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Sief M, Liu X, Hosny M, Abd El-Raheem AERM. Constant-Stress Modeling of Log-Normal Data under Progressive Type-I Interval Censoring: Maximum Likelihood and Bayesian Estimation Approaches. AXIOMS 2023; 12:710. [DOI: 10.3390/axioms12070710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
This paper discusses inferential approaches for the problem of constant-stress accelerated life testing when the failure data are progressive type-I interval censored. Both frequentist and Bayesian estimations are carried out under the assumption that the log-normal location parameter is nonconstant and follows a log-linear life-stress model. The confidence intervals of unknown parameters are also constructed based on asymptotic theory and Bayesian techniques. An analysis of a real data set is combined with a Monte Carlo simulation to provide a thorough assessment of the proposed methods.
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Affiliation(s)
- Mohamed Sief
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
- Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt
| | - Xinsheng Liu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - Mona Hosny
- Department of Mathematics, Faculty of Science for Girls, King Khalid University, Abha 61413, Saudi Arabia
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Mohie El-Din MM, Abd El-Raheem AM, Abd El-Azeem SO. On Step-Stress Accelerated Life Testing for Power Generalized Weibull Distribution Under Progressive Type-II Censoring. ANNALS OF DATA SCIENCE 2021; 8:629-644. [DOI: 10.1007/s40745-020-00270-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2019] [Revised: 04/13/2020] [Accepted: 04/18/2020] [Indexed: 09/01/2023]
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Abd El-Raheem A. Optimal design of multiple constant-stress accelerated life testing for the extension of the exponential distribution under type-II censoring. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2021; 382:113094. [DOI: 10.1016/j.cam.2020.113094] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Abd El-Raheem AM, Almetwally EM, Mohamed MS, Hafez EH. Accelerated life tests for modified Kies exponential lifetime distribution: binomial removal, transformers turn insulation application and numerical results. AIMS MATHEMATICS 2021; 6:5222-5255. [DOI: 10.3934/math.2021310] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study. MATHEMATICS 2020. [DOI: 10.3390/math8101786] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.
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