Several sampling distribution properties of the estimator for Cpk are presented under the assumption that the data are normal, independent and identically distributed. In this paper using these assumptions, the expectation, variance and skewness are calculated by statistical methods, since the sampling distribution is weakly skewed, it is concluded that a symmetric interval estimator for Cpk might be reasonable. Also a symmetric interval estimator has been developed.

The Taguchi method is a useful technique to improve the performance of products or Processes at a lower cost and in lesser time. This procedure can be categorized as the static and dynamic quality characteristics. The optimization of multiple responses has received increasing attention over the last few years in many manufacturing organizations.Several approaches dealing with multiple static quality characteristic problems have been reported in the literature. However, little attention has been made on optimizing the multiple dynamic quality characteristics.In this paper, we investigate multivariate signal response systems (Dynamic Taguchi) and propose a method based on multivariate Process capability. Simulated data shows that the proposed method can increase robustness of dynamic Taguchi method. Furthermore, the proposed method is capable to find the optimal value of controllable factors in a continuous space.

Acceptance sampling models have been widely applied in companies for evaluation the raw material as well as the final products. Meanwhile, Process capability indices (PCIs) have been used in various industrial environments as capability measures that are obtained based on Process departure from a target, Process yield, Process consistency and Process loss. In this research, first a repetitive group sampling (RGS) plan based on Process capability index is developed for variables inspection. Then the optimal parameters of proposed RGS plan are determined and also a new multiple dependent state (MDS) sampling plan, a double sampling plan (DSP) and a sampling plan for resubmitted lots are developed and finally, a comparison study is carried out between the proposed sampling plans and the results are elaborated.

Up to now, different tools have been introduced for analyses of Process capability such as Process capability indexes of Cp, Cpk and Cpm that developed for analyzing the capability of Process and adapting the quality specifications of product. Most studies in the literature only consider the Process with single capability variable, while there is a lack of studies that consider multi-variable Processes. Cpm index has been defined with Taguchi overview over robust design. In this research, the metric Lp model has introduced to investigate the optimum decision variables by considering nominal is better quality specification and reparation Cpm index. We also expand the proposed model for such a Processes with considering overall cost as well as Process quality. At the end of research, numerical example has been presented to exhibit usage of proposed model for obtaining the best levels of Process decision variables.

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.

Statistical Process control is an excellent quality assurance tool to improve the quality of manufacture and ultimately scores on end-customer satisfaction. SPC uses Process monitoring charts to record the key quality characteristics (KQCs) of the component in manufacture. This paper elaborates on one such KQC of the manufacturing of a connecting rod of an internal combustion engine. Here the journey to attain the Process potential capability index (Cp) and the Process performance capability index (Cpk) values greater than 1.33 is elaborated by identifying the root cause through quality control tools like the cause-and-effect diagram and examining each cause one after another. In this paper, the define-measure-analyze-improve-control (DMAIC) approach is employed. The definition phase starts with Process mapping and identifying the KQC. The next phase is the measurement phase comprising the cause-and-effect diagram and data collection of KQC measurements. Then follows the analysis phase where the Process potential and performance capability indices are calculated, followed by the analysis of variance (ANOVA) of the mean values. Finally, the Process monitoring charts are used to control the Process and prevent any deviations. By using this DMAIC approach, standard deviation is reduced from 0.48 to 0.048, the Cp values from 0.12 to 1.72, and the Cpk values from 0.12 to 1.37, respectively.