Comparison Various Estimation Methods for R = P (Y1 < X < Y2) Utilizing Restricted Generalized Weibull Distribution

Open Access

Original research article

Author(s):

Abbas N. Salman^a, Fatima H. Sail^b, Maymona M. Ameen^c, Taha A. Taha^d

^a Department of Mathematics, College of Education for Pure Science Ibn Al-Haitham, University of Baghdad, Baghdad, Iraq.
^b General Directorate of Education, Al-Karkh 2, Ministry of Education, Baghdad, Iraq.
^c Department of Quality Assurance and University Performance, University of Fallujah, Anbar, Iraq.
^d Directorate-General for Education of Anbar, Ministry of Education, Anbar, Iraq.

Advances in the Theory of Nonlinear Analysis and its Applications 7(4), 170–180.

Received: September 20, 2023

Accepted: November 29, 2023

Published: December 24, 2023

Abstract

The stress-strength S-S method employs a variety of estimation techniques, including maximum likelihood, shrinkage and least square, to determine and estimate the reliability of a particular system R = P (Y1 < X < Y2) while the system contains a single component with strength X subject to two stresses, Y1 and Y2. With the consumption of Monte Carlo simulation and the statistical measurement Mean Squared Error (MSE), the various estimation methods have been evaluated according to the Restricted Generalized Weibull Distribution (RGWD), the stresses Y1 and Y2 and the strength X constitute independent, non-identical random variables in our S-S model.

Keywords: Restricted generalized Weibull distribution; Stress–strength reliability; Maximum likelihood method; Shrinkage method; Least squares method; Mean squared error.

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APA Style

Salman, A. N., Sail, F. H., Ameen, M. M., & Taha, T. A. (2023). Comparison of various estimation methods for $R = P(Y_1 < X < Y_2)$ utilizing restricted generalized Weibull distribution. Advances in the Theory of Nonlinear Analysis and Its Application, 7(4), 170–180.