Accelerated life tests for modified Kies exponential lifetime distribution: binomial removal, transformers turn insulation application and numerical results

A. M. Abd El-Raheem; Ehab M. Almetwally; M. S. Mohamed; E. H. Hafez; A. M. Abd El-Raheem; Ehab M. Almetwally; M. S. Mohamed; E. H. Hafez

doi:10.3934/math.2021310

AIMS Mathematics

2021, Volume 6, Issue 5: 5222-5255. doi: 10.3934/math.2021310

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Research article

Accelerated life tests for modified Kies exponential lifetime distribution: binomial removal, transformers turn insulation application and numerical results

1.
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt
2.
Faculty of Business Administration, Delta University of Science and Technology, Egypt
3.
Department of Mathematics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt

Received: 30 December 2020 Accepted: 02 March 2021 Published: 12 March 2021
MSC : 62F09, 62G34

This paper is concerned with statistical inference of multiple constant-stress testing for progressive type-II censored data with binomial removal. The failure times of the test units are assumed to be independent and follow the modified Kies exponential (MKEx) distribution. The maximum likelihood method as well as Bayes method are used to derive both point and interval estimates of the parameters. Furthermore, a real data application for transformers turn insulation is used to illustrate the proposed methods. Moreover, this real data set is used to show that MKEx distribution can be a possible alternative model to the exponential, generalized exponential and Weibull distributions. Finally, simulation studies are carried out to investigate the accuracy of the different estimation methods.
- modified Kies family,
- constant-stress,
- progressive type-II censoring,
- maximum likelihood,
- Bayesian estimation,
- modified Kolmogorov-Smirnov
Citation: A. M. Abd El-Raheem, Ehab M. Almetwally, M. S. Mohamed, E. H. Hafez. Accelerated life tests for modified Kies exponential lifetime distribution: binomial removal, transformers turn insulation application and numerical results[J]. AIMS Mathematics, 2021, 6(5): 5222-5255. doi: 10.3934/math.2021310

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Abstract

This paper is concerned with statistical inference of multiple constant-stress testing for progressive type-II censored data with binomial removal. The failure times of the test units are assumed to be independent and follow the modified Kies exponential (MKEx) distribution. The maximum likelihood method as well as Bayes method are used to derive both point and interval estimates of the parameters. Furthermore, a real data application for transformers turn insulation is used to illustrate the proposed methods. Moreover, this real data set is used to show that MKEx distribution can be a possible alternative model to the exponential, generalized exponential and Weibull distributions. Finally, simulation studies are carried out to investigate the accuracy of the different estimation methods.

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