參數設計之品質損失最小演算法

Abstract

田口方法(Taguchi Method)或稱田口式品質工程，自一九八○年後，開始 盛行於美國，並推廣至全世界。它是一種低成本，高效益的品質改善技術 ；此種方法的特色在於有效地利用品質損失函數和訊號雜音比 (SN Ratio)來量測品質；利用線外品質管制(參數設計、直交實驗計劃)來改善 品質；利用線上品質管制來維持品質，是從工程技術觀點出發，達到品質 穩健(Robust)的一套系統性方法。然而近年來，田口方法的一些主要理論 遭到統計學者的批評，相對地，也有一些較具有統計理論基礎的方法被提 出。而事實上田口玄一所提出的兩步驟最佳化法(Two Step Optimization Procedure)，在某些情況下並不適用，而Box-Cox(1988)及 N.Logothetis(1988)等所提出的資料轉換(Data Transformation)方法也 只能解決一部份的問題；本研究旨在針對兩步驟最佳化程序中的一些缺失 ，利用迴歸分析及非線性規劃(Nonlinear Programming)技巧來構建一個 能使品質損失最小的演算法，最後並以實例來驗證本研究所構建的演算法 之有效性及可行性。 Taguchi Methods were introduced into the U.S. in 1980 and since then it has been widespread rapidly. It is a cost- effective quality improvement technique and a systematic method to get robust quality from the viewpoint of engineering tech- nology. Taguchi Methods enable us to evaluate the quality by using the "Loss Function" and the "Signal-to-Noise" ratio, to improve the quality by using te off-line quality techniques and to maintain the quality by using the on-line quality techniques. Recently some of the underlying principles of Taguchi's ideas have been criticized and the alternative satistical methods have been proposed. In fact, Taguchi's two-step opti- mization procedure in the parameter design is often inefficient if certain conditions are not satisfied. In this case, the procedure may not be able to attain the minimum quality loss although its "Signal-to-Noise" ratio is maximized. Box-Cox data transformation or β-transformation, suggested by N.Logothetis (1988), can only solve part of the problems. The objective of this thesis is to develop algorithms which will attain the min- imum quality loss by utilizing the techniques of regression analysis and nonlinear programming. Some examples in the industry was conducted to verify the effectiveness and the feasibility of this minimum quality loss algorithm.