A Mathematical Model Based on Principal Component Analysis for Optimization of Correlated Multiresponse Surfaces

以主成份分析為基礎的數學模式找出相關性的多重反應曲面最佳化

10.6220/joq.2012.19(3).02

Mahdi Bashiri；Taha Hossein Hejazi

多重反應取面 ； 相關性反應 ； 數學規劃 ； 主成份分析 ； Multiple Response Surface (MRS) ； correlated responses ； mathematical programming ； Principal Component Analysis (PCA)

品質學報

19卷3期（2012 / 06 / 01）

223 - 239

英文

多重品質特性（或反應變數）最佳化遠比單一因子的最佳化來得複雜，因為我們面臨不同單位、重要性與最佳化方向。在大多數真實情形下，反應是相關的，因此下結論變得困難。若把品質特性的相關性忽略，工程設計人員可能無法發現設計變數的設定可以同時改善所有反應的品質。本研究以多重相關性反應的最佳化為重點，並且提出一個以主成份分析為基礎的新的數學模式。並且利用兩個從文獻找來的範例說明所提出的方法有較好的效率。

Optimization of multiple quality characteristics (or response variables) is more complicated than optimization of a single one since we face different units, importance and optimality directions. In most real situations there are correlated responses that make conclusion more difficult. If correlations among quality characteristics are ignored, engineering designer may miss finding design variable settings which simultaneously improved the quality of all the responses. In this work optimization of multiple correlated responses was studied and a novel mathematical model was proposed based on Principal Component Analysis (PCA) to optimize correlated multiresponse problems. The proposed method is also demonstrated by two numerical examples from the literature to confirm the efficiencies.

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