本論文延申Tong et al. [11] 結合CCR 模型假設之資料包絡法與逐步迴歸方法的理念, 利用變異係數的反函數來建構程序, 以尋找動態系統中之最佳因子設計水準組合。此法有別於田口設計方法, 可在當品質特徵的輸出水準及訊號因子間的關係為非線性的情況下使用。此外, 本論文也提出一個演算法來搜尋最佳因子設計水準組合。文中並使用一個實例來說明本建議方法的運作程序並比較本論文建議的方法與Tong et al. [11] 所提出方法上的差別。

The thesis provides a robust design to identify the optimal combination of factor levels for dynamic systems with multiple quality characteristics. The reciprocal coefficient of variation is used to compute the relative efficiency of decision making unit in the data envelopment analysis approach, in which the constant return to scale model is considered. The proposed method makes free of the limitations of Taguchi method, it can reach a robust design when the relationship of the output of quality characteristic and signal factors is nonlinear. The use of the proposed method is illustrated via an example regarding the manufacturing of temperature control circuit.

Contents
1 Introduction ..................................................................1
2 Literature Review ......................................5
2.1 Taguchi Method for Dynamic System ....................5
2.2 Data Envelopment Analysis ............................6
2.3 The DEA Method for Dynamic Systems ..................11
3 The Proposed Method ...................................15
4 An Example and Numerical Study ........................20
4.1 An Example ......................................................20
4.2 Performance Comparision .............................27
5 Conclusions ...........................................33

List of Tables
4.1 Control factors and their levels of temperature control circuit ....21
4.2 Simulated data of RT−ON .............................22
4.3 Simulated data of RT−OFF ............................23
4.4 The OQP values and the efficiencies of location and dispersion effects correspond
to RT−ON and RT−OFF using the method proposed by Tong et al. [11] .......................24
4.5 Predicted OQP values of full design suggested by Tong et al. [11] .........................25
4.6 The OQP value of each DMU and the efficiency correspond to RT−ON and
RT−OFF using the proposed method ........................26
4.7 The value of β,σe2 , and η for RT−ON and RT−OFF .....29
4.8 Prediction equations of β and σe2 ...................29
4.9 Predicted SNRs for all factor-level combinations of a full factorial design. .....30
4.10 The proposed optimization combination of factor levels .............32
4.11 Comparisons of different optimal approaches ................................32

List of Figures
2.1 Efficiency measure (see also Diagram 1 of Farrell [4]) ................................9

[1] Banker, R. D., Charnes, A. and Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9): 1078-1092.
[2] Charnes, A., Cooper, W. W. and Rhodes, E. (1978). Measuring the efficient of
decision-making units. European Journal of Operational Research, 2: 429-444.
[3] Cooper, W. W., Seiford, L. M. and Tone, K. (2000). Data envelopment analysis: A
comprehensive text with models, applications, references, and DEA-solver software.
Kluwer Academic Publishers, Boston.
[4] Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal statistical Society, A, 120(3): 253-290.
[5] Hsieh, K.-L, Tong, L.-I, Chiu, H.-P. and Yeh, H.-Y. (2005). Optimization of a multiresponse problem in Taguchi’s dynamic system. Computers and Industrial Engineering, 49: 556-571.
[6] Per, A. and Niels, C. P. (1993). A procedure for ranking efficient units in data
envelopment analysis. Management Science, 39(10): 1261-1264.
[7] Tomishima A. (1984). Tolerance design by performance analysis design: An example of temperature control device. Reliability Design Case Studies for New Product Development, Taguchi G (ed.). Japanese Standard Association: Japan, 213-220.
[8] Tong, L.-I, Wang, C.-H. and Houng, J.-Y. (2001). Optimizing dynamic multiresponses problems by using dual response surface method. Quality Engineering,
14: 115-125.
[9] Tong, L.-I, Wang, C.-H., Chen, C.-C. and Chen, C.-T. (2004). Dynamic multiple
responses by ideal solution analysis. European Journal of Operational Research, 156:
433-444.
[10] Tsai, C.-W and Tong, L.-I. (2008), Optimization of multiple responses from designed experiments by using data envelopment analysis and the group method of data handling. Journal of Quality, 15(4): 259-268. (In Chinese)
[11] Tong, L.-I, Wang, C.-H. and Tsai, C.-W. (2008). Robust design for multiple dynamic quality characteristics using data envelopment analysis. Quality and Reliability Engineering International, 24(5): 557-571.
[12] Wu, F. C. and Chyu, C. C. (2004). Optimization of robust design for multiple quality characteristics. International Journal of Production Research, 42(2): 337-354.
[13] Wu, F.-C and Yeh, C.-H. (2005). Robust design of multiple dynamic quality characteristics. International Journal of Advanced Manufacturing Technology, 25: 579-588.
[14] Wade, D. C. and Larry, M. S. (2009). Data envelopment analysis (DEA) - Thirty
years on. European Journal of Operational Research, 192(1): 1-17.