A New Estimation Study of the Stress-Strength Reliability for the Topp–Leone Distribution Using Advanced Sampling Methods

Author:

Almarashi Abdullah M.1,Algarni Ali1,Hassan Amal S.2,Elgarhy M.3ORCID,Jamal Farrukh4ORCID,Chesneau Christophe5,Alrashidi Khudir1,Mashwani Wali Khan6ORCID,Nagy Heba F.2

Affiliation:

1. Faculty of Science, Department of Statistis, King Abdulaziz University, Jeddah, Saudi Arabia

2. Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt

3. The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra 31951, Algarbia, Egypt

4. Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan

5. Universit´e de Caen, LMNO, Campus II, Science 3, 14032, Caen, France

6. Institute of Numerical Sciences, Kohat University of Science & Technology, Kohat 26000, Pakistan

Abstract

In this manuscript, we investigate the estimation of the unknown reliability measure R = P [Y < X], in the case where Y and X are two independent random variables with Topp–Leone distributions. As the main contribution, various advanced sampling strategies are studied. The suggested strategies are simple random, ranked set, and median ranked set samplings. Firstly, based on the maximum likelihood, we give an efficient estimator of R when the observations of the two random variables are selected from the same simple random sample. Secondly, such an estimator is addressed when the observations of the two random variables are selected from the ranked set sampling method. Then, based on median ranked set sampling, the maximum likelihood estimator of R is addressed in all the four cases. When the observations from the two random variables are selected from the same set size, two cases are considered, while the other two cases are considered at different set sizes. A simulation research is developed to evaluate the behavior of the obtained estimates based on standard and median ranked set samplings with their simple random sampling equivalents. The ratio of mean square error is used to assess the effectiveness of these estimates.

Funder

King Abdulaziz University

Publisher

Hindawi Limited

Subject

Computer Science Applications,Software

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