A Modified Region Approach for Multivariate Measurement System Capability Analysis

Measurement system capability analysis is to determine whether the measurement system is capable for use in quality control. The existing research has been extended from univariate to multivariate cases. Two approaches, the multivariate analysis of variance (MANOVA) and the weighted principal components (WPC), were advocated in literature. The MANOVA method is constructed based on the volume ratio that treats the volume of constant‐density contours as the variability estimations. However, it ignores the fact that the relative position change of multivariate measurement errors could affect the measurement system capability. The WPC method uses dimension reduction to reduce the complexity but is unable to build the precision‐to‐tolerance ratio because it does not include tolerance. In this paper, we propose a modified‐region‐based method to compute the precision‐to‐tolerance ratio, the percent of repeatability and reproducibility, and the signal‐to‐noise ratio. This method also incorporates the variance–covariance structure of the measurement errors when dealing with the constant‐density contours of tolerances, total variation, and process variation. The performance of the modified‐region‐based method is evaluated based on a dataset from the literature and a set of relevant simulation. The proposed method proves to be effective compared with other methods.