It is very important to have a satisfactory measurement system, since it is useless to try to improve the manufacturing process without an adequate measurement system. Therefore, evaluation of the measurement system is the first step for the quality improvement of the manufacturing process. To estimate the measurement error we must conduct a controlled gage repeatability and reproducibility(gage R&R) study. Many manufacturers use a gage or instrument to measure multiple dimensions for the overall quality of the manufactured parts. In this case, it is necessary to estimate the gage R&R for multiple dimensions. When a gage measures a large number of dimensions of a part, it is very time-consuming and costly to measure all the dimensions. In this paper we propose the use of the principal component analysis method to identify a few principal components out of the original multivariate measurement capability to explain most of the measurement system variation pattern.