Gompertz Fréchet stress-strength Reliability Estimation
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.