IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v82y2020i1d10.1007_s13571-018-0169-y.html
   My bibliography  Save this article

Progressively Censored Reliability Sampling Plans Based on Mean Product Lifetime

Author

Listed:
  • Maram Salem

    (Cairo University)

  • Zeinab Amin

    (The American University in Cairo)

  • Moshira Ismail

    (Cairo University)

Abstract

Reliability sampling plans are often used to determine the compliance of the product with relevant quality standards and customers’ expectations and needs. This paper presents a proposed design of reliability sampling plans when the underlying lifetime model is Weibull based on progressively Type-II censored data in the presence of binomial removals. We employ Bayesian decision theory using the Bayes estimator of the mean product lifetime. When both parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. The Bayes estimators of the mean lifetime are evaluated using the Metropolis-within-Gibbs algorithm, under the assumption of mean squared error loss as well as the linear-exponential (LINEX) loss commonly used in the literature on asymmetric loss. The corresponding probability density functions are estimated using kernel density estimation. A cost function which includes the sampling cost, the cost of the testing time, as well as acceptance and rejection costs is proposed to determine the Bayes risk and the corresponding optimal sampling plan. We illustrate, through simulation studies as well as a real life data set, the application of the proposed method. Sensitivity of the proposed plans is performed.

Suggested Citation

  • Maram Salem & Zeinab Amin & Moshira Ismail, 2020. "Progressively Censored Reliability Sampling Plans Based on Mean Product Lifetime," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 1-33, May.
  • Handle: RePEc:spr:sankhb:v:82:y:2020:i:1:d:10.1007_s13571-018-0169-y
    DOI: 10.1007/s13571-018-0169-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-018-0169-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13571-018-0169-y?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. Siu-Keung Tse & Chunyan Yang, 2003. "Reliability sampling plans for the Weibull distribution under Type II progressive censoring with binomial removals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(6), pages 709-718.
    2. Robert Hammond & J. Bickel, 2013. "Approximating Continuous Probability Distributions Using the 10th, 50th, and 90th Percentiles," The Engineering Economist, Taylor & Francis Journals, vol. 58(3), pages 189-208.
    3. Chen, Jianwei & Li, Kim-Hung & Lam, Yeh, 2007. "Bayesian single and double variable sampling plans for the Weibull distribution with censoring," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1062-1073, March.
    4. 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.
    5. Siu-Keung Tse & Hak-Keung Yuen, 1998. "Expected experiment times for the Weibull distribution under progressive censoring with random removals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(1), pages 75-83.
    6. Wu, Shuo-Jye & Huang, Syuan-Rong, 2012. "Progressively first-failure censored reliability sampling plans with cost constraint," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2018-2030.
    7. 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.
    8. Jafar Ahmadi & M. Doostparast, 2006. "Bayesian estimation and prediction for some life distributions based on record values," Statistical Papers, Springer, vol. 47(3), pages 373-392, June.
    9. Yao Zhang & William Q. Meeker, 2005. "Bayesian life test planning for the Weibull distribution with given shape parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 237-249, June.
    10. Fernández, Arturo J. & Pérez-González, Carlos J. & Aslam, Muhammad & Jun, Chi-Hyuck, 2011. "Design of progressively censored group sampling plans for Weibull distributions: An optimization problem," European Journal of Operational Research, Elsevier, vol. 211(3), pages 525-532, June.
    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. Kuo-Ching Chiou, 2023. "Building Up of Fuzzy Evaluation Model of Life Performance Based on Type-II Censored Data," Mathematics, MDPI, vol. 11(17), pages 1-12, August.

    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. Abdullah Fathi & Al-Wageh A. Farghal & Ahmed A. Soliman, 2022. "Bayesian and Non-Bayesian Inference for Weibull Inverted Exponential Model under Progressive First-Failure Censoring Data," Mathematics, MDPI, vol. 10(10), pages 1-19, May.
    2. Mohammed S. Kotb & Huda M. Alomari, 2024. "Estimating the entropy of a Rayleigh model under progressive first-failure censoring," Statistical Papers, Springer, vol. 65(5), pages 3135-3154, July.
    3. Conghua Cheng & Jinyuan Chen & Jianming Bai, 2013. "Exact inferences of the two-parameter exponential distribution and Pareto distribution with censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1464-1479, July.
    4. Sen, Ananda & Kannan, Nandini & Kundu, Debasis, 2013. "Bayesian planning and inference of a progressively censored sample from linear hazard rate distribution," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 108-121.
    5. 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.
    6. Mohamed Sief & Xinsheng Liu & Abd El-Raheem Mohamed Abd El-Raheem, 2024. "Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution," Computational Statistics, Springer, vol. 39(5), pages 2791-2820, July.
    7. Félix Belzunce & Carolina Martínez-Riquelme, 2015. "Some results for the comparison of generalized order statistics in the total time on test and excess wealth orders," Statistical Papers, Springer, vol. 56(4), pages 1175-1190, November.
    8. 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.
    9. 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.
    10. Soliman, Ahmed A. & Abd-Ellah, Ahmed H. & Abou-Elheggag, Naser A. & Abd-Elmougod, Gamal A., 2012. "Estimation of the parameters of life for Gompertz distribution using progressive first-failure censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2471-2485.
    11. 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.
    12. 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.
    13. 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.
    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. Juma Aseed Mohamed Buajela & Sadun Naser Yassin Alheety, 2020. "The Effect of Career Commitment on Productivity in The Construction Sector of Libya: A pilot study," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 4(12), pages 351-358, December.
    16. Xie, Hongmei & Hu, Taizhong, 2010. "Some new results on multivariate dispersive ordering of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 964-970, April.
    17. 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.
    18. Benjamin Laumen & Erhard Cramer, 2019. "Stage life testing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 632-647, December.
    19. 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.
    20. 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.

    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:spr:sankhb:v:82:y:2020:i:1:d:10.1007_s13571-018-0169-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.