Figure 3.1. R code for a phase II control chart based on the T2 statistic.
Figure 3.2. Output for the mult.chart function: the MYT decomposition of the T2 statistic for an out-of-control observation.
Table 3.1. All possible MYT decompositions for an 18th observation which falls outside the upper control limit
Table 3.2. Summary of the individual T2 statistics
Table 3.3. Summary of all
Table 4.1. Comparison of the percentages of correct identification of the cause for out-of-control signals
참고문헌
- Alt, F. B. (1985). Multivariate quality control, In Kotz, S., Johnson, N. L., Read, C.R. (eds.) Encyclopedia of Statistical Sciences, 6, 111-122.
- Doganaksoy, N., Faltin, F. W., and Tucker, W. T. (1991). Identification of out-of-control multivariate characteristic in a multivariable manufacturing environment, Communications in Statistics - Theory and Methods, 20, 2775-2790. https://doi.org/10.1080/03610929108830667
- Hayter, A. J. and Tsui, K. L. (1994). Identification and quantification in multivariate quality control problems, Journal of Quality Technology, 26, 197-208. https://doi.org/10.1080/00224065.1994.11979526
- Hotelling, H. (1947). Multivariate Quality Control, Techniques of Statistical Analysis, Eisenhart, Hastay, and Wallis (eds), McGraw-Hill, New York.
- Jackson, J. E. (1991). A User's Guide to Principal Components, John Wiley & Sons, New York.
- Kenett, R. S. and Halevy, A. (1984). Some statistical aspects of quality conformance inspection in military specifications documents, Proceedings of the 5th International Conference of the Israeli Society for Quality Assurance, Tel Aviv, 23-35.
- Kourti, T. and MacGregor, J. F. (1996). Multivariate SPC methods for process and product monitoring, Journal of Quality Technology, 28, 409-428. https://doi.org/10.1080/00224065.1996.11979699
- Lee, S. (2015). Effects of parameter estimation in phase I on phase II control limits for monitoring autocorrelated data, The Korean Journal of Applied Statistics, 28, 1025-1034. https://doi.org/10.5351/KJAS.2015.28.5.1025
- Lee, S. (2018). Notes on identifying source of out-of-control signals in phase II multivariate process monitoring, The Korean Journal of Applied Statistics, 31, 1-12.
- Lim, J. and Lee, S. (2017). Phase II monitoring of changes in mean from high-dimensional data, Applied Stochastic Models in Business and Industry, 33, 626-639. https://doi.org/10.1002/asmb.2267
-
Mason, R. L., Tracy, N. D., and Young, J. C. (1995). Decomposition of
$T^2$ for multivariate control chart interpretation, Journal of Quality Technology, 27, 99-108. https://doi.org/10.1080/00224065.1995.11979573 -
Mason, R. L., Tracy, N. D., and Young, J. C. (1997). A practical approach for interpreting multivariate
$T^2$ control chart, Journal of Quality Technology, 29, 396-406. https://doi.org/10.1080/00224065.1997.11979791 - Mason, R. L. and Young, J. C. (1999). Improving the sensitivity of the 62 statistic in multivariate process control, Journal of Quality Technology, 31, 155-165. https://doi.org/10.1080/00224065.1999.11979912
- Montgomery, D. C. (2005). Introduction to Statistical Quality Control (5th ed), John Wiley & Sons, New York.
- Murphy, B. J. (1987). Selecting out-of-control variables with 62 multivariate quality procedures, The Statistician, 36, 571-583. https://doi.org/10.2307/2348668
- Shewhart, W. A. (1926). Quality control charts, Bell System Technical Journal, 2, 593-603.
- Timm, N. H. (1996). Multivariate quality control using finite intersection tests, Journal of Quality Technology, 28, 233-243. https://doi.org/10.1080/00224065.1996.11979663
- Woodall, W. H. and Montgomery, D. C. (1999). Research issues and ideas in statistical process control, Journal of Quality Technology, 31, 376-385. https://doi.org/10.1080/00224065.1999.11979944