Gompertz Fréchet stress-strength Reliability Estimation

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

Published
2021-12-30
How to Cite
Jabr, S. A., & Karam, N. S. (2021). Gompertz Fréchet stress-strength Reliability Estimation. Iraqi Journal of Science, 62(12), 4892-4902. https://doi.org/10.24996/ijs.2021.62.12.27
Section
Mathematics