Design and Analysis of Experiments

じっけんけいかくやの図書室から、Douglas C. Montgomery 「Design and Analysis of Experiments」をご紹介します。

内容の紹介

700ページを超える大ボリュームで実験計画法を網羅している名著です。統計学の基礎から始まり応答曲面法までたっぷり、じっくりと解説されています。
もちろん全編英語です。海外では主流の書籍だとか。（誰か日本語版をつくってほしい…）

第３章までを統計学の基礎である検定や推定、分散分析の説明に費やしており、第４章からいよいよ実験計画法の説明が始まります。
実験回数を削減していく方法の解説は第６章から始まり、日本スタイルの直交表（Orthogonal Array）という用語は現れず、一部実施要因計画（Fractional Factorial Design）として紹介されます。

数学の知識もそこまで必要ではないため、実験計画法を時間をかけてしっかり学びたい＆英語でも抵抗がない、という人にオススメです。

必要な前提知識

全体的に丁寧な解説が多いので高校レベルの数学（Σの計算や行列計算の方法）を理解できていれば問題なく読めると思います。

目次

• 1 Introduction
  • 1.1 Strategy of Experimentation
  • 1.2 Some Typical Applications of Experimental Design
  • 1.3 Basic Principles
  • 1.4 Guidelines for Designing Experiments
  • 1.5 A Brief History of Statistical Design
  • 1.6 Summary: Using Statistical Techniques in Experimentation

• 2 Simple Comparative Experiments
  • 2.1 Introduction
  • 2.2 Basic Statistical Concepts
  • 2.3 Sampling and Sampling Distributions
  • 2.4 Inferences About the Differences in Means, Randomized Designs
    • 2.4.1 Hypothesis Testing
    • 2.4.2 Confidence Intervals
    • 2.4.3 Choice of Sample Size
    • 2.4.4 The Case Where 𝜎²₁ ≠ 𝜎²₂
    • 2.4.5 The Case Where 𝜎²₁ and 𝜎²₂ Are Known
    • 2.4.6 Comparing a Single Mean to a Specified Value
    • 2.4.7 Summary
  • 2.5 Inferences About the Differences in Means, Paired Comparison Designs
    • 2.5.1 The Paired Comparison Problem
    • 2.5.2 Advantages of the Paired Comparison Design
  • 2.6 Inferences About the Variances of Normal Distributions

• 3 Experiments with a Single Factor: The Analysis of Variance
  • 3.1 An Example
  • 3.2 The Analysis of Variance
  • 3.3 Analysis of the Fixed Effects Model
    • 3.3.1 Decomposition of the Total Sum of Squares
    • 3.3.2 Statistical Analysis
    • 3.3.3 Estimation of the Model Parameters
    • 3.3.4 Unbalanced Data
  • 3.4 Model Adequacy Checking
    • 3.4.1 The Normality Assumption
    • 3.4.2 Plot of Residuals in Time Sequence
    • 3.4.3 Plot of Residuals Versus Fitted Values
    • 3.4.4 Plots of Residuals Versus Other Variables
  • 3.5 Practical Interpretation of Results
    • 3.5.1 A Regression Model
    • 3.5.2 Comparisons Among Treatment Means
    • 3.5.3 Graphical Comparisons of Means
    • 3.5.4 Contrasts
    • 3.5.5 Orthogonal Contrasts
    • 3.5.6 Scheffé’s Method for Comparing All Contrasts
    • 3.5.7 Comparing Pairs of Treatment Means
    • 3.5.8 Comparing Treatment Means with a Control
  • 3.6 Sample Computer Output
  • 3.7 Determining Sample Size
    • 3.7.1 Operating Characteristic and Power Curves
    • 3.7.2 Confidence Interval Estimation Method
  • 3.8 Other Examples of Single-Factor Experiments
    • 3.8.1 Chocolate and Cardiovascular Health
    • 3.8.2 A Real Economy Application of a Designed Experiment
    • 3.8.3 Discovering Dispersion Effects
  • 3.9 The Random Effects Model
    • 3.9.1 A Single Random Factor
    • 3.9.2 Analysis of Variance for the Random Model
    • 3.9.3 Estimating the Model Parameters
  • 3.10 The Regression Approach to the Analysis of Variance
    • 3.10.1 Least Squares Estimation of the Model Parameters
    • 3.10.2 The General Regression Significance Test
  • 3.11 Nonparametric Methods in the Analysis of Variance
    • 3.11.1 The Kruskal–Wallis Test
    • 3.11.2 General Comments on the Rank Transformation
• 4 Randomized Blocks, Latin Squares, and Related Designs
  • 4.1 The Randomized Complete Block Design
    • 4.1.1 Statistical Analysis of the RCBD
    • 4.1.2 Model Adequacy Checking
    • 4.1.3 Some Other Aspects of the Randomized Complete Block Design
    • 4.1.4 Estimating Model Parameters and the General Regression Significance Test
  • 4.2 The Latin Square Design
  • 4.3 The Graeco-Latin Square Design
  • 4.4 Balanced Incomplete Block Designs
    • 4.4.1 Statistical Analysis of the BIBD
    • 4.4.2 Least Squares Estimation of the Parameters
    • 4.4.3 Recovery of Interblock Information in the BIBD
• 5 Introduction to Factorial Designs
  • 5.1 Basic Definitions and Principles
  • 5.2 The Advantage of Factorials
  • 5.3 The Two-Factor Factorial Design
    • 5.3.1 An Example
    • 5.3.2 Statistical Analysis of the Fixed Effects Model
    • 5.3.3 Model Adequacy Checking
    • 5.3.4 Estimating the Model Parameters
    • 5.3.5 Choice of Sample Size
    • 5.3.6 The Assumption of No Interaction in a Two-Factor Model
    • 5.3.7 One Observation per Cell
  • 5.4 The General Factorial Design
  • 5.5 Fitting Response Curves and Surfaces
  • 5.6 Blocking in a Factorial Design
• 6 The 2^k Factorial Design
  • 6.1 Introduction
  • 6.2 The 2² Design
  • 6.3 The 2³ Design
  • 6.4 The General 2^k Design
  • 6.5 A Single Replicate of the 2^k Design
  • 6.6 Additional Examples of Unreplicated 2^k Designs
  • 6.7 2^k Designs are Optimal Designs
  • 6.8 The Addition of Center Points to the 2^k Design
  • 6.9 Why We Work with Coded Design Variables
• 7 Blocking and Confounding in the 2^k Factorial Design
  • 7.1 Introduction
  • 7.2 Blocking a Replicated 2^k Factorial Design
  • 7.3 Confounding in the 2^k Factorial Design
  • 7.4 Confounding the 2^k Factorial Design in Two Blocks
  • 7.5 Another Illustration of Why Blocking is Important
  • 7.6 Confounding the 2^k Factorial Design in Four Blocks
  • 7.7 Confounding the 2^k Factorial Design in 2^p Blocks
  • 7.8 Partial Confounding
• 8 Two-Level Fractional Factorial Designs
  • 8.1 Introduction
  • 8.2 The One-Half Fraction of the 2^k Design
    • 8.2.1 Definitions and Basic Principles
    • 8.2.2 Design Resolution
    • 8.2.3 Construction and Analysis of the One-Half Fraction
  • 8.3 The One-Quarter Fraction of the 2^k Design
  • 8.4 The General 2^k−pFractional Factorial Design
    • 8.4.1 Choosing a Design
    • 8.4.2 Analysis of 2^k−pFractional Factorials
    • 8.4.3 Blocking Fractional Factorials
  • 8.5 Alias Structures in Fractional Factorials and Other Designs
  • 8.6 Resolution III Designs
    • 8.6.1 Constructing Resolution III Designs
    • 8.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects
    • 8.6.3 Plackett–Burman Designs
  • 8.7 Resolution IV and V Designs
    • 8.7.1 Resolution IV Designs
    • 8.7.2 Sequential Experimentation with Resolution IV Designs
    • 8.7.3 Resolution V Designs
  • 8.8 Supersaturated Designs
  • 8.9 Summary
• 9 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs
  • 9.1 The 3^k Factorial Design
    • 9.1.1 Notation and Motivation for the 3^k Design
    • 9.1.2 The 3² Design
    • 9.1.3 The 3³ Design
    • 9.1.4 The General 3^k Design
  • 9.2 Confounding in the 3^k Factorial Design
    • 9.2.1 The 3^k Factorial Design in Three Blocks
    • 9.2.2 The 3^k Factorial Design in Nine Blocks
    • 9.2.3 The 3^k Factorial Design in 3^p Blocks
  • 9.3 Fractional Replication of the 3^k Factorial Design
    • 9.3.1 The One-Third Fraction of the 3^k Factorial Design
    • 9.3.2 Other 3^k−pFractional Factorial Designs
  • 9.4 Factorials with Mixed Levels
    • 9.4.1 Factors at Two and Three Levels
    • 9.4.2 Factors at Two and Four Levels
  • 9.5 Nonregular Fractional Factorial Designs
    • 9.5.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs
    • 9.5.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs
    • 9.5.3 Analysis of Nonregular Fractional Factorial Designs
  • 9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool
    • 9.6.1 Design Optimality Criterion
    • 9.6.2 Examples of Optimal Designs
    • 9.6.3 Extensions of the Optimal Design Approach
• 10 Fitting Regression Models
  • 10.1 Introduction
  • 10.2 Linear Regression Models
  • 10.3 Estimation of the Parameters in Linear Regression Models
  • 10.4 Hypothesis Testing in Multiple Regression
    • 10.4.1 Test for Significance of Regression
    • 10.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients
  • 10.5 Confidence Intervals in Multiple Regression
    • 10.5.1 Confidence Intervals on the Individual Regression Coefficients
    • 10.5.2 Confidence Interval on the Mean Response
  • 10.6 Prediction of New Response Observations
  • 10.7 Regression Model Diagnostics
    • 10.7.1 Scaled Residuals and PRESS
    • 10.7.2 Influence Diagnostics
  • 10.8 Testing for Lack of Fit
• 11 Response Surface Methods and Designs
  • 11.1 Introduction to Response Surface Methodology
  • 11.2 The Method of Steepest Ascent
  • 11.3 Analysis of a Second-Order Response Surface
    • 11.3.1 Location of the Stationary Point
    • 11.3.2 Characterizing the Response Surface
    • 11.3.3 Ridge Systems
    • 11.3.4 Multiple Responses
  • 11.4 Experimental Designs for Fitting Response Surfaces
    • 11.4.1 Designs for Fitting the First-Order Model
    • 11.4.2 Designs for Fitting the Second-Order Model
    • 11.4.3 Blocking in Response Surface Designs
    • 11.4.4 Optimal Designs for Response Surfaces
  • 11.5 Experiments with Computer Models
  • 11.6 Mixture Experiments
  • 11.7 Evolutionary Operation
• 12 Robust Parameter Design and Process Robustness Studies
  • 12.1 Introduction
  • 12.2 Crossed Array Designs
  • 12.3 Analysis of the Crossed Array Design
  • 12.4 Combined Array Designs and the Response Model Approach
  • 12.5 Choice of Designs
• 13 Experiments with Random Factors
  • 13.1 Random Effects Models
  • 13.2 The Two-Factor Factorial with Random Factors
  • 13.3 The Two-Factor Mixed Model
  • 13.4 Rules for Expected Mean Squares
  • 13.5 Approximate F-Tests
  • 13.6 Some Additional Topics on Estimation of Variance Components
    • 13.6.1 Approximate Confidence Intervals on Variance Components
    • 13.6.2 The Modified Large-Sample Method
• 14 Nested and Split-Plot Designs
  • 14.1 The Two-Stage Nested Design
    • 14.1.1 Statistical Analysis
    • 14.1.2 Diagnostic Checking
    • 14.1.3 Variance Components
    • 14.1.4 Staggered Nested Designs
  • 14.2 The General m-Stage Nested Design
  • 14.3 Designs with Both Nested and Factorial Factors
  • 14.4 The Split-Plot Design
  • 14.5 Other Variations of the Split-Plot Design
    • 14.5.1 Split-Plot Designs with More Than Two Factors
    • 14.5.2 The Split-Split-Plot Design
    • 14.5.3 The Strip-Split-Plot Design
• 15 Other Design and Analysis Topics (Available in e-text for students)
  • Problems
  • Appendix
  • Table I. Cumulative Standard Normal Distribution
  • Table II. Percentage Points of the t Distribution
  • Table III. Percentage Points of the 𝜒 ² Distribution
  • Table IV. Percentage Points of the F Distribution
  • Table V. Percentage Points of the Studentized Range Statistic
  • Table VI. Critical Values for Dunnett’s Test for Comparing Treatments with a Control
  • Table VII. Coefficients of Orthogonal Polynomials
  • Table VIII. Alias Relationships for 2^k−pFractional Factorial Designs with k ≤ 15 and n ≤ 64
  • OC Bibliography (Available in e-text for students)
  • Index

更新履歴

2025/7/21　公開