應用資料包絡分析法於多品質實驗之最適化

Abstract

實驗設計(design of experiments, DOE)與田口方法(Taguchi methods)是工業界常用來研發或改善產品/製程線外品質的手法，但是DOE與田口方法僅適用於單一品質特性的最適化，並無法有效地同時最適化多個品質特性，而隨著顧客需求日益多變與高科技產品之研發需要，產品/製程的設計往往涉及複雜的多品質特性最適化問題，因此如何有效地最適化多個品質特性是製造者贏得競爭優勢的關鍵課題。本研究以資料包絡分析法(data envelopment analysis, DEA)為基礎，利用相對效率的概念建構一系列的最適化程序，以改進現有之DOE與田口方法。本研究利用DEA可有效分析多投入多產出之特性，來衡量由DOE與田口方法規劃而得的實驗數據之品質績效，然後根據此品質績效求得最適的因子水準組合。因為不需對被衡量的產品/製程作特定之模型假設，本研究所提之最適化程序可以減少實務應用時之限制，實用性較DOE與田口方法為佳，此外，本研究之最適化程序不論所面臨的品質特性其數量多寡，均僅需最適化單一個目標函數，可避免必須取捨多個模型的困難，且所得之因子水準組合較使用DOE與田口方法所得的更為穩健，能使製造者從品質改善中獲得更多之工程經驗及實質效益。故本研究除了在理論上有助於多品質特性最適化之發展之外，在實務上亦有助於製造者最適化複雜的產品/製程設計，以滿足多元的顧客與技術需求。

Design of experiments (DOE) and Taguchi methods are extensively adopted in industry for determining an optimal factor-level combination of products/processes. Although adopted in various industries to continuously enhance product design in response to customer requirements, DOE and Taguchi methods only can optimize single quality characteristic design. However, in most design instances, increasing variation in customer requirements accompanies complex product design. Multiple quality characteristics must be considered when designing or developing complex products/processes. Therefore, simultaneously optimizing multiple quality characteristics is of priority concern for manufacturers hoping to gain a competitive advantage. This study presents novel product/process optimization procedures based on data envelopment analysis (DEA), capable of efficiently optimizing a product/process regardless of the system complexity. Given the ability to simultaneously evaluate multiple inputs and outputs for a measured system, quality performance of experimental data which collected from DOE and Taguchi methods is assessed using DEA. Next, a solving scheme is used to obtain the optimal factor-level combination of the product/process according to the quality performance. Capable of requiring no specific assumptions regarding a measured system, the proposed procedure using DEA can alleviate the limitations of application in practice, allowing it to determine an optimal factor-level combination for a product/process more efficient than conventionally adopted DOE and Taguchi methods. Moreover, the proposed optimization procedures can simply model the optimization problem in a single objective function to determine the optimal factor-level combination despite the number of quality characteristics of the measured product/process. Accordingly, difficulties associated with the simultaneous trade-off between numerous equations can be avoided. Therefore, the proposed optimization scheme can overcome the limitations of existing approaches when the number of responses is large. Furthermore, the obtained optimal factor-level combination is also more robust than that of DOE and Taguchi methods, enabling manufacturers to earn a profit from quality improvement. The proposed optimization procedures using DEA contribute to efforts to continuously improve optimization schemes for single and multiple quality characteristics, subsequently helping manufacturers to optimize complex designs to satisfy diversified customer and technology requirements.