主成份分析法在制定多變量製程能力指標上之應用研究

Development of New Multivariate Process Capability Indices Using Principal Component Analysis

潘浙楠(Jen-Nan Pan) ； 陳彥廷(Yen-Ting Chen)

《品質學報》 14卷3期 (2007/09) Pp. 317-335

摘要

產品之良窳是企業永續經營的關鍵，就目前科技產業而言，產品的功能越來越多，製程亦日趨複雜，僅憑單一品質特性並不足以反映產品品質。一般而言，工業製程中常有多個彼此相關的品質特性皆可能造成製程異常。為了建立多重品質特性下之製程能力指標，Chan et al. (1991)利用馬氏距離估算多變量製程能力指標。Taam et al. (1993)提出以修正的規格區域估算多變量製程能力指標，Hubele et al. (1991)則以修正的製程區域估算多變量製程能力指標。潘浙楠與李仁凱(2003)則考慮產品品質特性間的相關程度並對Taam et al. (1993)所提之指標做進一步修正，提出一組估算多變量製程之NMC(下標 p)及NMC(下標 pm)指標。NMC(下標 p)及NMC(下標 pm)指標雖可如實反映多變量製程之表現，但其修正規格區域會有高估的情形。本研究主要是利用主成份分析法中主成份軸正交的幾何概念，提出以另一種制定多變量製程能力指標的方式並對上述修正規格區域再進行轉軸與調整。吾人所提出之新多變量製程能力指標PMC(下標 p)及PMC(下標 pm)與上述各種多變量製程能力指標相較，更能準確反映製程實際的表現。
最後本研究藉由Sultan (1986)所提出產品硬度及拉抗強度之實例及Pan et al. (2004)文中塑料方形扁平式封裝(QFP)製程之資料為例說明PMC(下標 p)及PMC(下標 pm)多變量製程能力指標可正確評估多重品質特性製程在高相關下的表現。此外，以主成份分析法制定PMC(下標 p)及PMC(下標 pm)指標的方式更容易進行具三個以上產品品質特性之製程能力分析。

關鍵字

多變量製程能力指標 ； 主成份分析法 ； 塑料方形扁平式封裝QFP製程

並列摘要

Good quality of products is the key factor of business success. With the advent of modern technology, manufacturing processes become highly sophisticated and merely a single quality characteristic can not reflect the product quality. Generally speaking, the abnormality of an industrial process is caused by problems of several interrelated quality characteristics. In order to establish the multivariate process capability index, Chan et al. (1991) used Mahalanobis distance to calculate multivariate process capability index. Taam et al.(1993) used a modified tolerance region to estimate multivariate process capability indices and Hubele et al.(1991) used a modified process region to estimate multivariate process capability index. In this paper, the multivariate process capability indices established by Taam are modified according to the correlation of several quality characteristics. The two novel PMC(subscript p) and PMC(subscript pm) indices are developed using principal component analysis. The modified tolerance region is adjusted and rotated using the geometric concept of orthogonal principal axes. The results of our comparative study show that the two novel PMC(subscript p) and PMC(subscript pm) indices can correctly reflect the true capability of a multivariate manufacturing process.
Finally, two numerical examples of a product's hardness and tensile strength as well as the quad flat package (QFP) process data further demonstrate that the usefulness of our proposed PMC(subscript p) and PMC(subscript pm) indices in evaluating the process capability.

並列關鍵字

Multivariate process capability index ； Principal component analysis ； Quad flat package QFP

參考文獻

潘浙楠、李仁凱(2003)。多重品質特性下製程能力指標之比較研究。品質學報。10，149-176。

潘浙楠、李婉瑜(2006)。修正型損失函數在制定經濟工程規格上之應用研究。品質學報。13，241-256。

Chan, L. K.,Cheng, S. W.,Spiring, F. A.(1988).A new measure of process capability: _C.Journal of Quality Technology.20,162-173.

Chan, L. K.,Cheng, S. W.,Spiring, F. A.(1991).A multivariate measure of process capability.International Journal of Modeling and Simulation.11,1-6.

Hubele, N. F.,Shahriari, H.,Cheng, C. S.,Keats, J. B. (edited),Montgomery, D. C.(1991).Statistical Process Control in Manufacturing.New York:Marcel Dekker.