Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso
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 nov...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Technical University of Kosice
2021-03-01
|
| Series: | Kvalita Inovácia Prosperita |
| Subjects: | |
| Online Access: | https://www.qip-journal.eu/index.php/QIP/article/view/1552 |
| _version_ | 1827868122908983296 |
|---|---|
| author | Takumi Saruhashi Masato Ohkubo Yasushi Nagata |
| author_facet | Takumi Saruhashi Masato Ohkubo Yasushi Nagata |
| author_sort | Takumi Saruhashi |
| collection | DOAJ |
| description |
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.
|
| first_indexed | 2024-03-12T15:26:40Z |
| format | Article |
| id | doaj.art-6e01f14f3da14c03a404c4e44a701236 |
| institution | Directory Open Access Journal |
| issn | 1335-1745 1338-984X |
| language | English |
| last_indexed | 2024-03-12T15:26:40Z |
| publishDate | 2021-03-01 |
| publisher | Technical University of Kosice |
| record_format | Article |
| series | Kvalita Inovácia Prosperita |
| spelling | doaj.art-6e01f14f3da14c03a404c4e44a7012362023-08-10T13:15:17ZengTechnical University of KosiceKvalita Inovácia Prosperita1335-17451338-984X2021-03-0125110.12776/qip.v25i1.1552Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using LassoTakumi Saruhashi0Masato Ohkubo1Yasushi Nagata2Waseda University, Tokyo, JapanToyo University, Tokyo, JapanWaseda University, Tokyo, Japan 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. https://www.qip-journal.eu/index.php/QIP/article/view/1552average run lengthlikelihood ratio testL1 penalty functionmultivariate control chartstatistical process control |
| spellingShingle | Takumi Saruhashi Masato Ohkubo Yasushi Nagata Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso Kvalita Inovácia Prosperita average run length likelihood ratio test L1 penalty function multivariate control chart statistical process control |
| title | Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso |
| title_full | Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso |
| title_fullStr | Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso |
| title_full_unstemmed | Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso |
| title_short | Study on Likelihood-Ratio-Based Multivariate EWMA Control Chart Using Lasso |
| title_sort | study on likelihood ratio based multivariate ewma control chart using lasso |
| topic | average run length likelihood ratio test L1 penalty function multivariate control chart statistical process control |
| url | https://www.qip-journal.eu/index.php/QIP/article/view/1552 |
| work_keys_str_mv | AT takumisaruhashi studyonlikelihoodratiobasedmultivariateewmacontrolchartusinglasso AT masatoohkubo studyonlikelihoodratiobasedmultivariateewmacontrolchartusinglasso AT yasushinagata studyonlikelihoodratiobasedmultivariateewmacontrolchartusinglasso |