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New and Efficient Estimators of Reliability Characteristics for a Family of Lifetime Distributions under Progressive Censoring

Author

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  • Syed Ejaz Ahmed

    (Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada)

  • Reza Arabi Belaghi

    (Unit of Applied Statistics and Mathematics, Department of Energy and Technology, Swedish University of Agricultural Sciences, 75007 Uppsala, Sweden)

  • Abdulkadir Hussein

    (Department of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4, Canada)

  • Alireza Safariyan

    (Department of Statistics, Jahrom University, Jahrom 74137-66171, Iran)

Abstract

Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of the commonly used Maximum Likelihood Estimators (MLEs) by reducing their mean squared errors. We provide analytical asymptotic and bootstrap confidence intervals for the targeted parameters. Through a detailed simulation study, we demonstrate that the new estimators have better performance than the MLEs. Finally, we illustrate the application of the new methods to two industrial data sets, showcasing their practical relevance and effectiveness.

Suggested Citation

  • Syed Ejaz Ahmed & Reza Arabi Belaghi & Abdulkadir Hussein & Alireza Safariyan, 2024. "New and Efficient Estimators of Reliability Characteristics for a Family of Lifetime Distributions under Progressive Censoring," Mathematics, MDPI, vol. 12(10), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1599-:d:1398094
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    References listed on IDEAS

    as
    1. Ajit Chaturvedi & Shantanu Vyas, 2017. "Estimation and Testing Procedures for the Reliability Functions of Three Parameter Burr Distribution under Censorings," Statistica, Department of Statistics, University of Bologna, vol. 77(3), pages 207-235.
    2. Ajit Chaturvedi & Shantanu Vyas, 2017. "Estimation and Testing procedures for the Reliability functions of Exponentiated distributions under censorings," Statistica, Department of Statistics, University of Bologna, vol. 77(1), pages 13-31.
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    5. Akram Kohansal & Shirin Shoaee, 2021. "Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data," Statistical Papers, Springer, vol. 62(1), pages 309-359, February.
    6. Yuge Du & Wenhao Gui, 2022. "Statistical inference of adaptive type II progressive hybrid censored data with dependent competing risks under bivariate exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(12), pages 3120-3140, September.
    7. Ajit Chaturvedi & Shruti Nandchahal, 2016. "Shrinkage Estimators of the Reliability Characteristics of a Family of Lifetime Distributions," Statistica, Department of Statistics, University of Bologna, vol. 76(1), pages 57-82.
    8. 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.
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