IDEAS home Printed from https://ideas.repec.org/a/bpj/ecqcon/v22y2007i2p175-186n2.html
   My bibliography  Save this article

Point and Interval Estimation for the Lifetime Distribution of a k-Unit Parallel System Based on Progressively Type-II Censored Data

Author

Listed:
  • Pradhan Biswabrata

    (SQC & OR Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata -700 108, India)

Abstract

This work considers point and interval estimation for the lifetime distribution of a k-unit parallel system assuming exponential distribution for the components lifetime. The parameter of the distribution is estimated by the maximum likelihood method based on samples which are progressively Type-II censored. The expression for Fisher's information is derived. Approximate confidence intervals are constructed based on the asymptotic distribution of the maximum likelihood estimator and log-transformed maximum likelihood estimator. The confidence levels of the approximate confidence intervals are examined via simulation. They turn out to be quite satisfactory. An approximate β-expectation tolerance interval for the life distribution is also discussed.

Suggested Citation

  • Pradhan Biswabrata, 2007. "Point and Interval Estimation for the Lifetime Distribution of a k-Unit Parallel System Based on Progressively Type-II Censored Data," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 175-186, January.
    • Handle: RePEc:bpj:ecqcon:v:22:y:2007:i:2:p:175-186:n:2
    DOI: 10.1515/EQC.2007.175
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/EQC.2007.175
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/EQC.2007.175?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
    ---><---

    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. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    2. 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.
    3. 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.
    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. 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.
    2. 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.
    3. Hanan Haj Ahmad & Mohamed Aboshady & Mahmoud Mansour, 2024. "The Role of Risk Factors in System Performance: A Comprehensive Study with Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 12(11), pages 1-21, June.
    4. 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.
    5. Ahmed Elshahhat & Refah Alotaibi & Mazen Nassar, 2022. "Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    6. Ping Chan & Hon Ng & Feng Su, 2015. "Exact likelihood inference for the two-parameter exponential distribution under Type-II progressively hybrid censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 747-770, August.
    7. Prakash Chandra & Yogesh Mani Tripathi & Liang Wang & Chandrakant Lodhi, 2023. "Estimation for Kies distribution with generalized progressive hybrid censoring under partially observed competing risks model," Journal of Risk and Reliability, , vol. 237(6), pages 1048-1072, December.
    8. R. Alshenawy & Ali Al-Alwan & Ehab M. Almetwally & Ahmed Z. Afify & Hisham M. Almongy, 2020. "Progressive Type-II Censoring Schemes of Extended Odd Weibull Exponential Distribution with Applications in Medicine and Engineering," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    9. 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.
    10. El-Sherpieny, El-Sayed A. & Almetwally, Ehab M. & Muhammed, Hiba Z., 2020. "Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    11. 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.
    12. Mazen Nassar & Refah Alotaibi & Ahmed Elshahhat, 2023. "Reliability Estimation of XLindley Constant-Stress Partially Accelerated Life Tests using Progressively Censored Samples," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    13. Shu-Fei Wu & Yu-Lun Huang, 2024. "The Assessment of the Overall Lifetime Performance Index of Chen Products with Multiple Components," Mathematics, MDPI, vol. 12(13), pages 1-21, July.
    14. 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.
    15. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    16. 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.
    17. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.
    18. Wu, Shuo-Jye & Huang, Syuan-Rong, 2017. "Planning two or more level constant-stress accelerated life tests with competing risks," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 1-8.
    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.

    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:bpj:ecqcon:v:22:y:2007:i:2:p:175-186:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.