A spatial rank–based multivariate EWMA chart for monitoring process shape matrices

• Published in: Quality and reliability engineering international 2019-10, Vol.35 (6), p.1716-1734
• Main Authors: Huwang, Longcheen, Lin, Li‐Wei, Yu, Cheng‐Ting
• Format: Article
• Language: English
• Subjects: Control charts; Covariance matrix; EWMA; Monitoring; Multivariate analysis; Normal distribution; out of control; Rank tests; shape matrix; spatial rank covariance; spatial signs and ranks
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2471

In this article, we propose a nonparametric EWMA control chart for monitoring the shape matrix of a multivariate process based on a spatial rank test and the exponentially weighted moving average scheme. The proposed control chart is essentially developed using an estimated spatial rank covariance matrix to test the shape matrix of the covariance matrix of multivariate distributions with heavy tails. Based on our simulation studies, the proposed control chart outperforms the only existing nonparametric control chart in many practical out‐of‐control scenarios for monitoring the shape matrix of the covariance matrix of many multivariate processes. Further, we point out the weaknesses of both the nonparametric EWMA control charts for monitoring the shape matrix of multivariate processes in real applications and propose one possible method to overcome these weaknesses. We also use an example from a white wine production process to demonstrate the applicability and implementation of the proposed control chart.