A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions. Issue 1 (2nd January 2019)

• Record Type: Journal Article
• Authors: Liang, Wenjuan; Xiang, Dongdong; Pu, Xiaolong; Li, Yan; Jin, Lingzhu
• Is Part Of: Quality technology & quantitative management. Volume 16:Issue 1(2019)
• Page Start: 113
• Page End: 127
• Publication Date: 2019-01-02
• Subjects: Covariance matrix -- multivariate statistical process control -- robust -- sparsity -- spatial sign test; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2017.1372852
• Languages: English
• ISSNs: 1684-3703

Abstract

Abstract: Most existing control charts monitoring the covariance matrix of multiple variables were restricted to multivariate normal distribution. When the process distribution is non-normal, the performance of these control charts could potentially be (highly) affected, especially for heavy-tail distributions. To construct a robust multivariate control chart for monitoring the covariance matrix, we applied spatial sign covariance matrix and maximum norm to the exponentially weighted moving average (EWMA) scheme and proposed a Phase II control chart. The novel chart is distribution-free under the family of elliptical directions distributions. Comparison studies demonstrate that the novel method is very powerful in detecting various shifts, especially for heavy-tailed distributions. The implementation of the proposed control chart is demonstrated by a white wine data.