Process-oriented basis representation for a multivariate gauge study

The gauge repeatability and reproducibility (GR&R) study is typically conducted on a single quality characteristic for quality measurement. However, manufacturing tests in a GR&R study may have multiple characteristics whose distribution is usually assumed to be multivariate normal. There is little research for multivariate GR&R study in the past. Process-oriented basis representation (POBREP) is an effective method to identify specific causes of production problems and map those into a basis matrix. These patterns can then be analyzed individually using a GR&R study. In some cases, when the basis matrix is not a complete basis, the coefficient estimation of the POBREP vector could be solved by weighted least squares. Two indices such as precision to tolerance (P/T) ratio and the number of distinct categories (ndc) with their confidence interval were used to evaluate the adequacy for the measurement process. A real data set was used to demonstrate the application of the proposed methodology. The results show that the POBREP method outperforms other methods such as the principal component analysis and univariate methods.