最佳反應值信賴區間之高效率估計法及其製程改善應用

Efficient Approximation of Confidence Intervals for Optimal Responses and Its Applications to Process Improvement

鄭佳惠(Chia-Hui Cheng)

指導教授 ： 陳正剛

國立臺灣大學/工學院/工業工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.00629

摘要

尋找最佳的參數設定值一直是工程師或實驗者關心的議題。對一個二次反應曲面模式而言，其目的是決定穩定點 (stationary point) 的位置、反應值，以及本質為何(最大值、最小值或馬鞍點)。但在抽樣變異的影響下，穩定點探究的品質是需要被考慮的。若穩定點反應值之信賴區間能夠準確地被估計，將有助於估計品質優劣的評斷。Carter, Chinchilli, Campbell and Wampler (1984) 和Carter, Chinchilli, Myers and Campbell (1986) 分別提出了計算未受限和受限的最佳反應值信賴區間的估計，其信心水準至少在100(1-

關鍵字

最佳反應值 ； 製程改善 ； 信賴區間

並列摘要

Moving the operating conditions toward the optimum is always a critical issue for engineers or experimenters. For an empirical second-order response surface model, the objective is to determine the location, response and nature of the stationary point. However, the quality of the stationary point exploration may be in question under sampling variability. It will be therefore helpful if the confidence interval of the stationary-point response can be accurately estimated. Carter, Chinchilli, Campbell and Wampler (1984) and Carter, Chinchilli, Myers and Campbell (1986) have respectively described procedures for computing the conservative 100(1-

並列關鍵字

process improvement ； confidence interval ； optimal response

參考文獻

[1] Atkinson, A. C., and Donev, A. N. (1992), Optimum Experimental Designs, Clarendon Press, Oxford.

[2] Bisgaard, S., and Ankenman, B. (1996), “Standard Errors for the Eigenvalues in Second-order Response Surface Models”, Technometrics, 38, 238-246.

[3] Box, G. E. P., and Draper, N. R. (1987), Empirical Model-Building and Response Surfaces, John Wiley & Sons, New York.

[4] Broudiscou, A., Leardi, R., and Phan-Tan-Luu R. (1996), “Genetic Algorithm as a Tool for Selection of D-optimal design”, Chemometrics and Intelligent Laboratory Systems, 35, 105-116.

[5] Carter, W. H., Jr., Chinchilli, V. M., and Campbell, E. D. (1990), “A Large-Sample Confidence Region Useful in Characterizing the Stationary Point of a Quadratic Response Surface”, Technometrics, 32, 425-435.