IDEA Approach for Solving Multi-Responses Fuzziness Problem in Robust Design

利用乏晰資料包絡分析以解決穩健設計中之多變量模糊問題

李明賢(Caleb Ming-Hsien Li) ； 雷方奕(Abbas Al-Refaie) ； 哈珊(Mohammad Hasan) ； 葉兆雄(Benjamin Chao-Hsiung Yeh)

《品質學報》 21卷6期 (2014/12) Pp. 455-478

https://doi.org/10.6220/joq.2014.21(6).03

摘要

大多數製造業應用資料包絡分析（data envelopment analysis, DEA）模式均假設所有的資料都有特定的值，然而在某些情況下，資料可能是乏晰的。因此，本研究在田口方法中提出乏晰資料包絡分析（imprecise data envelopment analysis, IDEA）以解決多變量模糊問題。變量的乏晰性乃是因為製程本身的複雜性與模糊行為所致。因此，每個變量均用一個有上限和下限之區間所定義，這些多重變量值與其因素水準組合轉變成一個具有上限和下限的區間值，稱之為相對區間效率，每個實驗的因素水準組合可視為一組決策單位（decision making unit, DMU），兩種IDEA模式用來計算DMU之上限和下限效率值。最後，利用乏晰多目標DEA模式來決定最佳因素水準組合。並以兩個個案研究做為說明，利用本文所提供之方法在兩個個案中均獲得較優於主成份分析和渴望函數之結果。

關鍵字

乏晰資料包絡分析 ； 田口方法 ； 多變量

並列摘要

Most manufacturing applications on data envelopment analysis (DEA) models assume that all data have the form of specific numerical values. In some circumstances, however, the data may be imprecise. This research, therefore, proposes an approach for solving the multi-responses fuzziness problem in the Taguchi method using the Imprecise Data Envelopment Analysis (IDEA) approach. The response fuzziness is caused by complex and vague behavior of the process itself. Thus, each response is defined by an interval bounded by lower and upper values. The multiple response values correspond to each combination factor settings are transformed into a single measure with lower and upper values, called the relative interval efficiency. The combination of factor settings at each experiment is treated as a decision making unit (DMU). Two IDEA models are employed to calculate DMU's upper and lower efficiency values. Finally, a fuzzy multi objective data envelopment analysis (DEA) model is used to determine the best combination of factor settings. Two case studies are adopted for illustration; in both of which the proposed approach achieved competitive improvements against the principle component analysis and desirability function.

並列關鍵字

imprecise data envelopment analysis ； Taguchi method ； multi-responses

參考文獻

Al-Refaie, A.(2009).Optimizing SMT performance using comparisons of Efficiency between different systems technique in DEA.IEEE Transactions on Electronics Packaging Manufacturing.32(4),256-264.

Al-Refaie, A.(2010).Grey-data envelopment analysis approach for solving the multi-response problem in the Taguchi method.Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture.224(1),147-158.

Al-Refaie, A.(2010).Super-efficiency DEA approach for optimizing multiple quality characteristics in parameter design.International Journal of Artificial Life Research.1(2),58-71.

Al-Refaie, A.(2011).Optimizing correlated QCHs using principal components analysis and DEA techniques.Production Planning & Control: The Management of Operations.22(7),676-689.

Al-Refaie, A.(2012).Optimizing performance with multiple responses using cross-evaluation and aggressive formulation in data envelopment analysis.IIE Transactions.44(4),262-276.