Abstract
Recently, Chou et al. have considered the multivariate control chart for monitoring the process mean vector and covariance matrix for the related quality characteristics simultaneously by using log-likelihood ratio statistics. They have computed the approximation formula described with Bernoulli polynomials of degrees r≥30 by using software MATHEMATICA 4.0 for obtaining the control limit with sufficient accuracy for the specified type I error probability in the chart. However, they cannot have obtained the approximation formula for the power evaluation. By the way, Kanagawa et al. have proposed the (x̄, s)control chart for monitoring the mean and variance simultaneously based on Kullback-Leibler information when quality characteristics obey a univariate normal distribution. In this article, by adopting the procedure by Kanagawa et al., we propose the other approximation formula for determining simply the control limit with sufficient accuracy for the specified type I error probability. Furthermore, the power evaluation for the chart is also considered in theory.
| Original language | English |
|---|---|
| Pages (from-to) | 1205-1210 |
| Number of pages | 6 |
| Journal | International Journal of Advanced Manufacturing Technology |
| Volume | 25 |
| Issue number | 11-12 |
| DOIs | |
| Publication status | Published - Jun 2005 |
| Externally published | Yes |
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Keywords
- (x̄, s)control chart
- Covariance matrix
- Kullback-Leibler information
- Likelihood ratio statistic
- Mean vector
- Multivariate statistical control charts
ASJC Scopus subject areas
- Industrial and Manufacturing Engineering
Cite this
A study of multivariate (X̄, S) control chart based on Kullback-Leibler information. / Takemoto, Yasuhiko; Arizono, Ikuo.
In: International Journal of Advanced Manufacturing Technology, Vol. 25, No. 11-12, 06.2005, p. 1205-1210.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A study of multivariate (X̄, S) control chart based on Kullback-Leibler information
AU - Takemoto, Yasuhiko
AU - Arizono, Ikuo
PY - 2005/6
Y1 - 2005/6
N2 - Recently, Chou et al. have considered the multivariate control chart for monitoring the process mean vector and covariance matrix for the related quality characteristics simultaneously by using log-likelihood ratio statistics. They have computed the approximation formula described with Bernoulli polynomials of degrees r≥30 by using software MATHEMATICA 4.0 for obtaining the control limit with sufficient accuracy for the specified type I error probability in the chart. However, they cannot have obtained the approximation formula for the power evaluation. By the way, Kanagawa et al. have proposed the (x̄, s)control chart for monitoring the mean and variance simultaneously based on Kullback-Leibler information when quality characteristics obey a univariate normal distribution. In this article, by adopting the procedure by Kanagawa et al., we propose the other approximation formula for determining simply the control limit with sufficient accuracy for the specified type I error probability. Furthermore, the power evaluation for the chart is also considered in theory.
AB - Recently, Chou et al. have considered the multivariate control chart for monitoring the process mean vector and covariance matrix for the related quality characteristics simultaneously by using log-likelihood ratio statistics. They have computed the approximation formula described with Bernoulli polynomials of degrees r≥30 by using software MATHEMATICA 4.0 for obtaining the control limit with sufficient accuracy for the specified type I error probability in the chart. However, they cannot have obtained the approximation formula for the power evaluation. By the way, Kanagawa et al. have proposed the (x̄, s)control chart for monitoring the mean and variance simultaneously based on Kullback-Leibler information when quality characteristics obey a univariate normal distribution. In this article, by adopting the procedure by Kanagawa et al., we propose the other approximation formula for determining simply the control limit with sufficient accuracy for the specified type I error probability. Furthermore, the power evaluation for the chart is also considered in theory.
KW - (x̄, s)control chart
KW - Covariance matrix
KW - Kullback-Leibler information
KW - Likelihood ratio statistic
KW - Mean vector
KW - Multivariate statistical control charts
UR - http://www.scopus.com/inward/record.url?scp=18844365373&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=18844365373&partnerID=8YFLogxK
U2 - 10.1007/s00170-003-1947-9
DO - 10.1007/s00170-003-1947-9
M3 - Article
AN - SCOPUS:18844365373
VL - 25
SP - 1205
EP - 1210
JO - International Journal of Advanced Manufacturing Technology
JF - International Journal of Advanced Manufacturing Technology
SN - 0268-3768
IS - 11-12
ER -