Weighted approach for multivariate analysis of variance in measurement system analysis

In a process that is integral to a measurement system, some variation is likely to occur. Measurement system analysis is an important area of study that is able to determine the amount of variation. In evaluating a measurement systemʹs variation, the most adequate technique, once an instrument is calibrated, is gauge repeatability and reproducibility (GR&R). For evaluating multivariate measurement systems, however, discussion has been scarce. Some researchers have applied multivariate analysis of variance to estimate the evaluation indexes; here the geometric mean is used as an agglutination strategy for the eigenvalues extracted from variance–covariance matrices. This approach, however, has some weaknesses. This paper thus proposes new multivariate indexes based on four weighted approaches. Statistical analysis of empirical and data from the literature indicates that the most effective weighting strategy in multivariate GR&R studies is based on an explanation of the percentages of the eigenvalues extracted from a measurement system’ matrix.