The process control methods based on the statistical analysis apply the analysis method or mathematical model under the assumption that the process characteristic is normally distributed. However, the distribution of data collected by the automatic measurement system in real time is often not followed by normal distribution. As the statistical analysis tools, the process capability index (PCI) has been used a lot as a measure of process capability analysis in the production site. However, PCI has been usually used without checking the normality test for the process data. Even though the normality assumption is violated, if the analysis method under the assumption of the normal distribution is performed, this will be an incorrect result and take a wrong action. When the normality assumption is violated, we can transform the non-normal data into the normal data by using an appropriate normal transformation method. There are various methods of the normal transformation. In this paper, we consider the Box-Cox transformation among them. Hence, the purpose of the study is to expand the analysis method for the multivariate process capability index using Box-Cox transformation. This study proposes the multivariate process capability index to be able to use according to both methodologies whether data is normally distributed or not. Through the computational examples, we compare and discuss the multivariate process capability index between before and after Box-Cox transformation when the process data is not normally distributed.

Recently, the manufacturing process system in the industrial field has become more and more complex and has been influenced by many and various factors. Moreover, these factors have the dependent correlation rather than independent of each other. Therefore, the statistical analysis has been extended from the univariate method to the multivariate method. The process capability indices have been widely used as statistical tools to assess the manufacturing process performance. Especially, the multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. The various multivariate process capability indices have been studying by many researchers in recent years. Hence, the purpose of the study is to compare the useful and various multivariate process capability indices through the simulation. Among them, we compare the useful models of several multivariate process capability indices such as MCpm, MC+pm and MCpl. These multivariate process capability indices are incorporates both the process variation and the process deviation from target or consider the expected loss caused by the process deviation from target. Through the computational examples, we compare these process capability indices and discuss their usefulness and effectiveness.

In the industrial fields, the process capability index has been using to evaluate the variation of quality in the process. The traditional process capability indices such as Cp, Cpk, Cpm, and C┼pm have been applied in the industrial fields. These traditional process capability indices are mainly applied in the univariate analysis. However, the main streams in the recent industry are the multivariate manufacturing process and the multiple quality characteristics are corrected each other. Therefore, the multivariate statistical method should be used in the process capability analysis. The multivariate process indices need to be enhanced with more useful information and extensive application in the recent industrial fields. Hence, the purpose of the study is to develop a more effective multivariate process index (MCpI ) using the multivariate inverted normal loss function. The multivariate inverted normal loss function has the flexibility for the any type of the symmetrical and asymmetrical loss functions as well as the economic information. Especially, the proposed modeling method for the multivariate inverted normal loss function (MINLF) and the expected loss from MINLF in this paper can be applied to the any type of the symmetrical and asymmetrical loss functions. And this modeling method can be easily expanded from a bivariate case to a multivariate case.

  Process Capability indices(PCIs) have been widely used in manufacturing industries to provide a quantitative measure of process performance. PCIs have been developed to represent process capability more exactly. The traditional process capability indice

The traditional process capability indices Cp, Cpk, Cpm, Cpm+ have been used to characterize process performance on the basis of univariate quality characteristics. Cp, Cpk consider the process variation, Cpm considers both the process variation and the p

As we understand it, Process Capability indices are intended to provide single-number assessments of ability to meet specification limits on quality characteristics of interest. As a consequence of the varied ways in which PCIs are used, there have been two natural lines of research work: ① studies on the properties of PCIs and their estimators in many different environments; ② construction of new PCIs purporting to have better properties in certain circumstances. The most of existing process capability indices are concerned with the single variable. But, in many cases, a quality characteristic is composed with several factors. In that case, we want to know the integrated process capability of a quality characteristic not those of each factor. In this paper, we proposed a new multivariate system process capability index called MSPCI:SCpsk which is the geometric mean of performance measure Cpsk'S, and will be used as the criterion to assess multiple response process designs. Numerical illustration is done for SCpsk, Cp(f), Cp, Cpk, Cpm, and Cpsk.