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.

1. 서 론
 2. 이론적 배경
  2.1 기호
  2.2 정규성 검정 및 Box-Cox 변환
  2.3 다변량 공정능력 지수 MCpI
 3. Box-Cox를 이용한 다변량 공정능력분석
 4. 수치 예
  4.1 원본 데이터와 통계량(Original Data andStatistics)
  4.2 원본 데이터에 대한 정규성 검정(NormalityTest for the Original Data)
  4.3 Box-Cox 변환 및 변환된 데이터(Box-CoxTransformation and Transformed Data)
  4.4 변환된 데이터에 대한 정규성 검정(NormalityTest for the Transformed Data)
  4.5 다변량 공정능력지수 MCpI  의 비교(Comparison MCpI between Before and After Box-Cox)
 5. 결 론
 References

• Hye-Jin Moon(Department of Industrial and Management Engineering, Incheon National University) | 문혜진
• Young-Bae Chung(Department of Industrial and Management Engineering, Incheon National University) | 정영배 Corresponding Author