algorithm," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 802-821, December.
    11. 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.
    12. Kai Liu & Xiaojun Zhu & N. Balakrishnan, 2018. "Exact inference for Laplace distribution under progressive Type-II censoring based on BLUEs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 211-227, February.
    13. Parsi, Safar & Bairamov, Ismihan, 2009. "Expected values of the number of failures for two populations under joint Type-II progressive censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3560-3570, August.
    14. Amit Singh Nayal & Bhupendra Singh & Vrijesh Tripathi & Abhishek Tyagi, 2024. "Analyzing stress-strength reliability $$\delta =\text{ P }[U," 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. 15(6), pages 2453-2472, June.
    15. Benjamin Laumen & Erhard Cramer, 2021. "k‐step stage life testing," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 203-233, May.
    16. Rui Hua & Wenhao Gui, 2022. "Revisit to progressively Type-II censored competing risks data from Lomax distributions," Journal of Risk and Reliability, , vol. 236(3), pages 377-394, June.
    17. Olayan Albalawi & Naresh Chandra Kabdwal & Qazi J. Azhad & Rashi Hora & Basim S. O. Alsaedi, 2022. "Estimation of the Generalized Logarithmic Transformation Exponential Distribution under Progressively Type-II Censored Data with Application to the COVID-19 Mortality Rates," Mathematics, MDPI, vol. 10(7), pages 1-19, March.
    18. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.
    19. Bander Al-Zahrani & Areej M. AL-Zaydi, 2022. "Moments of progressively type-II censored order statistics from the complementary exponential geometric distribution and associated inference," 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(3), pages 1052-1065, June.
    20. 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.

    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:navres:v:66:y:2019:i:8:p:632-647. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.