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.

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.

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.

Process Capability indices show the ability of a Process to produce products according to the pre-specified requirements. Since final quality characteristics of a product are usually interrelated to its previous amounts in earlier workstations, one need to model and consider the relationship among them to assess the Process Capability properly. Hence, conducting Process Capability analysis in multivariate environment is inevitable; unfortunately, the analysis in multivariate environment is usually complex and requires extensive calculations. Sometimes it is preferable to simplify the analysis by assuming independency among quality characteristics and evaluating Process performance with respect to each individual quality characteristic using univariate Process Capability indices such as CP, CPK, CPM, and CPMK. However, this simplification introduces some error in the analysis leading to under or overestimation of the Process Capability index. This paper models the interrelationship among quality characteristics that are produced in different workstations to provide an overall Process Capability index. Ridge residual regression is used as a vehicle to evaluate Process Capability and helps quality engineers to provide a reasonable quality policy for controlling and reducing variation in quality characteristics.

The notion of fuzzy Process Capability indices is studied by parchami et al. [1], were the specification limits are triangular fuzzy numbers. In this note, their results are revised for the general case, where the specification limits are L-R fuzzy intervals.

A profile is a relationship between a response variable and one or more independent variables being controlled during the time. Process Capability Indices (PCI) are measured to evaluate the performance of Processes in producing conforming products. Despite frequent applications of profile and a variety of available methods to monitor its different types, little researches have been carried out on determining Capability indices of profile Process. PCIs such as P C and PK C in profile state, are used to evaluate Process Capability in producing conforming profiles. This paper presents a functional approach for nonlinear profiles which usually expressed as nonlinear regression. Thus, functions such as pertaining technical specification limits, mean and natural tolerance limits are determined as nonlinear profiles and also functional limit is applied to determine Functional Capability Indices (FCI) P C and PK C of functional nonlinear profile. Easy calculation and the ability to calculate FC in each period and at each point are from the advantages of this method over the other methods.