Open Access

ARTICLE

Product Spacing of Stress–Strength under Progressive Hybrid Censored for Exponentiated-Gumbel Distribution

R. Alshenawy^1,2, Mohamed A. H. Sabry³, Ehab M. Almetwally^4,*, Hisham M. Elomngy²

1 Department of Mathematics and Statistics, King Faisal University, Al-Ahsa, 31982, Saudi Arabia
2 Department of Applied Statistics and Insurance, Mansoura University, Mansoura, 35516, Egypt
3 Department of Mathematical Statistics, Cairo University, Cairo, 12613, Egypt
4 Department of Statistics, Delta University for Science and Technology, Mansoura, 11152, Egypt

* Corresponding Author: Ehab M. Almetwally. Email:

Computers, Materials & Continua 2021, 66(3), 2973-2995. https://doi.org/10.32604/cmc.2021.014289

Received 11 September 2020; Accepted 15 October 2020; Issue published 28 December 2020

Abstract

Maximum product spacing for stress–strength model based on progressive Type-II hybrid censored samples with different cases has been obtained. This paper deals with estimation of the stress strength reliability model R = P(Y < X) when the stress and strength are two independent exponentiated Gumbel distribution random variables with different shape parameters but having the same scale parameter. The stress–strength reliability model is estimated under progressive Type-II hybrid censoring samples. Two progressive Type-II hybrid censoring schemes were used, Case I: A sample size of stress is the equal sample size of strength, and same time of hybrid censoring, the product of spacing function under progressive Type-II hybrid censoring schemes. Case II: The sample size of stress is a different sample size of strength, in which the life-testing experiment with a progressive censoring scheme is terminated at a random time T ∈ (0,∞). The maximum likelihood estimation and maximum product spacing estimation methods under progressive Type-II hybrid censored samples for the stress strength model have been discussed. A comparison study with classical methods as the maximum likelihood estimation method is discussed. Furthermore, to compare the performance of various cases, Markov chain Monte Carlo simulation is conducted by using iterative procedures as Newton Raphson or conjugate-gradient procedures. Finally, two real datasets are analyzed for illustrative purposes, first data for the breaking strengths of jute fiber, and the second data for the waiting times before the service of the customers of two banks.

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