Statistical Inference for the Modified Fréchet-Lomax Exponential Distribution Under Constant-Stress PALT with Progressive First-Failure Censoring

Ahmed T. Farhat, Dina A. Ramadan, Hanan Haj Ahmad () and Beih S. El-Desouky
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Ahmed T. Farhat: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Dina A. Ramadan: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Hanan Haj Ahmad: Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia
Beih S. El-Desouky: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2025, vol. 13, issue 16, 1-28

Abstract: Life testing of products often requires extended observation periods. To shorten the duration of these tests, products can be subjected to more extreme conditions than those encountered in normal use; an approach known as accelerated life testing (ALT) is considered. This study investigates the estimation of unknown parameters and the acceleration factor for the modified Fréchet-Lomax exponential distribution (MFLED), utilizing Type II progressively first-failure censored (PFFC) samples obtained under the framework of constant-stress partially accelerated life testing (CSPALT). Maximum likelihood (ML) estimation is employed to obtain point estimates for the model parameters and the acceleration factor, while the Fisher information matrix is used to construct asymptotic confidence intervals (ACIs) for these estimates. To improve the precision of inference, two parametric bootstrap methods are also implemented. In the Bayesian context, a method for eliciting prior hyperparameters is proposed, and Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) method. These estimates are evaluated under both symmetric and asymmetric loss functions, and the corresponding credible intervals (CRIs) are computed. A comprehensive simulation study is conducted to compare the performance of ML, bootstrap, and Bayesian estimators in terms of mean squared error and coverage probabilities of confidence intervals. Finally, real-world failure time data of light-emitting diodes (LEDs) are analyzed to demonstrate the applicability and efficiency of the proposed methods in practical reliability studies, highlighting their value in modeling the lifetime behavior of electronic components.

Keywords: constant-stress; partially accelerated life test; modified Fréchet-Lomax exponential distribution; bootstrap methods; asymptotic confidence intervals; Bayesian estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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