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Hashem AF, Alotaibi N, Alyami SA, Abdelkawy MA, Elgawad MAA, Yousof HM, Abdel-Hamid AH. Utilizing Bayesian inference in accelerated testing models under constant stress via ordered ranked set sampling and hybrid censoring with practical validation. Sci Rep 2024; 14:14406. [PMID: 38909118 PMCID: PMC11193780 DOI: 10.1038/s41598-024-64718-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2024] [Accepted: 06/12/2024] [Indexed: 06/24/2024] Open
Abstract
This research investigates the application of the ordered ranked set sampling (ORSSA) procedure in constant-stress partially accelerated life-testing (CSPALTE). The study adopts the assumption that the lifespan of a specific item under operational stress follows a half-logistic probability distribution. Through Bayesian estimation methods, it concentrates on estimating the parameters, utilizing both asymmetric loss function and symmetric loss function. Estimations are conducted using ORSSAs and simple random samples, incorporating hybrid censoring of type-I. Real-world data sets are utilized to offer practical context and validate the theoretical discoveries, providing concrete insights into the research findings. Furthermore, a rigorous simulation study, supported by precise numerical calculations, is meticulously conducted to gauge the Bayesian estimation performance across the two distinct sampling methodologies. This research ultimately sheds light on the efficacy of Bayesian estimation techniques under varying sampling strategies, contributing to the broader understanding of reliability analysis in CSPALTE scenarios.
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Affiliation(s)
- Atef F Hashem
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia.
- Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt.
| | - Naif Alotaibi
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
| | - Salem A Alyami
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
| | - Mohamed A Abdelkawy
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
- Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt
| | - Mohamed A Abd Elgawad
- Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
- Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt
| | - Haitham M Yousof
- Department of Statistics, Mathematics and Insurance, Benha University, Benha, 13518, Egypt
| | - Alaa H Abdel-Hamid
- Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef, 62511, Egypt
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Inference for a Progressive-Stress Model Based on Ordered Ranked Set Sampling under Type-II Censoring. MATHEMATICS 2022. [DOI: 10.3390/math10152771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
The progressive-stress accelerated life test is discussed under the ordered ranked set sampling procedure. It is assumed that the lifetime of an item under use stress is exponentially distributed and the law of inverse power is considered as the relationship between the scale parameter and the applied stress. The involved parameters are estimated using the Bayesian technique, under symmetric and asymmetric loss functions, based on ordered ranked set samples and simple random samples subject to type-II censoring. Real and simulated data sets are used to illustrate the theoretical results presented in this paper. Finally, a simulation study followed by numerical calculations is performed to evaluate the Bayesian estimation performance based on the two sampling types.
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Alotaibi N, Hashem AF, Elbatal I, Alyami SA, Al-Moisheer AS, Elgarhy M. Inference for a Kavya–Manoharan Inverse Length Biased Exponential Distribution under Progressive-Stress Model Based on Progressive Type-II Censoring. ENTROPY 2022; 24:e24081033. [PMID: 36010697 PMCID: PMC9407453 DOI: 10.3390/e24081033] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Revised: 07/11/2022] [Accepted: 07/22/2022] [Indexed: 02/01/2023]
Abstract
In this article, a new one parameter survival model is proposed using the Kavya–Manoharan (KM) transformation family and the inverse length biased exponential (ILBE) distribution. Statistical properties are obtained: quantiles, moments, incomplete moments and moment generating function. Different types of entropies such as Rényi entropy, Tsallis entropy, Havrda and Charvat entropy and Arimoto entropy are computed. Different measures of extropy such as extropy, cumulative residual extropy and the negative cumulative residual extropy are computed. When the lifetime of the item under use is assumed to follow the Kavya–Manoharan inverse length biased exponential (KMILBE) distribution, the progressive-stress accelerated life tests are considered. Some estimating approaches, such as the maximum likelihood, maximum product of spacing, least squares, and weighted least square estimations, are taken into account while using progressive type-II censoring. Furthermore, interval estimation is accomplished by determining the parameters’ approximate confidence intervals. The performance of the estimation approaches is investigated using Monte Carlo simulation. The relevance and flexibility of the model are demonstrated using two real datasets. The distribution is very flexible, and it outperforms many known distributions such as the inverse length biased, the inverse Lindley model, the Lindley, the inverse exponential, the sine inverse exponential and the sine inverse Rayleigh model.
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Affiliation(s)
- Naif Alotaibi
- Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.F.H.); (I.E.); (S.A.A.)
- Correspondence:
| | - Atef F. Hashem
- Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.F.H.); (I.E.); (S.A.A.)
- Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt
| | - Ibrahim Elbatal
- Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.F.H.); (I.E.); (S.A.A.)
| | - Salem A. Alyami
- Department of Mathematics and Statistics, College of Science Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia; (A.F.H.); (I.E.); (S.A.A.)
| | - A. S. Al-Moisheer
- Department of Mathematics, College of Science, Jouf University, P.O. Box 848, Sakaka 72351, Saudi Arabia;
| | - Mohammed Elgarhy
- The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Egypt;
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Abdel-Ghaly A, Aly H, Abdel-Rahman E. Inference of extended Weibull distribution using ramp stress accelerated life testing under censoring. JOURNAL OF STATISTICS & MANAGEMENT SYSTEMS 2021. [DOI: 10.1080/09720510.2020.1818453] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Abdalla Abdel-Ghaly
- Department of Statistics, Faculty of Economics and Political Science, Cairo University, Giza, Egypt
| | - Hanan Aly
- Department of Statistics, Faculty of Economics and Political Science, Cairo University, Giza, Egypt
| | - Elham Abdel-Rahman
- Department of Statistics, Faculty of Economics and Political Science, Cairo University, Giza, Egypt
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Mahto AK, Tripathi YM, Wu SJ. Statistical inference based on progressively type-II censored data from the Burr X distribution under progressive-stress accelerated life test. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2020.1815021] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Amulya Kumar Mahto
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, India
| | | | - Shuo-Jye Wu
- Department of Statistics, Tamkang University New Taipei City, Taiwan
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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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Abd El-Raheem A. Optimal design of multiple accelerated life testing for generalized half-normal distribution under type-I censoring. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2020; 368:112539. [DOI: 10.1016/j.cam.2019.112539] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Abd El-Raheem AM. Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring. J STAT COMPUT SIM 2019. [DOI: 10.1080/00949655.2019.1656722] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- A. M. Abd El-Raheem
- Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt
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Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals. MATHEMATICS 2019. [DOI: 10.3390/math7070646] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The competing risk model based on Lindley distribution is discussed under the progressive type-II censored sample data with binomial removals. The maximum likelihood estimation of the unknown parameters of the distribution is established. Using the Lindley approximation method, we also obtain the Bayesian estimation of the unknown parameters of the distribution under different loss functions. The performance of different estimates is studied in this article. A real practical dataset is analyzed for illustration.
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Wang C, Liu H. Estimation for the scaled half-logistic distribution under Type-I progressively hybrid censoring scheme. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2017.1291968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Chao Wang
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P. R. China
| | - Hong Liu
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, P. R. China
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