Abstract
Purpose: When applying exponentially weighted moving average (EWMA) multivariate control charts to multivariate statistical process control, in many cases, only some elements of the controlled parameters change. In such situations, control charts applying Lasso are useful. This study proposes a novel multivariate control chart that assumes that only a few elements of the controlled parameters change. Methodology/Approach: We applied Lasso to the conventional likelihood ratio-based EWMA chart; specifically, we considered a multivariate control chart based on a log-likelihood ratio with sparse estimators of the mean vector and variance-covariance matrix. Findings: The results show that 1) it is possible to identify which elements have changed by confirming each sparse estimated parameter, and 2) the proposed procedure outperforms the conventional likelihood ratio-based EWMA chart regardless of the number of parameter elements that change. Research Limitation/Implication: We perform sparse estimation under the assumption that the regularization parameters are known. However, the regularization parameters are often unknown in real life; therefore, it is necessary to discuss how to determine them. Originality/Value of paper: The study provides a natural extension of the conventional likelihood ratio-based EWMA chart to improve interpretability and detection accuracy. Our procedure is expected to solve challenges created by changes in a few elements of the population mean vector and population variance-covariance matrix.
Highlights
Weighted moving average (EWMA) multivariate control charts are used when small changes occur continuously
The Lasso-based multivariate Exponentially weighted moving average (EWMA) (LEWMA) control chart (Zou and Qiu, 2009), which assumes that a few elements of the mean vector change, and the Lasso multivariate EWMC (LEWMC) control chart (Maboudou-Tchao and Diawara, 2013), which supposes that a few elements of the variance-covariance matrix change, apply Lasso to MEWMA and MEWMC control charts, respectively
The purpose of this study is to propose a novel multivariate control chart, which assumes that a few elements of the mean vector and the variance-covariance matrix change
Summary
Weighted moving average (EWMA) multivariate control charts are used when small changes occur continuously. In the case of multivariate control charts, Hotelling’ s control chart (Hotelling, 1947) for detecting changes in the mean vector was originally used. The control chart does not always detect small changes, so research regarding multivariate EWMA control charts to constantly detect small changes, has become popular. Lowly et al (1992) proposed a multivariate EWMA (MEWMA) control chart for detecting changes in the mean vector, and Hawkins and Maboudou-Tchao (2008) proposed a multivariate exponentially weighted moving covariance matrix (MEWMC) control chart for detecting changes in the variance-covariance matrix. To identify changes in both the mean vector and the variance-covariance matrix, Zhang, Li and Wang (2010) proposed a control chart based on the likelihood ratio, using exponential weighted moving average estimators of the mean vector and covariance matrix, termed the ELR control chart
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