Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions

Refah Alotaibi, Faten S. Alamri, Ehab M. Almetwally, Min Wang and Hoda Rezk
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Refah Alotaibi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Faten S. Alamri: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Ehab M. Almetwally: Department of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
Min Wang: Department of Management Science and Statistics, The University of Texas at San Antonio, San Antonio, TX 78249, USA
Hoda Rezk: Department of Statistics, Al-Azhar University, Cairo 11751, Egypt

Mathematics, 2022, vol. 10, issue 9, 1-19

Abstract: Accelerated life testing (ALT) is a time-saving technology used in a variety of fields to obtain failure time data for test units in a fraction of the time required to test them under normal operating conditions. This study investigated progressive-stress ALT with progressive type II filtering with the lifetime of test units following a Nadarajah–Haghighi (NH) distribution. It is assumed that the scale parameter of the distribution obeys the inverse power law. The maximum likelihood estimates and estimated confidence intervals for the model parameters were obtained first. The Metropolis–Hastings (MH) algorithm was then used to build Bayes estimators for various squared error loss functions. We also computed the highest posterior density (HPD) credible ranges for the model parameters. Monte Carlo simulations were used to compare the outcomes of the various estimation methods proposed. Finally, one data set was analyzed for validation purposes.

Keywords: Bayesian approach; non-Bayesian approach; progressive-stress model; inverse power low; Nadarajah–Haghighi distribution; type II progressive censoring; balanced squared loss function; balanced LINEX loss function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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