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| موضوع: كتاب Design and Analysis of Experiments الجمعة 01 أكتوبر 2021, 10:42 pm | |
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أخواني في الله أحضرت لكم كتاب Design and Analysis of Experiments Ninth Edition DOUGLAS C. MONTGOMERY Arizona State University
و المحتوى كما يلي :
Contents Preface iii 1 Introduction 1 1.1 Strategy of Experimentation 1 1.2 Some Typical Applications of Experimental Design 7 1.3 Basic Principles 11 1.4 Guidelines for Designing Experiments 13 1.5 A Brief History of Statistical Design 19 1.6 Summary: Using Statistical Techniques in Experimentation 20 1.7 Problems 21 2 Simple Comparative Experiments 23 2.1 Introduction 24 2.2 Basic Statistical Concepts 25 2.3 Sampling and Sampling Distributions 28 2.4 Inferences About the Differences in Means, Randomized Designs 33 2.4.1 Hypothesis Testing 33 2.4.2 Confidence Intervals 39 2.4.3 Choice of Sample Size 41 2.4.4 The Case Where ????2 1 ≠ ????22 44 2.4.5 The Case Where ????2 1 and ????22 Are Known 47 2.4.6 Comparing a Single Mean to a Specified Value 47 2.4.7 Summary 48 2.5 Inferences About the Differences in Means, Paired Comparison Designs 50 2.5.1 The Paired Comparison Problem 50 2.5.2 Advantages of the Paired Comparison Design 52 2.6 Inferences About the Variances of Normal Distributions 53 2.7 Problems 55 ixx Contents 3 Experiments with a Single Factor: The Analysis of Variance 64 3.1 An Example 65 3.2 The Analysis of Variance 67 3.3 Analysis of the Fixed Effects Model 69 3.3.1 Decomposition of the Total Sum of Squares 69 3.3.2 Statistical Analysis 72 3.3.3 Estimation of the Model Parameters 76 3.3.4 Unbalanced Data 78 3.4 Model Adequacy Checking 78 3.4.1 The Normality Assumption 79 3.4.2 Plot of Residuals in Time Sequence 81 3.4.3 Plot of Residuals Versus Fitted Values 81 3.4.4 Plots of Residuals Versus Other Variables 86 3.5 Practical Interpretation of Results 86 3.5.1 A Regression Model 87 3.5.2 Comparisons Among Treatment Means 88 3.5.3 Graphical Comparisons of Means 88 3.5.4 Contrasts 89 3.5.5 Orthogonal Contrasts 92 3.5.6 Scheffé’s Method for Comparing All Contrasts 93 3.5.7 Comparing Pairs of Treatment Means 95 3.5.8 Comparing Treatment Means with a Control 98 3.6 Sample Computer Output 99 3.7 Determining Sample Size 103 3.7.1 Operating Characteristic and Power Curves 103 3.7.2 Confidence Interval Estimation Method 104 3.8 Other Examples of Single-Factor Experiments 105 3.8.1 Chocolate and Cardiovascular Health 105 3.8.2 A Real Economy Application of a Designed Experiment 107 3.8.3 Discovering Dispersion Effects 109 3.9 The Random Effects Model 111 3.9.1 A Single Random Factor 111 3.9.2 Analysis of Variance for the Random Model 112 3.9.3 Estimating the Model Parameters 113 3.10 The Regression Approach to the Analysis of Variance 119 3.10.1 Least Squares Estimation of the Model Parameters 120 3.10.2 The General Regression Significance Test 121 3.11 Nonparametric Methods in the Analysis of Variance 123 3.11.1 The Kruskal–Wallis Test 123 3.11.2 General Comments on the Rank Transformation 124 3.12 Problems 125 4 Randomized Blocks, Latin Squares, and Related Designs 135 4.1 The Randomized Complete Block Design 135 4.1.1 Statistical Analysis of the RCBD 137 4.1.2 Model Adequacy Checking 145 4.1.3 Some Other Aspects of the Randomized Complete Block Design 145 4.1.4 Estimating Model Parameters and the General Regression Significance Test 150Contents xi 4.2 The Latin Square Design 153 4.3 The Graeco-Latin Square Design 160 4.4 Balanced Incomplete Block Designs 162 4.4.1 Statistical Analysis of the BIBD 163 4.4.2 Least Squares Estimation of the Parameters 167 4.4.3 Recovery of Interblock Information in the BIBD 169 4.5 Problems 171 5 Introduction to Factorial Designs 179 5.1 Basic Definitions and Principles 179 5.2 The Advantage of Factorials 182 5.3 The Two-Factor Factorial Design 183 5.3.1 An Example 183 5.3.2 Statistical Analysis of the Fixed Effects Model 186 5.3.3 Model Adequacy Checking 191 5.3.4 Estimating the Model Parameters 194 5.3.5 Choice of Sample Size 196 5.3.6 The Assumption of No Interaction in a Two-Factor Model 197 5.3.7 One Observation per Cell 198 5.4 The General Factorial Design 201 5.5 Fitting Response Curves and Surfaces 206 5.6 Blocking in a Factorial Design 215 5.7 Problems 220 6 The 2k Factorial Design 230 6.1 Introduction 230 6.2 The 22 Design 231 6.3 The 23 Design 240 6.4 The General 2k Design 252 6.5 A Single Replicate of the 2k Design 254 6.6 Additional Examples of Unreplicated 2k Designs 268 6.7 2k Designs are Optimal Designs 280 6.8 The Addition of Center Points to the 2k Design 285 6.9 Why We Work with Coded Design Variables 290 6.10 Problems 292 7 Blocking and Confounding in the 2k Factorial Design 308 7.1 Introduction 308 7.2 Blocking a Replicated 2k Factorial Design 309 7.3 Confounding in the 2k Factorial Design 311 7.4 Confounding the 2k Factorial Design in Two Blocks 311 7.5 Another Illustration of Why Blocking Is Important 319 7.6 Confounding the 2k Factorial Design in Four Blocks 320xii Contents 7.7 Confounding the 2k Factorial Design in 2p Blocks 322 7.8 Partial Confounding 323 7.9 Problems 325 8 Two-Level Fractional Factorial Designs 328 8.1 Introduction 329 8.2 The One-Half Fraction of the 2k Design 329 8.2.1 Definitions and Basic Principles 329 8.2.2 Design Resolution 332 8.2.3 Construction and Analysis of the One-Half Fraction 332 8.3 The One-Quarter Fraction of the 2k Design 344 8.4 The General 2k−p Fractional Factorial Design 351 8.4.1 Choosing a Design 351 8.4.2 Analysis of 2k−p Fractional Factorials 354 8.4.3 Blocking Fractional Factorials 355 8.5 Alias Structures in Fractional Factorials and Other Designs 360 8.6 Resolution III Designs 362 8.6.1 Constructing Resolution III Designs 362 8.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects 364 8.6.3 Plackett–Burman Designs 367 8.7 Resolution IV and V Designs 376 8.7.1 Resolution IV Designs 376 8.7.2 Sequential Experimentation with Resolution IV Designs 377 8.7.3 Resolution V Designs 383 8.8 Supersaturated Designs 384 8.9 Summary 385 8.10 Problems 386 9 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 405 9.1 The 3k Factorial Design 406 9.1.1 Notation and Motivation for the 3k Design 406 9.1.2 The 32 Design 407 9.1.3 The 33 Design 408 9.1.4 The General 3k Design 413 9.2 Confounding in the 3k Factorial Design 413 9.2.1 The 3k Factorial Design in Three Blocks 413 9.2.2 The 3k Factorial Design in Nine Blocks 416 9.2.3 The 3k Factorial Design in 3p Blocks 417 9.3 Fractional Replication of the 3k Factorial Design 418 9.3.1 The One-Third Fraction of the 3k Factorial Design 418 9.3.2 Other 3k−p Fractional Factorial Designs 421 9.4 Factorials with Mixed Levels 422 9.4.1 Factors at Two and Three Levels 422 9.4.2 Factors at Two and Four Levels 424 9.5 Nonregular Fractional Factorial Designs 425Contents xiii 9.5.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs 427 9.5.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs 436 9.5.3 Analysis of Nonregular Fractional Factorial Designs 441 9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 442 9.6.1 Design Optimality Criterion 443 9.6.2 Examples of Optimal Designs 443 9.6.3 Extensions of the Optimal Design Approach 453 9.7 Problems 454 10 Fitting Regression Models (online at www.wiley.com/college/montgomery) 460 10.1 Introduction 461 10.2 Linear Regression Models 461 10.3 Estimation of the Parameters in Linear Regression Models 462 10.4 Hypothesis Testing in Multiple Regression 473 10.4.1 Test for Significance of Regression 473 10.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients 475 10.5 Confidence Intervals in Multiple Regression 478 10.5.1 Confidence Intervals on the Individual Regression Coefficients 478 10.5.2 Confidence Interval on the Mean Response 478 10.6 Prediction of New Response Observations 479 10.7 Regression Model Diagnostics 480 10.7.1 Scaled Residuals and PRESS 480 10.7.2 Influence Diagnostics 483 10.8 Testing for Lack of Fit 483 10.9 Problems 485 11 Response Surface Methods and Designs 489 11.1 Introduction to Response Surface Methodology 490 11.2 The Method of Steepest Ascent 492 11.3 Analysis of a Second-Order Response Surface 497 11.3.1 Location of the Stationary Point 497 11.3.2 Characterizing the Response Surface 499 11.3.3 Ridge Systems 505 11.3.4 Multiple Responses 506 11.4 Experimental Designs for Fitting Response Surfaces 511 11.4.1 Designs for Fitting the First-Order Model 511 11.4.2 Designs for Fitting the Second-Order Model 511 11.4.3 Blocking in Response Surface Designs 518 11.4.4 Optimal Designs for Response Surfaces 521 11.5 Experiments with Computer Models 535 11.6 Mixture Experiments 542 11.7 Evolutionary Operation 553 11.8 Problems 558xiv Contents 12 Robust Parameter Design and Process Robustness Studies (online at www.wiley.com/college/montgomery) 569 12.1 Introduction 569 12.2 Crossed Array Designs 571 12.3 Analysis of the Crossed Array Design 573 12.4 Combined Array Designs and the Response Model Approach 576 12.5 Choice of Designs 582 12.6 Problems 585 13 Experiments with Random Factors 589 13.1 Random Effects Models 589 13.2 The Two-Factor Factorial with Random Factors 590 13.3 The Two-Factor Mixed Model 597 13.4 Rules for Expected Mean Squares 602 13.5 Approximate F-Tests 605 13.6 Some Additional Topics on Estimation of Variance Components 609 13.6.1 Approximate Confidence Intervals on Variance Components 609 13.6.2 The Modified Large-Sample Method 613 13.7 Problems 615 14 Nested and Split-Plot Designs 618 14.1 The Two-Stage Nested Design 619 14.1.1 Statistical Analysis 619 14.1.2 Diagnostic Checking 624 14.1.3 Variance Components 626 14.1.4 Staggered Nested Designs 626 14.2 The General m-Stage Nested Design 628 14.3 Designs with Both Nested and Factorial Factors 630 14.4 The Split-Plot Design 634 14.5 Other Variations of the Split-Plot Design 640 14.5.1 Split-Plot Designs with More Than Two Factors 640 14.5.2 The Split-Split-Plot Design 645 14.5.3 The Strip-Split-Plot Design 649 14.6 Problems 650 15 Other Design and Analysis Topics (online at www.wiley.com/college/montgomery) 656 15.1 Nonnormal Responses and Transformations 657 15.1.1 Selecting a Transformation: The Box–Cox Method 657 15.1.2 The Generalized Linear Model 659Contents xv 15.2 Unbalanced Data in a Factorial Design 666 15.2.1 Proportional Data: An Easy Case 667 15.2.2 Approximate Methods 668 15.2.3 The Exact Method 670 15.3 The Analysis of Covariance 670 15.3.1 Description of the Procedure 671 15.3.2 Computer Solution 679 15.3.3 Development by the General Regression Significance Test 680 15.3.4 Factorial Experiments with Covariates 682 15.4 Repeated Measures 692 15.5 Problems 694 Appendix (online at www.wiley.com/college/montgomery) 697 Table I. Cumulative Standard Normal Distribution 698 Table II. Percentage Points of the t Distribution 700 Table III. Percentage Points of the ????2 Distribution 701 Table IV. Percentage Points of the F Distribution 702 Table V. Percentage Points of the Studentized Range Statistic 707 Table VI. Critical Values for Dunnett’s Test for Comparing Treatments with a Control 709 Table VII. Coefficients of Orthogonal Polynomials 711 Table VIII. Alias Relationships for 2k−p Fractional Factorial Designs with k ≤ 15 and n ≤ 64 712 Bibliography (online at www.wiley.com/college/montgomery) 724 Index 73 I n d e x 22 factorial design, 231 23 factorial design, 240 2k factorial design, 230, 252 2k−1fractional factorial design, 329 2k−2 design, 344 2k−p fractional factorial design, 351 32 factorial design, 406 33 factorial design, 407 3k factorial design, 405, 413 3k−1 fractional factorial design, 418 3k−p fractional factorial designs, 431 A Additivity of the Latin square, 154 Additivity of the RCBD, 145 Adjusted R2, 265, 475 Agricultural era of experimentation, 19 Agricultural versus industrial experiments, 19 Alias matrix, 360, 427 Aliases, 330 Allowed-to-vary factors, 15 Alternate fraction, 331 Alternative hypothesis, 34 Analysis of combined array designs, 576 (online, Chapter 12) Analysis of covariance as an alternative to blocking, 670, 679 (online, Chapter 15) Analysis of covariance, 136, 670 (online, Chapter 15) Analysis of variance (ANOVA), 67, 69, 73, 112 Analysis of variance identity for the RCBD, 138 Analysis of variance partition of the total sum of squares, 70 ANOVA F-test, 73 ANOVA method for estimating variance components, 113, 591 Approximate F-tests, 605 Assumptions in the t-test, 37 B Balanced incomplete block designs (BIBD), 162 Bartlett’s test for equality of variances, 82 Bayesian D-optimal designs, 453 Best-guess approach to experimentation, 4 Blocking, 11, 12, 135, 153, 215, 308, 518 Blocking fractional factorials, 355, 367 Blocking in a 2k design, 215, 308, 311 Blocking in response surface designs, 518 Box plot, 25, 66 Box-Behnken designs, 513 Box-Cox method for choosing a transformation, 657 (online, Chapter 15) Break through innovation, 2 C Canonical form of the second-order model, 499 Cause-and-effect diagram, 16 Center points in the 2k design, 285, 513 Central composite design (CCD), 288, 512, 513 Central limit theorem, 31 Chi-square distribution, 31 Chi-square test on the variance of a normal distribution, 53 Coded and natural variables, 236 Coded variables, 236, 290 Coding the data in ANOVA, 75 Column generators, 329, 344 Combined array designs, 572, 576 (online, Chapter 12) Comparison of means, 88, 95 Complete randomization, 11 Completely randomized design, 68 Components of interaction, 408 Components of variance model, 68, 111 Confidence interval for a contrast, 91 Confidence interval on the mean response in regression, 478 (online, Chapter 10) Confidence interval, 40, 41 Confidence intervals on means in ANOVA, 77 Confirmation runs, 18, 343 Confounding, 311, 320, 413 Constant variance assumption in ANOVA, 81 Constrained optimization, 508 Construction of optimal designs, 524 Contour plot, 499, 506 Contrasts, 89, 93 Controllable variables, 3 Cook’s distance, 483 (online, Chapter 10) 731732 Index Corrected sum of squares, 29 Critical region, 34 Crossed array designs, 571 (online Chapter 12) Crossover designs, 159 D Defining relation for a fractional factorial, 329 Definitive screening designs, 530 Degrees of freedom, 31 Design factors, 15 Design generators. 344 Design projection, 258 Design resolution, 332 Designs with nested and factorial factors, 630 Desirability function optimization, 508 Deterministic computer models, 535 Dispersion effects, 109 Distance based designs for mixture experiments, 551 D−optimal designs, 281 Dot diagram, 24, Dunnett’s test to compare means with a control, 98 E Eigenvalues, 499 Empirical models, 2 Equiradial design, 515 Estimating variance components, 113 Estimator, 28 Evolutionary operation (EVOP), 553 Expected mean squares, 71, 112 Expected value of a random variable, 27 Experiments with computer models, 535 Extra sum of squares method, 476 Extreme vertices designs for mixture experiments, 551 F Face-centered CCD, 514 Factor screening experiment, 13, 15 Factorial experiment, 4, 179 Factorial experiments with covariates, 682 (online, Chapter 15) F-distribution, 33 First-order model, 17 Fisher’s least significant difference (LSD) method to compare pairs of means, 97 Fixed effects model, 68 Fold over of fractional factorial designs, 364, 366, 377 Fold over of resolution III designs, 364, 366 Fraction of design space plot, 284, 517 Fractional factorial experiment, 7 Fractional factorial split-plot designs, 644 F-test on two variances of independent normal distributions, 54 Full model, 121, 476 G Gaussian process model, 537 Generalized interaction, 320, 344 Generalized linear model (GLM), 659 G-optimal designs, 282 Graeco-Latin square design, 160 Guidelines for designing experiments, 13 H Half-normal probability plot, 261 Hall designs, 427 Held-constant factors, 15 Histogram, 25 Hybrid designs, 516 Hypothesis testing, 24, 33 I Incremental innovation, 2 Influential observations in regression, 482 (online, Chapter 10) Innovation and designed experiments, 2 Interaction, 17, 180 Interblock information in the BIBD, 169 Interpretation of ANOVA results, 87 I-optimal designs, 282 K Kruskal-Wallis test, 123 L Lack of fit testing in regression, 483 (online, Chapter 10) Latin square designs, 153, 218 Lenth’s method, 262 Levene’s test for equality of variances, 83 Leverage points, 483 Linear predictor in the GLM, 660 (online, Chapter 15) Linear statistical model, 68 M Main effect of a factor, 17, 180 Mean of a distribution, 27 Means model, 67 Mechanistic models, 2 Method of least squares, 463 Method of steepest ascent, 239, 492 Minimal resolution IV designs, 376 Minimum variance estimator, 29 Missing values in the Latin square design, 157 Missing values in the RCBD, 149 Mixed level factorial designs, 422 Mixed models, 597 Mixture experiment, 10, 542 Multifactor split plot designs, 640 Multiple comparisons following ANOVA, 87, 93, 95, 142 Multiple response optimization, 506Index 733 N Nested designs, 619 Nested designs with m stages, 628 No-confounding designs, 428 Nonregular fractional factorial design, 369, 425, 427, 436, 447 Normal distribution, 30 Normal probability plot, 37 Normal probability plot of residuals, 79 Normal probability plotting of effects, 254 Normality assumption in ANOVA, 79 Nuisance factors, 135 Null hypothesis, 34 O One-factor-at-a-time (OFAT) approach to experimentation, 4 Operating characteristic curve, 42, 103 Optimal designs, 19, 280, 281, 282, 442, 522, 524 Optimal designs for mixture experiments, 547 Optimal designs for robustness studies, 582 Optimization experiment, 14 Orthogonal contrasts, 92 Orthogonal design, 233, 469 Outliers, 266, 480 P Paired comparison design, 47, 52 Paired t-test, 47 Partial aliasing, 36 Partial confounding, 314, 323 Partial fold over, 381 Partial F-test, 477 Path of steepest ascent, 492 Plackett-Burman designs, 367 Power curve, 42, 103 Power family of transformations, 657 (online, Chapter 15) Power of a test, 34 Prediction interval, 479 Prediction of new observations in regression, 479 (online, Chapter 10) Pre-experimental planning, 17 PRESS statistic, 99, 482 (online, Chapter 10) Principal block, 314, 321 Principal fraction, 330 Probability distributions, 26 Projection of fractional factorials, 354 Projection property, 329 P-value, 36 Q Quantitative versus qualitative factors in ANOVA, 87 R2R , 474 (online, Chapter 10) Random effects model, 68, 111, 589 Random error term, 67 Randomization, 11, 135 Randomization test, 39 Randomization tests and ANOVA, 76 Randomized complete block design (RCBD), 135, 136 Rank transformation in ANOVA, 124 RCBD with random treatments and blocks, 147 Reduced model, 122, 476 Reference distribution, 35 Regression approach to ANOVA, 119 Regression models, 87 REML method for estimating variance components, 118, 147, 595 Repeated measures designs, 692 Replicated design, 5 Replication versus repeat run, 12 Replication, 11 Residual plotting, 79, 81, 86, 145 Residuals, 79 Resolution III designs, 362 Resolution IV designs, 376 Resolution V designs, 383 Response surface, 206, 490 Response surface methodology, 490 Response surface models, 490 Response variable, 3 Restricted form of the mixed model, 597 Rising ridge systems, 506 Robust design, 20, 569 Rotatability, 512 Rotatable CCD, 513 R-student, 482 (online, Chapter 10) Rules for expected mean squares, 602 S Sample mean, 28 Sample size in ANOVA, 103 Sample standard deviation, 28 Sample variance, 28 Sampling distributions, 30 Scatter diagram, 66 Scheffé’s method for comparing all contrasts, 93 Scientific or engineering method, 2 Second-order model, 17 Sequences of fractional factorials, 341 Sequential experimentation, 14, 21, 341, 491 Signal-to-noise ratios, 573 Simplex centroid design, 542 Simplex design for fitting a first-order model, 511 Simplex designs for mixtures, 542 Simplex lattice design, 542 Single replicate of the 2k design, 254 Single-factor fold over, 364 Small composite designs, 515734 Index Space filling designs, 536 Space filling designs for mixture experiments, 551 Sparsity of effects principle, 329, 331 Spherical CCD, 513 Split-plot designs, 634 Split-split-plot designs, 645 Standard error, 35 Standard Latin square, 157 Standard normal distribution, 30 Standardized contrast, 91 Standardized residuals, 80, 480 Stationary point, 497 Stationary ridge systems, 505 Stochastic computer models, 535 Strategy of experimentation, 1, 3 Strip-split plot designs, 649 Studentized residuals, 481 (online, Chapter 10) Subplot error, 635 Subplots or split-plots, 635 Supersaturated designs, 384 Tt− distribution, 32 Test statistic, 34 Testing significance of regression, 473 Tests on individual terms in regression, 475 Transformations, 657 (online, Chapter 15) Tukey’s test to compare pairs of means, 95 Two-sample t-test, 35, 50 Two-sample t-test with unequal variances, 44 Two-stage nested designs, 619 Type I error, 34 Type II error, 34 Types of experiments, 13 U Unbalanced data in a factorial, 666 (online, Chapter 15) Unbalanced data in ANOVA, 78 Unbiased estimator, 29 Uncontrollable variables, 3 Unrestricted form of the mixed model, 599 V Variance components, 111 Variance dispersion graph, 517 Variance of a distribution, 27 Variance stabilizing transformations, 82, 85, 657 (online, Chapter 15) W Whole plot error, 635 Whole plots, 635 ZZ -test, 47
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