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

Fabricio Alves De Almeida,Alexandre Fonseca Torres,Simone Carneiro Streitenberger,Jose Henrique De Freitas Gomes,Anderson Paulo De Paiva

doi:10.1109/access.2020.3019031

Fabricio Alves De Almeida, Alexandre Fonseca Torres + Show 3 more

Open Access

https://doi.org/10.1109/access.2020.3019031

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Abstract

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.

Highlights

Multivariate statistical techniques are widely used to analyze data that has a significant variance-covariance structure [1]
In order to contribute to gage repeatability and reproducibility (GR&R) strategies applied with factor analysis, this study presents a new approach based on rotated factor scores, weighting by their respective eigenvalues
The contributions of this paper can be summarized as follows: 1) A new proposal to verify the measurement system for extensive and correlated data is presented; 2) The use of orthogonal rotation methods promotes a better interpretation of latent variables, providing a simpler loading structure to assess data quality; 3) The weighting through the eigenvalues of each factor gives the corresponding degree of importance to each response cluster

Summary

INTRODUCTION

Multivariate statistical techniques are widely used to analyze data that has a significant variance-covariance structure [1]. In order to contribute to GR&R strategies applied with factor analysis, this study presents a new approach based on rotated factor scores (quartimax and varimax), weighting by their respective eigenvalues For this application, a data collection that follows the guidelines of a measurement system analysis is considered. The contributions of this paper can be summarized as follows: 1) A new proposal to verify the measurement system for extensive and correlated data is presented; 2) The use of orthogonal rotation methods promotes a better interpretation of latent variables, providing a simpler loading structure to assess data quality; 3) The weighting through the eigenvalues of each factor gives the corresponding degree of importance to each response cluster.

FACTOR ANALYSIS

ORTHOGONAL ROTATION METHODS

NUMERICAL EXAMPLE: A RSW PROCESS

Findings

CONCLUSION