The research aims to develop physical exercises with auxiliary training tools that work to develop the explosive power of the arms and legs, and then find out their effect on the accuracy of shooting from free throw and correction from jumping of advanced basketball players, as the researchers found a problem that these players have weakness in the skill of throwing Free throwing and shooting by jumping calculated with two points as a result of adopting unhealthy physical and technical positions, which led to a lack of focus and accuracy, and thus negatively affected the performance technique of free throw and jump shot, as most teams use traditional exercises without the use of auxiliary training tools, and this topic gave researchers the perception of a need for Study and research to prepare exercises with training aids in a manner similar to the form of performing a skill. It works to increase the percentage of shooting accuracy from the free throw and the correction from the jump by giving it a greater role in the training process. The researchers used the experimental approach with the design of the one experimental group and the two pre and posttests to suit the nature of the research, and the research sample was represented by the players of the Sports Club in basketball for the applicants and their number (12) players representing (20%) of the original community, and after applying the exercises to the research sample , it emerged that there are A positive effect of physical exercises using training tools to assist in developing the accuracy of correction from free throw and correction from jumping, and the results of the study found that the more physical exercises are close to the shape of skill performance with the gradual increase in strength and the maintenance of the speed factor, this led to its development better and faster With regard to the physical aspect, the skills of the free throw and the correction by the two-point jump , the researchers recommend the need to gradually give the resistors according to the movement path for shooting basketball while preserving the speed factor in performance, and the use of physical exercises that are similar to the way they perform basic movements with basketball as much as possible.
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.