A Gage Study Through the Weighting of Latent Variables Under Orthogonal Rotation

A new approach to identify and diagnose the quality of extensive and multivariate data is presented, using the gage repeatability and reproducibility (GR&R) study through the weighting of rotated factor scores. The proposal uses axis rotation to improve the explanation and interpretations of latent information, providing a statistically appropriate alternative when dealing with two or more correlated data sets. To analyze data with a significant variance-covariance structure, factor analysis (FA) is applied for calculating the eigenvalues and extracting of the rotated scores. Once obtained, these scores are then weighted with their respective eigenvalue for each factor. This procedure results in a single response vector, which is capable of properly interpreting all of the quality responses analyzed. To illustrate an application of the method, a real data set from a resistance spot welding process is selected, and two different types of rotation are compared. The proposed method provided an output that contemplated all of the significant variability of the data in a unique and significant way. In addition, the method enabled a reduction in the data dimensionality, thus minimizing the time for analysis and computational effort.