Optimal Design of Experiments: A Case Study Approach
Optimal Design of Experiments: A Case Study Approach
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DOI：
10.1002/9781119974017
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
P. Goos;B. Jones
中科院分区：
文献类型：
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作者：
P. Goos;B. Jones
前言。1一个简单的比较实验。1.1关键概念。1.2对比实验的设置。1.3总结。2最佳筛选实验。2.1关键概念。2.2案例：提取实验。2.2.1问题与设计。2.2.2数据分析。2.3窥探黑盒子。2.3.1主效应模型。2.3.2双因素交互效应模型。2.3.3因子缩放。2.3.4普通最小二乘估计。2.3.5显著性检验和统计功效计算。2.3.6方差膨胀。2.3.7混叠2.3.8优化设计2.3.9生成最优实验设计。2.3.10再次进行提取实验。2.3.11筛选成功的原则：稀疏性、层次性和遗传性。2.4背景阅读。2.4.1筛选。2.4.2寻找最佳设计的算法。2.5总结。3筛选实验添加运行数。3.1关键概念。3.2病例：增强提取实验。3.2.1问题与设计。3.2.2数据分析。3.3窥视黑匣子。3.3.1跟踪设计的优化选择。3.3.2设计构造算法。3.3.3折叠设计。3.4背景阅读。3.5总结。4带有分类因子的响应面设计。4.1关键概念。4.2案例：稳健的最优工艺实验。4.2.1问题与设计。4.2.2数据分析。4.3窥视黑盒子。4.3.1二次效应。4.3.2多级分类因素的虚拟变量。4.3.3计算d效率。4.3.4构建设计空间地块分数。4.3.5计算预测的平均相对方差。4.3.6计算i效率。4.3.7保证基于普通最小二乘的推理的有效性。4.3.8设计区域。4.4背景阅读。5不规则形状设计区域的响应面设计。5.1关键概念。5.2案例：产量最大化实验。5.2.1问题与设计。5.2.2数据分析。5.3窥视黑匣子。5.3.1三次因子效应。5.3.2欠拟合检验。5.3.3在设计构造算法中加入因子约束。5.4背景阅读。6带有工艺变量的“混合”实验。6.1关键概念。6.2案例：轧机实验。6.2.1问题与设计。6.2.2数据分析。6.3窥探黑盒子。6.3.1混合约束。6.3.2混合约束对模型的影响。6.3.3混合实验数据常用模型。6.3.4混合料试验优化设计。6.3.5设计混合试验构建算法。6.4背景阅读。6.5总结。7分块响应面设计。7.1关键概念。7.2案例：油酥面团实验。7.2.1问题与设计。7.2.2数据分析。7.3窥视黑盒子。7.3.1模型。7.3.2广义最小二乘估计7.3.3方差分量的估计。7.3.4显著性检验。7.3.5分组实验的优化设计。7.3.6正交分块。7.3.7最优与正交块。7.4背景阅读。7.5总结。8分块筛选实验。8.1关键概念。8.2案例：稳定性改善实验。8.2.1问题与设计。8.2.2关于设计问题的事后思考。8.2.3数据分析。8.3窥视黑盒子。8.3.1涉及块效应的模型。8.3.2固定方块效果。8.4背景阅读。8.5总结。9存在协变量时的实验设计。9.1关键概念。9.2案例：聚丙烯实验。9.2.1问题与设计。9.2.2数据分析。9.3窥视黑盒子。9.3.1协变量或伴随变量。9.3.2存在协变量时的模型和设计准则。9.3.3设计对时间趋势具有鲁棒性。9.3.4设计构造算法。9.3.5随机化或不随机化。9.3.6最后的想法。9.4背景阅读。10分块情节设计。10.1关键概念。10.2案例：风洞实验。10.2.1问题与设计。10.2.2数据分析。10.3窥探黑盒子。10.3.1分割图术语。10.3.2模型。10.3.3从分裂图设计推断。10.3.4伪装成分裂情节设计。10.3.5要求的整块和运行数。10.3.6分块试验的优化设计。10.3.7最优分块设计的设计构建算法。10.3.8分图实验数据分析困难。10.4背景阅读。10.5总结。11双向分块设计。11.1关键概念。11.2案例：电池电芯实验。11.2.1问题与设计。11.2.2数据分析。11.3窥探黑盒子。11.3.1双向分割图模型。11.3.2广义最小二乘估计。11.3.3双向分裂图实验的优化设计。11.3.4 d -最优双向分割图设计的设计构建算法。11.3.5扩展和相关设计。11.4背景阅读。11.5总结。参考书目。索引。
Preface. Acknowledgments. 1 A simple comparative experiment. 1.1 Key concepts. 1.2 The setup of a comparative experiment. 1.3 Summary. 2 An optimal screening experiment. 2.1 Key concepts. 2.2 Case: an extraction experiment. 2.2.1 Problem and design. 2.2.2 Data analysis. 2.3 Peek into the black box. 2.3.1 Main-effects models. 2.3.2 Models with two-factor interaction effects. 2.3.3 Factor scaling. 2.3.4 Ordinary least squares estimation. 2.3.5 Significance tests and statistical power calculations. 2.3.6 Variance inflation. 2.3.7 Aliasing. 2.3.8 Optimal design. 2.3.9 Generating optimal experimental designs. 2.3.10 The extraction experiment revisited. 2.3.11 Principles of successful screening: sparsity, hierarchy, and heredity. 2.4 Background reading. 2.4.1 Screening. 2.4.2 Algorithms for finding optimal designs. 2.5 Summary. 3 Adding runs to a screening experiment. 3.1 Key concepts. 3.2 Case: an augmented extraction experiment. 3.2.1 Problem and design. 3.2.2 Data analysis. 3.3 Peek into the black box. 3.3.1 Optimal selection of a follow-up design. 3.3.2 Design construction algorithm. 3.3.3 Foldover designs. 3.4 Background reading. 3.5 Summary. 4 A response surface design with a categorical factor. 4.1 Key concepts. 4.2 Case: a robust and optimal process experiment. 4.2.1 Problem and design. 4.2.2 Data analysis. 4.3 Peek into the black box. 4.3.1 Quadratic effects. 4.3.2 Dummy variables for multilevel categorical factors. 4.3.3 Computing D-efficiencies. 4.3.4 Constructing Fraction of Design Space plots. 4.3.5 Calculating the average relative variance of prediction. 4.3.6 Computing I-efficiencies. 4.3.7 Ensuring the validity of inference based on ordinary least squares. 4.3.8 Design regions. 4.4 Background reading. 4.5 Summary. 5 A response surface design in an irregularly shaped design region. 5.1 Key concepts. 5.2 Case: the yield maximization experiment. 5.2.1 Problem and design. 5.2.2 Data analysis. 5.3 Peek into the black box. 5.3.1 Cubic factor effects. 5.3.2 Lack-of-fit test. 5.3.3 Incorporating factor constraints in the design construction algorithm. 5.4 Background reading. 5.5 Summary. 6 A "mixture" experiment with process variables. 6.1 Key concepts. 6.2 Case: the rolling mill experiment. 6.2.1 Problem and design. 6.2.2 Data analysis. 6.3 Peek into the black box. 6.3.1 The mixture constraint. 6.3.2 The effect of the mixture constraint on the model. 6.3.3 Commonly used models for data from mixture experiments. 6.3.4 Optimal designs for mixture experiments. 6.3.5 Design construction algorithms for mixture experiments. 6.4 Background reading. 6.5 Summary. 7 A response surface design in blocks. 7.1 Key concepts. 7.2 Case: the pastry dough experiment. 7.2.1 Problem and design. 7.2.2 Data analysis. 7.3 Peek into the black box. 7.3.1 Model. 7.3.2 Generalized least squares estimation. 7.3.3 Estimation of variance components. 7.3.4 Significance tests. 7.3.5 Optimal design of blocked experiments. 7.3.6 Orthogonal blocking. 7.3.7 Optimal versus orthogonal blocking. 7.4 Background reading. 7.5 Summary. 8 A screening experiment in blocks. 8.1 Key concepts. 8.2 Case: the stability improvement experiment. 8.2.1 Problem and design. 8.2.2 Afterthoughts about the design problem. 8.2.3 Data analysis. 8.3 Peek into the black box. 8.3.1 Models involving block effects. 8.3.2 Fixed block effects. 8.4 Background reading. 8.5 Summary. 9 Experimental design in the presence of covariates. 9.1 Key concepts. 9.2 Case: the polypropylene experiment. 9.2.1 Problem and design. 9.2.2 Data analysis. 9.3 Peek into the black box. 9.3.1 Covariates or concomitant variables. 9.3.2 Models and design criteria in the presence of covariates. 9.3.3 Designs robust to time trends. 9.3.4 Design construction algorithms. 9.3.5 To randomize or not to randomize. 9.3.6 Final thoughts. 9.4 Background reading. 9.5 Summary. 10 A split-plot design. 10.1 Key concepts. 10.2 Case: the wind tunnel experiment. 10.2.1 Problem and design. 10.2.2 Data analysis. 10.3 Peek into the black box. 10.3.1 Split-plot terminology. 10.3.2 Model. 10.3.3 Inference from a split-plot design. 10.3.4 Disguises of a split-plot design. 10.3.5 Required number of whole plots and runs. 10.3.6 Optimal design of split-plot experiments. 10.3.7 A design construction algorithm for optimal split-plot designs. 10.3.8 Difficulties when analyzing data from split-plot experiments. 10.4 Background reading. 10.5 Summary. 11 A two-way split-plot design. 11.1 Key concepts. 11.2 Case: the battery cell experiment. 11.2.1 Problem and design. 11.2.2 Data analysis. 11.3 Peek into the black box. 11.3.1 The two-way split-plot model. 11.3.2 Generalized least squares estimation. 11.3.3 Optimal design of two-way split-plot experiments. 11.3.4 A design construction algorithm for D-optimal two-way split-plot designs. 11.3.5 Extensions and related designs. 11.4 Background reading. 11.5 Summary. Bibliography. Index.