Mathematical Researches

Evaluation of production products is a process of necessity to check product quality. One of the criteria for evaluating the quality of the manufactured product is the quality characteristic of the process performance index, which has recently considered a number of researchers in statistical articles. Estimation of process performance index can be done according to the type of statistical distribution of product quality by different methods, including the maximum likelihood method, the least error squared method, the maximum product of distances and quantization. In this article, the estimation of the process performance index is presented using the gamma distribution using method of estimation, moment, maximum likelihood and interval shrinkage estimator. To provide the interval contraction estimator, after proving the unbiasedness of the torque estimators asymptotically, it is shown that the performance index estimator is also unbiased. Next, the efficiency of the estimators is compared using the square error criterion.