Phase I Distribution-Free Analysis of Multivariate Data

• Published in: Technometrics Vol. 59; no. 4; pp. 484 - 495
• Main Authors: Capizzi, Giovanna, Masarotto, Guido
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02-10-2017; American Society for Quality and the American Statistical Association; American Society for Quality
• Subjects: Change-point detection; Control charts; Data analysis; Diagnostic systems; LASSO; Multivariate analysis; Multivariate signed ranks; Nonparametric methods; Skewed distributions; Statistical process control
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1080/00401706.2016.1272494

In this study, a new distribution-free Phase I control chart for retrospectively monitoring multivariate data is developed. The suggested approach, based on the multivariate signed ranks, can be applied to individual or subgrouped data for detection of location shifts with an arbitrary pattern (e.g., isolated, transitory, sustained, progressive, etc.). The procedure is complemented with a LASSO-based post-signal diagnostic method for identification of the shifted variables. A simulation study shows that the method compares favorably with parametric control charts when the process is normally distributed, and largely outperforms other multivariate nonparametric control charts when the process distribution is skewed or heavy-tailed. An R package can be found in the supplementary material.