利用部分最小平方法監控多維度多重線性輪廓

Multivariate Multiple Linear Profile Monitoring Based on Partial Least Squares Regression

陳易駿

指導教授 ： 黃榮臣

國立清華大學/理學院/統計學研究所/碩士(2014年)

https://doi.org/10.6843/NTHU.2014.00452

摘要

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。

關鍵字

輪廓監控 ； 部分最小平方法

並列摘要

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.

參考文獻

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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.

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