応答曲面法は，製品特性や品質特性 (応答) と，(複数の) 設計因子の値との関係について，実験計画法によって (主に) 2次曲面の式を推定し，応答の予測や最適化を行う統計理論・手法の体系である．応答曲面法で用いられる実験計画は応答曲面計画，応答と設計因子間の関係式は応答曲面式と呼ばれる．本研究では，推定する応答曲面式のパラメータ数が実験回数より多い過飽和応答曲面計画における変数選択法，応答が複数あり互いに相関を持つときの応答曲面式の同時推定，欠測データが生じた場合の応答曲面式の予測精度の評価，を中心に応答曲面法に関連する統計学的手法・多変量解析手法の提案と発展を行った．
Response surface methodology is composed of statistical theories and methods for estimating a functional relationship of (mainly) a second-order model between a product or quality characteristic (response) and the values of factors by the design of experiments and conducting prediction and optimization of the response. Experimental designs used in response surface methodology are called response surface designs and a functional relationship between the response and the factors is called a response surface model. In this research, statistical methods and multivariate analysis in response surface methodology were proposed and developed, such as variable selection methods for supersaturated response surface designs with more estimated parameters than experimental runs, simultaneous estimation of response surface models for multivariate responses having correlations, and evaluation of the prediction variance of the estimated response surface model with missing data.

研究種目 : 若手研究 (B)
研究期間 : 2015～2019
課題番号 : 15K15952
研究分野 : 統計科学