延伸最陡上升法應用於多反應製程最佳化之改善研究

一般而言，產品的製造過程常與數個品質特性有關，隨著產品發展的複雜性與多樣性，品質最佳化必須同時評估數個反應變數的績效。在反應曲面法中，針對線上實務的問題是讓多個反應變數達到製程最佳化，而解決多反應值最佳化的基本方法為整合目標函數，同時各個反應值必須以數學方法結合形成單一目標函數，單一目標函數的建立需要考慮品質控制的限制範圍。本篇研究主要針對望大、望小與望目不同的品質特性，提供慾望方程式的設計概念以呈現多反應值的模式，並且應用最陡上升方向在慾望方程式的搜尋方法，而在實務問題應用上可針對不同品質特性的績效作調整，而慾望方程式中的函數轉換在本質上是屬於高度非線性。為了達到即時線上製程最佳化，本文中結合了最陡上升法與一階泰勒展開方程式來逼近非線性慾望方程式。最後，以最陡上升梯度方向搜尋法處理線上多反應值最佳化的問題，同時透過一個中央合成設計的問題來說明模擬的結果希望藉由此方法對於參數最佳化的調整有更進一步助益並且適用於更複雜的工業製程。

關鍵字

多重反應值；慾望方程式；泰勒級數展開式；最陡上升法；中央合成設計

並列摘要

In practice, a manufactured product is often evaluated by several response variables simultaneously. One of the most practical problems in response surface methodology is how to proceed with on-line process optimization entailing more than single response variable. A common approach to solving multi-response optimization problem is a unifying objective function approach; that is, the individual responses are mathematically combined to form a single objective function. Unifying objective approaches are employed in the quality control area to optimize several responses at the same time. In this thesis, it is proposed to use the desirability function approach to perform the multi-response modeling, and then apply the method of steepest ascent direction to the resulting desirability function. Yet, the resultant desirability function is highly nonlinear in nature due to functional transformation. To facilitate on-line process optimization using the method of steepest ascent, the first-order Taylor series expansion will be employed to approximate the nonlinear desirability function. At last, the method of steepest ascent proceeds to conduct on-line multi-response process optimization. The proposed procedure for on-line process improvement is illustrated through a numerical example taken from the literature.

並列關鍵字

Multi-response ； Desirability Function ； Taylor Series Expansion ； Steepest Ascent.

參考文獻

Ch’ng C. K., Quah S. H., and Low H. C., 2005, A New Approach for Multi-Response Optimization. Quality Engineering, 17: 621-626.

Derringer, G. and Suich, R., 1980, Simultaneous Optimization of Several Response Variables. Journal of Quality Technology, 12, 214-219.

Antony J., 2000, Multi-response Optimization in Industrial Experiments Using Taguchi’s Quality Loss Function and Principal Component Analysis. Quality and Reliability Engineering International, 16: 3-8.

Khuri, A. and Conlon, M., 1981, Simultaneous Optimization of Multiple Responses Represented by Polynomial Regression Functions. Technometrics, 23, 363-375.

Kim, K. J and Dennis, K. J. Lin, 1999, Simultaneous Optimization of Mechanical Properties of Steel by Maximizing Exponential Desirability functions. Applied Statistics, 49, Part 3, 311-325.

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延伸最陡上升法應用於多反應製程最佳化之改善研究

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