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


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.

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