應用灰關聯分析法於多品質特性與等級類別品質特性之最佳化

Abstract

隨著產品或製程複雜度的增加，在改善製程品質時，往往需要考量到多個品質特性的同時最佳化；此外，在衡量某些產品的品質特性時，往往受限於成本或無適當量測工具等情況，需要以目視外觀的分類方式來衡量品質特性的好壞，此時品質特性須以等級類別資料(ordered categorical response)的型式呈現。以往中外文獻所發展之線外製程參數最佳化之方法，大多是針對可以量測的品質特性而設計，但這些方法都牽涉到相當複雜的數學模式或艱深的統計分析技巧，對於無太多統計或數學背景的製程工程師並不適用，而使這些最佳化方法不具實用價值。因此，本研究之主要目的是根據田口(Taguchi)直交表實驗，分別針對靜態及動態系統中的連續型多品質特性以及等級類別品質特性，導入灰色系統理論中的灰關聯分析(Grey relational analysis)技巧並結合理想解類似度順序偏好法(technique for order preference by similarity to ideal solution，簡稱TOPSIS)能同時衡量最佳方案與理想解及負理想解的特色，發展出一套簡單易用且有效的線外製程品質改善分析程序，以供一般無太多數學或統計背景之製程品管工程人員應用。最後並以實際製程的案例來說明如何應用本研究所發展的演算流程以驗證其有效性。

More than one quality characteristic must be simultaneously considered to enhance the product quality in light of the increasing complexity of modern product design. In addition, in some cases, the quality characteristic is measured by ordered categories. Most of the existed optimizing methods for multiple responses or ordered categorical response involved complicated mathematical theory, therefore they cannot practically be used for engineers without an extensive statistical background. Furthermore, considering time and cost, the manufacturer can always conduct a partial experimental design only. That is, the experimental data obtained using an orthogonal array table is a Grey system with incomplete information particularly in optimizing multiple responses case. Hence, this study developed an optimization method for multiple responses and ordered categorical response using Grey relational analysis and the technique for order preference by similarity to the ideal solution (TOPSIS) to effectively enhance the off-line quality control. The calculation for Grey relational analysis is rather easy, therefore, engineers can use it practically. Finally, real-word cases are utilized to demonstrate the feasibility and verify the effectiveness of the proposed procedure.