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Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

Amer Ibrahim Al-Omari1, *, Ibrahim M. Almanjahie2, Amal S. Hassan3, Heba F. Nagy4
1 Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, 25113, Jordan.
2 Department of Mathematics, College of Science, King Khalid University, Abha, 62529, Saudi Arabia.
3 Statistical Research and Studies Support Unit, King Khalid University, Abha, 62529, Saudi Arabia.
4 Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt.
* Corresponding Author: Amer Ibrahim Al-Omari. Email: .

Computers, Materials & Continua 2020, 64(2), 835-857. https://doi.org/10.32604/cmc.2020.10944

Received 08 April 2020; Accepted 24 April 2020; Issue published 10 June 2020

Abstract

In reliability analysis, the stress-strength model is often used to describe the life of a component which has a random strength (X) and is subjected to a random stress (Y). In this paper, we considered the problem of estimating the reliability R=P [Y<X] when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution. The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample, ranked set sampling and median ranked set sampling methods. Four different reliability estimators under median ranked set sampling are derived. Two estimators are obtained when both strength and stress have an odd or an even set size. The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa. The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study. The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample. In general, the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.

Keywords

Stress-Strength model, ranked set sampling, median ranked set sampling, maximum likelihood estimation, mean square error.

Cite This Article

A. Ibrahim Al-Omari, I. M. Almanjahie, A. S. Hassan and H. F. Nagy, "Estimation of the stress-strength reliability for exponentiated pareto distribution using median and ranked set sampling methods," Computers, Materials & Continua, vol. 64, no.2, pp. 835–857, 2020.

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This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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