TY - JOUR

T1 - Study on likelihood-ratio-based multivariate EWMA control chart using Lasso

AU - Saruhashi, Takumi

AU - Ohkubo, Masato

AU - Nagata, Yasushi

N1 - Funding Information:
We would like to thank the anonymous referees for their valuable comments. This work was partly supported by JSPS Grants-in-Aid for Scientific Research Grant Number 18K11202.
Publisher Copyright:
© 2021 by the authors.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Average run length

KW - L1 penalty function

KW - Likelihood ratio test

KW - Multivariate control chart

KW - Statistical process control

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U2 - 10.12776/QIP.V25I1.1552

DO - 10.12776/QIP.V25I1.1552

M3 - Article

AN - SCOPUS:85104517248

SN - 1335-1745

VL - 25

SP - 3

EP - 15

JO - Quality Innovation Prosperity

JF - Quality Innovation Prosperity

IS - 1

ER -