Reliability Estimation of a Component exposed to k Stresses for Gompertz-Frechet distribution

Abstract

In this paper, the reliability of the stress-strength model is derived for probability p (max (Y1,Y2,…, >,Yk) < X ) of a component having its strength X exposed to k independent stresses (Y-1,Y2,…,Yk) and also as a special case k=2. when X and Y1,Y2,…,Yk flowing Gompertz-Fréchet distribution with unknown shape parameters θ,λ and known parameters α,β,γ. Different methods used to estimate reliability R and Gompertz-Fréchet distribution parameters which are Maximum Likelihood, Least square, Weighted Least square, Regression and Ranked set sampling methods, and the comparison between these estimators by simulation study based on mean square error criteria (MSE). The comparison confirms that the performance of the maximum likelihood estimator works better than the other estimators.