### Comparing reliability of Frechet Distribution under ranked set sampling by using with application

#### Abstract

In order to achieve the objectives sought by the researcher, he must collect data and information on that research, and because some data is difficult to obtain or cannot be obtained for reasons of cost, effort and time, he must choose the method of inspection, which ensures the achievement of research objectives at the minimum time Less effort and less cost. In order to solve these problems, it is necessary to use the sampling method, which ensures that the time, effort and cost of data are reduced. Under these circumstances, the concept of ranked group sampling (RSS) seems useful for obtaining a lot of information. Therefore, the purpose of the thesis is to estimate the Frechet Distribution parameters of the shape parameter (θ)and the scale parameter (λ) using three estimation methods: the maximum possible method, the least square method and the Shrinkage method , And then find an estimate of the reliability function and then choose the best estimate using some statistical criteria. The simulation method of Monte Carlo was used to determine the superiority of the methods used by comparing the average error squares and the amount of bias. The results of the simulation experiments showed that the best method for estimating the reliability function in the order of the concentration of the ordered groups is the method Shrinkage of 40% The Least squares and the Maximum Likelihood in the rate of 30%. Real data representing the failure times of the dental restoration ceramics were also used to apply the best method. The results of the applied side showed that the shrinkage method was appropriate with the actual data of the failure times for the dental restoration ceramics.

#### Keywords

معاينة المجموعة المرتبة، توزيع فريچت، طريقة الامكان الاعظم، طريقة المربعات الصغرى، طريقة المقدر المقلص#### Metrics