| Project/Area Number |
15K15952
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Statistical science
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| Research Institution | Keio University |
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Principal Investigator |
MATSUURA Shun 慶應義塾大学, 理工学部(矢上), 准教授 (70583368)
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 応答曲面法 / 実験計画法 / 中心複合計画 / 分散共分散行列 / 予測精度 / 欠測データ / 重回帰モデル / 共変推定量 / 変数選択 / 正規性検定 / 調合誤差因子実験 / パラメータ設計 / 応答分散 / 相関係数 / 過飽和実験計画 / リッジ回帰 / D最適規準 / 統計的品質管理 / 調合誤差因子 / 多変量管理図 |
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| Outline of Final Research Achievements |
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.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では，製品・工程の設計で用いられる応答曲面法に関連する統計的品質管理手法，多変量解析手法の基礎的研究に取り組み，新たな解析手法の提案およびその理論の発展を行った．具体的には，過飽和応答曲面計画，多応答曲面の同時推定，調合誤差因子実験，欠測データを伴う応答曲面推定などに関する統計学的課題に対して成果を得た．これらの研究成果は，品質管理・工程設計において応答曲面法がより有効に活用されるための基礎を提供すると考える．
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