Discrimination of Out-of-Control Condition Using AIC in (x, s) Control Chart

• Takemoto, Yasuhiko ;
• Arizono, Ikuo ;
• Satoh, Takanori
• Accepted : 2013.05.23
• Published : 2013.06.30
• 38 9

Abstract

The $\overline{x}$ control chart for the process mean and either the R or s control chart for the process dispersion have been used together to monitor the manufacturing processes. However, it has been pointed out that this procedure is flawed by a fault that makes it difficult to capture the behavior of process condition visually by considering the relationship between the shift in the process mean and the change in the process dispersion because the respective characteristics are monitored by an individual control chart in parallel. Then, the ($\overline{x}$, s) control chart has been proposed to enable the process managers to monitor the changes in the process mean, process dispersion, or both. On the one hand, identifying which process parameters are responsible for out-of-control condition of process is one of the important issues in the process management. It is especially important in the ($\overline{x}$, s) control chart where some parameters are monitored at a single plane. The previous literature has proposed the multiple decision method based on the statistical hypothesis tests to identify the parameters responsible for out-of-control condition. In this paper, we propose how to identify parameters responsible for out-of-control condition using the information criterion. Then, the effectiveness of proposed method is shown through some numerical experiments.

Keywords

($\overline{x}$, s) Control Chart;Kullback-Leibler Information;Information Criterion;Multiple Decision Method;Statistical Process Control

References

1. Abramowitz, M. and Stegun, I. A. (1964), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, US Government Printing Office, Washington, DC.
2. Akaike, H. (1974), A new look at the statistical model identification, IEEE Transaction on Automatic Control, 19(6), 716-723. https://doi.org/10.1109/TAC.1974.1100705
3. Arizono, I. and Ohta, H. (1987), An improvement of variables sampling plans based on Kullback-Leibler information, International Journal of Production Research, 25(9), 1393-1400. https://doi.org/10.1080/00207548708919920
4. Kanagawa, A., Arizono, I., and Ohta, H. (1997), Design of the control chart based on Kullback-Leibler information, In: Hans-Joachim, L. and Peter-Theodor W. (eds.), Frontiers in Statistical Quality Control 5, Physica-Verlag, Heidelberg, Germany, 183-192.
5. Kobayashi, L., Arizono, I., and Takemoto, Y. (2003), Economical operation of (${\overline{x}},s$) control chart indexed by Taguchi's loss function, International Journal of Production Research, 41(6), 1115-1132. https://doi.org/10.1080/0020754021000042427
6. Kullback, S. (1959), Information Theory and Statistics, John Wiley and Sons, New York, NY.
7. Montgomery, D. C. (2005), Introduction to Statistical Quality Control, John Wiley and Sons, New York, NY.
8. Patnaik, P. B. (1949), The non-central $X^2$-and F-distributions and their applications, Biometrika, 36, 202-232.
9. Samuel, T. R., Pignatiello, J. J., and Calvin, J. A. (1998), Identifying the time of a step change in a normal process variance, Quality Engineering, 10(3), 529-538. https://doi.org/10.1080/08982119808919167
10. Takemoto, Y. and Arizono, I. (2005), A study of multivariate ((${\overline{x}},s$) control chart based on Kullback-Lei-bler information, International Journal of Advanced Manufacturing Technology, 25(11/12), 1205-1210. https://doi.org/10.1007/s00170-003-1947-9
11. Takemoto, Y. and Arizono, I. (2009), Estimation of change point in process state on CUSUM ((${\overline{x}},s$) control chart, Industrial Engineering and Management Systems, 8(3), 139-147.
12. Takemoto, Y., Watakabe, K., and Arizono, I. (2003), A study of cumulative sum ((${\overline{x}},s$) control charts, International Journal of Production Research, 41(9), 1873-1886. https://doi.org/10.1080/0020754031000118729
13. Watakabe, K. and Arizono, I. (1999), The power of the ((${\overline{x}},s$) control chart based on the log-likelihood ratio statistic, Narval Research Logistics, 46(8), 928-951. https://doi.org/10.1002/(SICI)1520-6750(199912)46:8<928::AID-NAV4>3.0.CO;2-R