Calculating and Plotting Contour Curves of a Response Surface

反應曲面之計算與圖形繪製

10.6220/joq.2015.22(4).04

陳文魁(Wen-Kuei Chen)；胡承方(Cheng-Feng Hu)；方聰然(Tsung-Jan Fang)

反應曲面法 ； 演進作業程序 ； 等效曲線 ； RSM ； EVOP ； contour curve

品質學報

22卷4期（2015 / 08 / 30）

337 - 345

英文

生產控制的主要目標是保持最佳的生產過程。為了最佳化流程，通常建議使用演進作業程序（Evolution of Operations Program, EVOP）或反應曲面法（Response Surface Methodology, RSM）。在EVOP時，實驗設計和改進程序同時進行，亦在不干擾正常生產過程中進行。RSM主要是利用實驗設計的順序，以獲得最佳的反應。即使是有RSM結果，但其過程分析仍有個問題產生，即在反應曲線的計算和圖形繪製。通常情況下，反應面曲線是橢圓狀，且要從控制條件曲線得到解決方案，需透過一個隱函數獲得，其求解計算是有反覆又疊代的過程。而本文正是提供一個明確的計算方法，以便容易找到特定反應曲面，並在所有組合條件下求得。

The main goal of manufacturing control is to keep production process optimal all way along. In order to optimize a process, an approach such as evolutionary operation program (EVOP) or response surface methodology (RSM) is usually recommended. In EVOP, experimental designs and improvements are introduced, while an ongoing full-scale manufacturing process keeps producing satisfied results. The concept is that process improvement should not interrupt production. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Though the RSM results can be acquired, the process analyzer still has problems with dealing the calculation and plotting of the contour curve. Normally the response surface curve is oval-like, thus a solution of control conditions to the contour is an implicit function. Its solving calculation involves an iterative procedure. This article is to provide an explicit calculation method to find all condition combinations for a specific contour. Some features of the RSM contour are discussed as well in this article.

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