產品品質的監控是近年生產製程越來越重視的議題，如何更有效率地監控產品製程是很多學者在品質管制系統上共同努力的目標。在很多實際的製程中，製程的品質可以用一個或多個解釋變數與反應變數之間的某特定函數來界定，而這類的資料型態被稱為輪廓型資料。現今已有不少研究線性輪廓監控方法的文獻，但現有的線性輪廓監控方法僅適用於樣本數足以估計所有輪廓參數的情況，對於樣本數不足以估計所有輪廓參數的情形，尚未存在有效的方法來監控輪廓製程。
本文將針對多維度多重線性輪廓的製程監控，在樣本數不足的狀況下，提出一種利用部分最小平方法建構的管制圖。我們將使用這個管制圖來監控輪廓製程失控與否，並且將會利用統計模擬來評估其優劣。最後我們將利用一個實例來說明在實際情形下如何使用我們所提出的管制圖來執行輪廓製程的監控。

Quality control of the manufacturing process and how to monitor the process more effectively are important issues in the recent. In many practical manufacturing processes, the quality can be expressed by a function of one or more explanatory variables and response variables, and this kind of data is known as profile data. There are many literatures talking about the methods of linear profile monitoring today, but the current methods of linear profile monitoring apply only to the case that the number of observations is sufficient to estimate all regression parameters. For the case that the number of observations is not sufficient to estimate all parameters, there still have no effective methods to monitor the linear profile.
For the multivariate multiple linear profile monitoring in the case that the number of observations is not sufficient, this article would propose a control chart based on the partial least squares. We would also use the proposed control chart to perform linear profile monitoring, and then perform the statistical simulation to assess the efficiency. Finally, we would use an example to illustrate how to monitor the linear profile using the proposed control chart.

De Jong, S. (1993). “SIMPLS: An Alternative Approach of Partial Least Squares Regression”. Chemometrics and Intelligent Laboratory Systems, 18, pp. 251-263.
De Jong, S., and Ter Braak, C. J. F. (1994). “Comments on the PLS Kernel Algorithm”. Journal of Chemometrics, 8, pp. 169–174.
Eyvazian, M., Noorossana, R., Saghaei, A., and Amiri, A. (2011). “Phase II Monitoring of Multivariate Multiple Linear Regression Profiles”. Quality and Reliability Engineering International, 27, pp. 281-296.
Giri, N. C. (2004). “Multivariate Statistical Analysis: Revised and Expanded”. 2nd ed., Marcel Dekker, New York.
Hotelling, H. (1947). “Multivariate Quality Control”. Techniques of Statistical Analysis, Eisenhart, Hastay, and Wallis (Ed.), McGraw-Hill, New York.
Indahl, U. G., Liland, K. H., and Næs, T. (2009). “Canonical Partial Least Squares - a Unified PLS Approach to Classification and Regression Problems”. Journal of Chemometrics, 23, pp. 495–504.
Kang, L., and Albin, S. L. (2000). “On-line Monitoring When the Process Yields a Linear Profile”. Journal of Quality Technology, 32, pp. 418-426.
Lowry, C. A., Woodall, W. H., Champ, C. W., and Rigdon, S. E. (1992). “A Multivariate Exponentially Weighted Moving Average Control Chart”. Technometrics, 34, pp. 46-53.
Mestek, O., Pavlik, J., and Suchanek, M. (1994). “Multivariate Control Charts: Control Charts for Calibration Curves”. Journal of Analytical Chemistry, 350, pp. 344-351.
Montgomery, D. C. (2012). “Statistical Quality Control: A Modern Introduction”. 7th ed., John Wiley & Sons, Canada.

Page, E. S. (1954). “Continuous Inspection Schemes”. Biometric, 41, pp. 100-115.
Parker, P. A., Morton, M., Draper, N., and Line, W. (2001). “A Single-Vector Force Calibration Method Featuring the Modern Design of Experiments”. NASA Langley Research Center, AIAA 2001-0170, January 2001.
Rännar, S., Lindgren, F., Geladi, P., and Wold, S. (1994). “A PLS Kernel Algorithm for Data Sets with Many Variables and Fewer Objects. Part 1: Theory and Algorithm”. Journal of Chemometrics, 8, pp. 111–125.
Roberts, S. W. (1959). “Control Charts Based on Geometric Moving Averages”. Technometrics, 1, pp. 234-250.
Shewhart, W. A. (1924). “Some Applivations of Statistical Methods to the Analysis of Physical and Engineering Data”. Bell System Technical Journal, 3, pp. 43-87.
Wold, H. (1966). “Estimation of Principle Components and Related Models by Iterative Least Squares”. Multivariate Analysis, Krishnaiah, P. R. (Ed.), Academic Press, New York, pp. 391-420.
Wold, H. (1966). “Nonlinear Estimation by Iterative Least Squares Procedures”. Research Papers in Statistics, Festschrift for Neyman, J. and David, F. (Ed.), Wiley, New York, pp. 411-444.
Zou, C., Tsung, F., and Wang, Z. (2007). “Monitoring General Linear Profiles Using Multivariate Exponential Weighted Moving Average Schemes”. Technometrics, 49, pp. 395-408.