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Article

Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study

by
A. M. Abd El-Raheem
1,
M. H. Abu-Moussa
2,
Marwa M. Mohie El-Din
3 and
E. H. Hafez
4,*
1
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt
2
Department of Mathematics, Faculty of Science, Cairo University, Giza 12511, Egypt
3
Department of Mathematics, Faculty of Engineering, Egyptian Russian University, Cairo 11829, Egypt
4
Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1786; https://doi.org/10.3390/math8101786
Submission received: 7 September 2020 / Revised: 3 October 2020 / Accepted: 4 October 2020 / Published: 15 October 2020
(This article belongs to the Special Issue Probability, Statistics and Their Applications)
Review Reports Versions Notes

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.
Keywords: progressive-stress; progressive type-II censoring; maximum likelihood estimation; bayes estimation; Tierney and Kadane approximation; simulation study progressive-stress; progressive type-II censoring; maximum likelihood estimation; bayes estimation; Tierney and Kadane approximation; simulation study

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MDPI and ACS Style

Abd El-Raheem, A.M.; Abu-Moussa, M.H.; Mohie El-Din, M.M.; Hafez, E.H. Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study. Mathematics 2020, 8, 1786. https://doi.org/10.3390/math8101786

AMA Style

Abd El-Raheem AM, Abu-Moussa MH, Mohie El-Din MM, Hafez EH. Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study. Mathematics. 2020; 8(10):1786. https://doi.org/10.3390/math8101786

Chicago/Turabian Style

Abd El-Raheem, A. M., M. H. Abu-Moussa, Marwa M. Mohie El-Din, and E. H. Hafez. 2020. "Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study" Mathematics 8, no. 10: 1786. https://doi.org/10.3390/math8101786

APA Style

Abd El-Raheem, A. M., Abu-Moussa, M. H., Mohie El-Din, M. M., & Hafez, E. H. (2020). Accelerated Life Tests under Pareto-IV Lifetime Distribution: Real Data Application and Simulation Study. Mathematics, 8(10), 1786. https://doi.org/10.3390/math8101786

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