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

Syed Ejaz Ahmed, Reza Arabi Belaghi, Abdulkadir Hussein () and Alireza Safariyan
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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

Mathematics, 2024, vol. 12, issue 10, 1-18

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.

Keywords: bootstrap; lifetime; preliminary test; progressive censoring; reliability; stress–strength; Stein-type shrinkage estimators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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