Gompertz Fréchet stress-strength Reliability Estimation

Sarah A.  Jabr; Nada S.  Karam

doi:10.24996/ijs.2021.62.12.27

Authors

Sarah A. Jabr Mathematical Department / College Of Education / AL-Mustanseriya University
Nada S. Karam Mathematical Department, College Of Education, AL-Mustanseriya University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2021.62.12.27

Keywords:

Reliability, Stress- Strength, Gompertz Fréchet Distribution, Maximum Likelihood Estimator, Least square Estimator, Weighted Least square Estimator, Regression Estimator, Ranked set sampling estimator

Abstract

In this paper, the reliability of the stress-strength model is derived for probability P(Y<X) of a component having its strength X exposed to one independent stress Y, when X and Y are following Gompertz Fréchet distribution with unknown shape parameters and known parameters . Different methods were used to estimate reliability R and Gompertz Fréchet distribution parameters, which are maximum likelihood, least square, weighted least square, regression, and ranked set sampling. Also, a comparison of these estimators was made by a simulation study based on mean square error (MSE) criteria. The comparison confirms that the performance of the maximum likelihood estimator is better than that of the other estimators.