Monitoring the Mean Vector and the Covariance Matrix of Bivariate Processes
This paper proposes the joint use of two charts based on the non-central chi-square statistic (NCS statistic) for monitoring the mean vector and the covariance matrix of bivariate processes, named as the joint NCS charts. The expression to compute the ARL, which is defined as the average number of s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Associação Brasileira de Engenharia de Produção (ABEPRO)
2010-02-01
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| Series: | Brazilian Journal of Operations & Production Management |
| Online Access: | http://abepro.org.br/bjopm/index.php/bjopm/article/view/11 |
| _version_ | 1828815467252285440 |
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| author | Marcela Aparecida Guerreiro Machado Antônio Fernando Branco Costa |
| author_facet | Marcela Aparecida Guerreiro Machado Antônio Fernando Branco Costa |
| author_sort | Marcela Aparecida Guerreiro Machado |
| collection | DOAJ |
| description | This paper proposes the joint use of two charts based on the non-central chi-square statistic (NCS statistic) for monitoring the mean vector and the covariance matrix of bivariate processes, named as the joint NCS charts. The expression to compute the ARL, which is defined as the average number of samples the joint charts need to signal an out-of-control condition, is derived. The joint NCS charts might be more sensitive to changes in the mean vector or, alternatively, more sensitive to changes in the covariance matrix, accordingly to the values of their design parameters. In general, the joint NCS charts are faster than the combined T2 and |S| charts in signaling out-of-control conditions. Once the proposed scheme signals, the user can immediately identify the out-of-control variable. The risk of<br />misidentifying the out-of-control variable is small (less than 5.0%). |
| first_indexed | 2024-12-12T10:44:52Z |
| format | Article |
| id | doaj.art-8cf635a8054f45c2aed18ae740fb6a58 |
| institution | Directory Open Access Journal |
| issn | 1679-8171 |
| language | English |
| last_indexed | 2024-12-12T10:44:52Z |
| publishDate | 2010-02-01 |
| publisher | Associação Brasileira de Engenharia de Produção (ABEPRO) |
| record_format | Article |
| series | Brazilian Journal of Operations & Production Management |
| spelling | doaj.art-8cf635a8054f45c2aed18ae740fb6a582022-12-22T00:26:56ZengAssociação Brasileira de Engenharia de Produção (ABEPRO)Brazilian Journal of Operations & Production Management1679-81712010-02-01514762Monitoring the Mean Vector and the Covariance Matrix of Bivariate ProcessesMarcela Aparecida Guerreiro MachadoAntônio Fernando Branco CostaThis paper proposes the joint use of two charts based on the non-central chi-square statistic (NCS statistic) for monitoring the mean vector and the covariance matrix of bivariate processes, named as the joint NCS charts. The expression to compute the ARL, which is defined as the average number of samples the joint charts need to signal an out-of-control condition, is derived. The joint NCS charts might be more sensitive to changes in the mean vector or, alternatively, more sensitive to changes in the covariance matrix, accordingly to the values of their design parameters. In general, the joint NCS charts are faster than the combined T2 and |S| charts in signaling out-of-control conditions. Once the proposed scheme signals, the user can immediately identify the out-of-control variable. The risk of<br />misidentifying the out-of-control variable is small (less than 5.0%).http://abepro.org.br/bjopm/index.php/bjopm/article/view/11 |
| spellingShingle | Marcela Aparecida Guerreiro Machado Antônio Fernando Branco Costa Monitoring the Mean Vector and the Covariance Matrix of Bivariate Processes Brazilian Journal of Operations & Production Management |
| title | Monitoring the Mean Vector and the Covariance Matrix of Bivariate Processes |
| title_full | Monitoring the Mean Vector and the Covariance Matrix of Bivariate Processes |
| title_fullStr | Monitoring the Mean Vector and the Covariance Matrix of Bivariate Processes |
| title_full_unstemmed | Monitoring the Mean Vector and the Covariance Matrix of Bivariate Processes |
| title_short | Monitoring the Mean Vector and the Covariance Matrix of Bivariate Processes |
| title_sort | monitoring the mean vector and the covariance matrix of bivariate processes |
| url | http://abepro.org.br/bjopm/index.php/bjopm/article/view/11 |
| work_keys_str_mv | AT marcelaaparecidaguerreiromachado monitoringthemeanvectorandthecovariancematrixofbivariateprocesses AT antoniofernandobrancocosta monitoringthemeanvectorandthecovariancematrixofbivariateprocesses |