Design and Analysis of Experiments

ISBN-13: 9781119816959 / Angielski / Miękka / 2021 / 688 str.

Douglas C. Montgomery

Spis treści

OC Content available in eBookSS Student solution available in interactive e-textPreface iii1 Introduction 11.1 Strategy of Experimentation 11.2 Some Typical Applications of Experimental Design 71.3 Basic Principles 111.4 Guidelines for Designing Experiments 131.5 A Brief History of Statistical Design 191.6 Summary: Using Statistical Techniques in Experimentation 202 Simple Comparative Experiments 222.1 Introduction 222.2 Basic Statistical Concepts 232.3 Sampling and Sampling Distributions 272.4 Inferences About the Differences in Means, Randomized Designs 322.4.1 Hypothesis Testing 322.4.2 Confidence Intervals 382.4.3 Choice of Sample Size 392.4.4 The Case Where sigma21 <> sigma22 432.4.5 The Case Where sigma21 and sigma22 Are Known 452.4.6 Comparing a Single Mean to a Specified Value 462.4.7 Summary 472.5 Inferences About the Differences in Means, Paired Comparison Designs 472.5.1 The Paired Comparison Problem 472.5.2 Advantages of the Paired Comparison Design 502.6 Inferences About the Variances of Normal Distributions 523 Experiments with a Single Factor: The Analysis of Variance 553.1 An Example 553.2 The Analysis of Variance 583.3 Analysis of the Fixed Effects Model 593.3.1 Decomposition of the Total Sum of Squares 603.3.2 Statistical Analysis 623.3.3 Estimation of the Model Parameters 663.3.4 Unbalanced Data 683.4 Model Adequacy Checking 683.4.1 The Normality Assumption 693.4.2 Plot of Residuals in Time Sequence 713.4.3 Plot of Residuals Versus Fitted Values 713.4.4 Plots of Residuals Versus Other Variables 763.5 Practical Interpretation of Results 763.5.1 A Regression Model 773.5.2 Comparisons Among Treatment Means 783.5.3 Graphical Comparisons of Means 783.5.4 Contrasts 793.5.5 Orthogonal Contrasts 823.5.6 Scheffé's Method for Comparing All Contrasts 833.5.7 Comparing Pairs of Treatment Means 853.5.8 Comparing Treatment Means with a Control 883.6 Sample Computer Output 893.7 Determining Sample Size 933.7.1 Operating Characteristic and Power Curves 933.7.2 Confidence Interval Estimation Method 943.8 Other Examples of Single-Factor Experiments 953.8.1 Chocolate and Cardiovascular Health 953.8.2 A Real Economy Application of a Designed Experiment 973.8.3 Discovering Dispersion Effects 993.9 The Random Effects Model 1013.9.1 A Single Random Factor 1013.9.2 Analysis of Variance for the Random Model 1023.9.3 Estimating the Model Parameters 1033.10 The Regression Approach to the Analysis of Variance 1093.10.1 Least Squares Estimation of the Model Parameters 1103.10.2 The General Regression Significance Test 1113.11 Nonparametric Methods in the Analysis of Variance 1133.11.1 The Kruskal-Wallis Test 1133.11.2 General Comments on the Rank Transformation 1144 Randomized Blocks, Latin Squares, and Related Designs 1154.1 The Randomized Complete Block Design 1154.1.1 Statistical Analysis of the RCBD 1174.1.2 Model Adequacy Checking 1254.1.3 Some Other Aspects of the Randomized Complete Block Design 1254.1.4 Estimating Model Parameters and the General Regression Significance Test 1304.2 The Latin Square Design 1334.3 The Graeco-Latin Square Design 1404.4 Balanced Incomplete Block Designs 1424.4.1 Statistical Analysis of the BIBD 1434.4.2 Least Squares Estimation of the Parameters 1474.4.3 Recovery of Interblock Information in the BIBD 1495 Introduction to Factorial Designs 1525.1 Basic Definitions and Principles 1525.2 The Advantage of Factorials 1555.3 The Two-Factor Factorial Design 1565.3.1 An Example 1565.3.2 Statistical Analysis of the Fixed Effects Model 1595.3.3 Model Adequacy Checking 1645.3.4 Estimating the Model Parameters 1675.3.5 Choice of Sample Size 1695.3.6 The Assumption of No Interaction in a Two-Factor Model 1705.3.7 One Observation per Cell 1715.4 The General Factorial Design 1745.5 Fitting Response Curves and Surfaces 1795.6 Blocking in a Factorial Design 1886 The 2k Factorial Design 1946.1 Introduction 1946.2 The 22 Design 1956.3 The 23 Design 2036.4 The General 2k Design 2156.5 A Single Replicate of the 2k Design 2186.6 Additional Examples of Unreplicated 2k Designs 2316.7 2k Designs are Optimal Designs 2436.8 The Addition of Center Points to the 2k Design 2486.9 Why We Work with Coded Design Variables 2537 Blocking and Confounding in the 2k Factorial Design 2567.1 Introduction 2567.2 Blocking a Replicated 2k Factorial Design 2567.3 Confounding in the 2k Factorial Design 2597.4 Confounding the 2k Factorial Design in Two Blocks 2597.5 Another Illustration of Why Blocking is Important 2677.6 Confounding the 2k Factorial Design in Four Blocks 2687.7 Confounding the 2k Factorial Design in 2p Blocks 2707.8 Partial Confounding 2718 Two-Level Fractional Factorial Designs 2748.1 Introduction 2748.2 The One-Half Fraction of the 2k Design 2758.2.1 Definitions and Basic Principles 2758.2.2 Design Resolution 2788.2.3 Construction and Analysis of the One-Half Fraction 2788.3 The One-Quarter Fraction of the 2k Design 2908.4 The General 2k.pFractional Factorial Design 2978.4.1 Choosing a Design 2978.4.2 Analysis of 2k.pFractional Factorials 3008.4.3 Blocking Fractional Factorials 3018.5 Alias Structures in Fractional Factorials and Other Designs 3068.6 Resolution III Designs 3088.6.1 Constructing Resolution III Designs 3088.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects 3108.6.3 Plackett-Burman Designs 3138.7 Resolution IV and V Designs 3228.7.1 Resolution IV Designs 3228.7.2 Sequential Experimentation with Resolution IV Designs 3238.7.3 Resolution V Designs 3298.8 Supersaturated Designs 3298.9 Summary 3319 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 3329.1 The 3k Factorial Design 3339.1.1 Notation and Motivation for the 3k Design 3339.1.2 The 32 Design 3349.1.3 The 33 Design 3359.1.4 The General 3k Design 3409.2 Confounding in the 3k Factorial Design 3409.2.1 The 3k Factorial Design in Three Blocks 3409.2.2 The 3k Factorial Design in Nine Blocks 3439.2.3 The 3k Factorial Design in 3p Blocks 3449.3 Fractional Replication of the 3k Factorial Design 3459.3.1 The One-Third Fraction of the 3k Factorial Design 3459.3.2 Other 3k.pFractional Factorial Designs 3489.4 Factorials with Mixed Levels 3499.4.1 Factors at Two and Three Levels 3499.4.2 Factors at Two and Four Levels 3519.5 Nonregular Fractional Factorial Designs 3529.5.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs 3549.5.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs 3629.5.3 Analysis of Nonregular Fractional Factorial Designs 3689.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 3699.6.1 Design Optimality Criterion 3709.6.2 Examples of Optimal Designs 3709.6.3 Extensions of the Optimal Design Approach 37810 Fitting Regression Models 38210.1 Introduction 38210.2 Linear Regression Models 38310.3 Estimation of the Parameters in Linear Regression Models 38410.4 Hypothesis Testing in Multiple Regression 39510.4.1 Test for Significance of Regression 39510.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients 39710.5 Confidence Intervals in Multiple Regression 39910.5.1 Confidence Intervals on the Individual Regression Coefficients 40010.5.2 Confidence Interval on the Mean Response 40010.6 Prediction of New Response Observations 40110.7 Regression Model Diagnostics 40210.7.1 Scaled Residuals and PRESS 40210.7.2 Influence Diagnostics 40510.8 Testing for Lack of Fit 40511 Response Surface Methods and Designs 40811.1 Introduction to Response Surface Methodology 40811.2 The Method of Steepest Ascent 41111.3 Analysis of a Second-Order Response Surface 41611.3.1 Location of the Stationary Point 41611.3.2 Characterizing the Response Surface 41811.3.3 Ridge Systems 42411.3.4 Multiple Responses 42511.4 Experimental Designs for Fitting Response Surfaces 43011.4.1 Designs for Fitting the First-Order Model 43011.4.2 Designs for Fitting the Second-Order Model 43011.4.3 Blocking in Response Surface Designs 43711.4.4 Optimal Designs for Response Surfaces 44011.5 Experiments with Computer Models 45411.6 Mixture Experiments 46111.7 Evolutionary Operation 47212 Robust Parameter Design and Process Robustness Studies 47712.1 Introduction 47712.2 Crossed Array Designs 47912.3 Analysis of the Crossed Array Design 48112.4 Combined Array Designs and the Response Model Approach 48412.5 Choice of Designs 49013 Experiments with Random Factors 49313.1 Random Effects Models 49313.2 The Two-Factor Factorial with Random Factors 49413.3 The Two-Factor Mixed Model 50013.4 Rules for Expected Mean Squares 50513.5 Approximate F-Tests 50813.6 Some Additional Topics on Estimation of Variance Components 51213.6.1 Approximate Confidence Intervals on Variance Components 51213.6.2 The Modified Large-Sample Method 51614 Nested and Split-Plot Designs 51814.1 The Two-Stage Nested Design 51814.1.1 Statistical Analysis 51914.1.2 Diagnostic Checking 52414.1.3 Variance Components 52614.1.4 Staggered Nested Designs 52614.2 The General m-Stage Nested Design 52814.3 Designs with Both Nested and Factorial Factors 53014.4 The Split-Plot Design 53414.5 Other Variations of the Split-Plot Design 54014.5.1 Split-Plot Designs with More Than Two Factors 54014.5.2 The Split-Split-Plot Design 54514.5.3 The Strip-Split-Plot Design 54915 Other Design and Analysis Topics (Available in e-text for students) W-1Problems P-1Appendix A-1Table I. Cumulative Standard Normal Distribution A-2Table II. Percentage Points of the t Distribution A-4Table III. Percentage Points of the Chi-Square Distribution A-5Table IV. Percentage Points of the F Distribution A-6Table V. Percentage Points of the Studentized Range Statistic A-11Table VI. Critical Values for Dunnett's Test for Comparing Treatments with a Control A-13Table VII. Coefficients of Orthogonal Polynomials A-15Table VIII. Alias Relationships for 2k.pFractional Factorial Designs with k <= 15 and n <= 64 A-16OC Bibliography (Available in e-text for students) B-1Index I-1