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أخواني في الله أحضرت لكم كتاب Statistical Design and Analysis of Experiments With Applications to Engineering and Science Second Edition Robert L. Mason Southwest Research Institute San Antonio, Texas Richard F. Gunst Department of Statistical Science Southern Methodist University Dallas, Texas James L. Hess Leggett and Platt. Inc. Carthage, Missouri
و المحتوى كما يلي :
Contents Preface vii PART I FUNDAMENTAL STATISTICAL CONCEPTS 1 1. Statistics in Engineering and Science 3 1.1. The Role of Statistics in Experimentation, 5 1.2. Populations and Samples, 9 1.3. Parameters and Statistics, 19 1.4. Mathematical and Statistical Modeling, 24 Exercises, 28 2. Fundamentals of Statistical Inference 33 2.1. Traditional Summary Statistics, 33 2.2. Statistical Inference, 39 2.3. Probability Concepts, 42 2.4. Interval Estimation, 48 2.5. Statistical Tolerance Intervals, 50 2.6. Tests of Statistical Hypotheses, 52 2.7. Sample Size and Power, 56 Appendix: Probability Calculations, 59 Exercises, 64 xixii CONTENTS 3. Inferences on Means and Standard Deviations 69 3.1. Inferences on a Population or Process Mean, 72 3.1.1. Confidence Intervals, 73 3.1.2. Hypothesis Tests, 76 3.1.3. Choice of a Confidence Interval or a Test, 78 3.1.4. Sample Size, 79 3.2. Inferences on a Population or Process Standard Deviation, 81 3.2.1. Confidence Intervals, 82 3.2.2. Hypothesis Tests, 84 3.3. Inferences on Two Populations or Processes Using Independent Pairs of Correlated Data Values, 86 3.4. Inferences on Two Populations or Processes Using Data from Independent Samples, 89 3.5. Comparing Standard Deviations from Several Populations, 96 Exercises, 99 PART II DESIGN AND ANALYSIS WITH FACTORIAL STRUCTURE 107 4. Statistical Principles in Experimental Design 109 4.1. Experimental-Design Terminology, 110 4.2. Common Design Problems, 115 4.2.1. Masking Factor Effects, 115 4.2.2. Uncontrolled Factors, 117 4.2.3. Erroneous Principles of Efficiency, 119 4.2.4. One-Factor-at-a-Time Testing, 121 4.3. Selecting a Statistical Design, 124 4.3.1. Consideration of Objectives, 125 4.3.2. Factor Effects, 126 4.3.3. Precision and Efficiency, 127 4.3.4. Randomization, 128 4.4. Designing for Quality Improvement, 128 Exercises, 132CONTENTS xiii 5. Factorial Experiments in Completely Randomized Designs 140 5.1. Factorial Experiments, 141 5.2. Interactions, 146 5.3. Calculation of Factor Effects, 152 5.4. Graphical Assessment of Factor Effects, 158 Appendix: Calculation of Effects for Factors with More than Two Levels, 160 Exercises, 163 6. Analysis of Completely Randomized Designs 170 6.1. Balanced Multifactor Experiments, 171 6.1.1. Fixed Factor Effects, 171 6.1.2. Analysis-of-Variance Models, 173 6.1.3. Analysis-of-Variance Tables, 176 6.2. Parameter Estimation, 184 6.2.1. Estimation of the Error Standard Deviation, 184 6.2.2. Estimation of Effects Parameters, 186 6.2.3. Quantitative Factor Levels, 189 6.3. Statistical Tests, 194 6.3.1. Tests on Individual Parameters, 194 6.3.2. F-Tests for Factor Effects, 195 6.4. Multiple Comparisons, 196 6.4.1. Philosophy of Mean-Comparison Procedures, 196 6.4.2. General Comparisons of Means, 203 6.4.3. Comparisons Based on t-Statistics, 209 6.4.4. Tukey’s Significant Difference Procedure, 212 6.5. Graphical Comparisons, 213 Exercises, 221 7. Fractional Factorial Experiments 228 7.1. Confounding of Factor Effects, 229 7.2. Design Resolution, 237 7.3. Two-Level Fractional Factorial Experiments, 239xiv CONTENTS 7.3.1. Half Fractions, 239 7.3.2. Quarter and Smaller Fractions, 243 7.4. Three-Level Fractional Factorial Experiments, 247 7.4.1. One-Third Fractions, 248 7.4.2. Orthogonal Array Tables, 252 7.5. Combined Two- and Three-Level Fractional Factorials, 254 7.6. Sequential Experimentation, 255 7.6.1. Screening Experiments, 256 7.6.2. Designing a Sequence of Experiments, 258 Appendix: Fractional Factorial Design Generators, 260 Exercises, 266 8. Analysis of Fractional Factorial Experiments 271 8.1. A General Approach for the Analysis of Data from Unbalanced Experiments, 272 8.2. Analysis of Marginal Means for Data from Unbalanced Designs, 276 8.3. Analysis of Data from Two-Level, Fractional Factorial Experiments, 278 8.4. Analysis of Data from Three-Level, Fractional Factorial Experiments, 287 8.5. Analysis of Fractional Factorial Experiments with Combinations of Factors Having Two and Three Levels, 290 8.6. Analysis of Screening Experiments, 293 Exercises, 299 PART III Design and Analysis with Random Effects 309 9. Experiments in Randomized Block Designs 311 9.1. Controlling Experimental Variability, 312 9.2. Complete Block Designs, 317 9.3. Incomplete Block Designs, 318 9.3.1. Two-Level Factorial Experiments, 318 9.3.2. Three-Level Factorial Experiments, 323 9.3.3. Balanced Incomplete Block Designs, 325CONTENTS xv 9.4. Latin-Square and Crossover Designs, 328 9.4.1. Latin Square Designs, 328 9.4.2. Crossover Designs, 331 Appendix: Incomplete Block Design Generators, 332 Exercises, 342 10. Analysis of Designs with Random Factor Levels 347 10.1. Random Factor Effects, 348 10.2. Variance-Component Estimation, 350 10.3. Analysis of Data from Block Designs, 356 10.3.1. Complete Blocks, 356 10.3.2. Incomplete Blocks, 357 10.4. Latin-Square and Crossover Designs, 364 Appendix: Determining Expected Mean Squares, 366 Exercises, 369 11. Nested Designs 378 11.1. Crossed and Nested Factors, 379 11.2. Hierarchically Nested Designs, 381 11.3. Split-Plot Designs, 384 11.3.1. An Illustrative Example, 384 11.3.2. Classical Split-Plot Design Construction, 386 11.4. Restricted Randomization, 391 Exercises, 395 12. Special Designs for Process Improvement 400 12.1. Assessing Quality Performance, 401 12.1.1. Gage Repeatability and Reproducibility, 401 12.1.2. Process Capability, 404 12.2. Statistical Designs for Process Improvement, 406 12.2.1. Taguchi’s Robust Product Design Approach, 406 12.2.2. An Integrated Approach, 410 Appendix: Selected Orthogonal Arrays, 414 Exercises, 418xvi CONTENTS 13. Analysis of Nested Designs and Designs for Process Improvement 423 13.1. Hierarchically Nested Designs, 423 13.2. Split-Plot Designs, 428 13.3. Gage Repeatability and Reproducibility Designs, 433 13.4. Signal-to-Noise Ratios, 436 Exercises, 440 PART IV Design and Analysis with Quantitative Predictors and Factors 459 14. Linear Regression with One Predictor Variable 461 14.1. Uses and Misuses of Regression, 462 14.2. A Strategy for a Comprehensive Regression Analysis, 470 14.3. Scatterplot Smoothing, 473 14.4. Least-Squares Estimation, 475 14.4.1. Intercept and Slope Estimates, 476 14.4.2. Interpreting Least-Squares Estimates, 478 14.4.3. No-Intercept Models, 480 14.4.4. Model Assumptions, 481 14.5. Inference, 481 14.5.1. Analysis-of-Variance Table, 481 14.5.2. Tests and Confidence Intervals, 484 14.5.3. No-Intercept Models, 485 14.5.4. Intervals for Responses, 485 Exercises, 487 15. Linear Regression with Several Predictor Variables 496 15.1. Least Squares Estimation, 497 15.1.1. Coefficient Estimates, 497 15.1.2. Interpreting Least-Squares Estimates, 499 15.2. Inference, 503 15.2.1. Analysis of Variance, 503 15.2.2. Lack of Fit, 505 15.2.3. Tests on Parameters, 508 15.2.4. Confidence Intervals, 510CONTENTS xvii 15.3. Interactions Among Quantitative Predictor Variables, 511 15.4. Polynomial Model Fits, 514 Appendix: Matrix Form of Least-Squares Estimators, 522 Exercises, 525 16. Linear Regression with Factors and Covariates as Predictors 535 16.1. Recoding Categorical Predictors and Factors, 536 16.1.1. Categorical Variables: Variables with Two Values, 536 16.1.2. Categorical Variables: Variables with More Than Two Values, 539 16.1.3. Interactions, 541 16.2. Analysis of Covariance for Completely Randomized Designs, 542 16.3. Analysis of Covariance for Randomized Complete Block Designs, 552 Appendix: Calculation of Adjusted Factor Averages, 556 Exercises, 558 17. Designs and Analyses for Fitting Response Surfaces 568 17.1. Uses of Response-Surface Methodology, 569 17.2. Locating an Appropriate Experimental Region, 575 17.3. Designs for Fitting Response Surfaces, 580 17.3.1. Central Composite Design, 582 17.3.2. Box–Behnken Design, 585 17.3.3. Some Additional Designs, 586 17.4. Fitting Response-Surface Models, 588 17.4.1. Optimization, 591 17.4.2. Optimization for Robust Parameter Product-Array Designs, 594 17.4.3. Dual Response Analysis for Quality Improvement Designs, 597 Appendix: Box–Behnken Design Plans; Locating Optimum Responses, 600 Exercises, 606xviii CONTENTS 18. Model Assessment 614 18.1. Outlier Detection, 614 18.1.1. Univariate Techniques, 615 18.1.2. Response-Variable Outliers, 619 18.1.3. Predictor-Variable Outliers, 626 18.2. Evaluating Model Assumptions, 630 18.2.1. Normally Distributed Errors, 630 18.2.2. Correct Variable Specification, 634 18.2.3. Nonstochastic Predictor Variables, 637 18.3. Model Respecification, 639 18.3.1. Nonlinear-Response Functions, 640 18.3.2. Power Reexpressions, 642 Appendix: Calculation of Leverage Values and Outlier Diagnostics, 647 Exercises, 651 19. Variable Selection Techniques 659 19.1. Comparing Fitted Models, 660 19.2. All-Possible-Subset Comparisons, 662 19.3. Stepwise Selection Methods, 665 19.3.1. Forward Selection, 666 19.3.2. Backward Elimination, 668 19.3.3. Stepwise Iteration, 670 19.4. Collinear Effects, 672 Appendix: Cryogenic-Flowmeter Data, 674 Exercises, 678 APPENDIX: Statistical Tables 689 1. Table of Random Numbers, 690 2. Standard Normal Cumulative Probabilities, 692 3. Student t Cumulative Probabilities, 693 4. Chi-Square Cumulative Probabilities, 694 5. F Cumulative Probabilities, 695 6. Factors for Determining One-sided Tolerance Limits, 701 7. Factors for Determining Two-sided Tolerance Limits, 702xix 8. Upper-Tail Critical Values for the F-Max Test, 703 9. Orthogonal Polynomial Coefficients, 705 10. Critical Values for Outlier Test Using Lk and Sk, 709 11. Critical Values for Outlier Test Using Ek, 711 12. Coefficients Used in the Shapiro–Wilk Test for Normality, 713 13. Critical Values for the Shapiro–Wilk Test for Normality, 716 14. Percentage Points of the Studentized Range, 718 INDEX 72 Index Added factors, 260 Adjacent value, 70 Adjusted factor-level average, 362 analysis of covariance, 551, 555, 556 Alias, 230, 319, 324 All-possible subset comparisons, 662 Alternative hypothesis, 52, 55 Analysis of covariance (ANACOVA), 535, 543 Analysis of marginal means, 276 Analysis of variance (ANOVA), 481, 503 model, 173 table, 176, 481, 504, 546 Assignable causes, 173 Assumptions analysis of covariance model, 544, 554 fixed effects analysis of variance model, 173 linear regression analysis, 463, 481 random effects analysis of variance model, 349 Average, 33 Backward elimination, 668 Balance, 145, 248, 252 Balanced incomplete block design (BIB), 325, 357 Balancing, 316 Bartlett’s test, 98 Bias measurement, 402 Block, 110, 316 Block design, 311, 317, 318, 400, 552 complete, 317, 356 incomplete, 318, 357 Bonferroni comparisons, 211 Box–Behnken design, 248, 585 Box–Cox procedure, 642 Boxplot comparisons, 70 Cm (Cp)statistic, 661 Canonical analysis, 593, 604 Capability study, 404 Carryover effects, 331 Categorical variable, 536, 539 Central composite design, 248, 582 Central limit property, 47 Chi-square probability distribution, 46, 62, 82 Coding, 541, 578 Coefficient of determination, 482, 504, 661 adjusted, 505, 661 Collinear predictors, 518 Collinearity detection, 672 Combined array design, 594 Complete block design, 317, 356 Completely randomized design, 141, 170, 229, 542 three-level, 247 two-level, 239 Comprehensive regression analysis, 470 Computer-generated design, 580 Confidence coefficient, 75 Confidence interval, 49 equivalence to hypothesis test, 78 for analysis of variance model, 186 for factor level means, 275 for normal distribution parameters, 49, 76, 83, 92, 94 for ratio of expected mean squares, 355 723 Statistical Design and Analysis of Experiments: With Applications to Engineering and Science, Second Edition Robert L. Mason, Richard F. Gunst and James L. Hess Copyright ¶ 2003 John Wiley & Sons, Inc. ISBN: 0-471-37216-1724 INDEX Confidence interval (continued) for regression model parameters, 484, 510 for regression model response mean, 485, 524 interpretation, 50, 75 simultaneous, 524 Confidence level, 55 Confounding, 112, 318 effects, 229 partial, 320 pattern, 233, 281, 287 Constrained factor space, 588 Contrast, 161, 197, 230 orthogonal, 198 sum of squares, 200 Correlation coefficient, 468 Covariate, 110, 542 Criteria for comparing fitted models, 661 Critical value, 55 Crossed array design, 594 Crossover design, 331 Curvature, 413 Data, 4 collection, 4 Defining contrast, 239, 319, 324 Defining equation, 239, 321 Degrees of freedom, 46, 73, 90, 180 Density, 20, 42 Design problems erroneous efficiency, 119 error variation, 115 masked factors, 115 one-factor-at-a-time, 121 uncontrolled factors, 117 Design resolution, 237 Design selection criteria efficiency, 127 factor effects, 126 objective, 125 precision, 127 randomization, 128 Deviations, 35 DFBETAS, 625 DFFITS, 625 Discrimination, 402 Distribution, 19 frequency, 21 normal, 20 sampling, 21, 45 Dot notation, 153 Dual response model, 598 Effects, 110 calculation of, 152, 156, 160 coding of factor levels, 154 confounded, 230 fixed, 171 graphical assessment, 158 interaction, 153, 175 joint factor, 145, 178 linear, 290 main, 153 parameters, 277 plot, 280 polynomial, 190 quadratic, 290 random, 171, 347, 424 representation, 153 Effects sum of squares, see Sum of squares Error mean square (MSE), 185, 273, 482, 504 Error rates comparisonwise, 201 experimentwise, 201 type I, 201 type II, 202 Error standard deviation, 184 Estimate, 44 Estimated error standard deviation, 73, 157, 276, 482, 504 Estimated experimental error, 185 Evolutionary operation (EVOP), 130 Expected mean square, 350, 366, 425 Experimental error, 411 Experimental layout, 112 Experimental region, 110, 575 Experimental studies, 4 Experimental unit, 110 F probability distribution, 46, 62 F ratio, 46, 93, 195, 661 F statistic, 93 Face-centered cube design, 583 Factor, 12 Factor effects, see Effects, 171 Factor levels, 110, 189 quantitative, 189 random, 347 space, 111INDEX 725 Factorial experiments, 141, 228, 580 Factors, 12 balanced, 382 control, 408, 598 crossed, 379 environmental, 408 hard to vary, 391 nested, 379 noise, 598 uncontrolled, 117 F-max test, 97 Fold-over designs, 260 Forward selection, 666 Fractional factorial, 228, 321 Fractional factorial experiment, 144, 228, 278, 287, 290, 580 analysis of, 278, 287, 290 French curve, 516 Gage R&R studies, 401, 433 Graeco-Latin-Square design, 330 Grouping, 316 Grubbs test, 617 Hierarchical model, see Model Hierarchically nested designs, 381, 423 Histogram relative-frequency, 22 Hybrid design, 588 Hypothesis tests analysis of covariance model parameters, 544 analysis of variance model parameters, 194, 275 decision rules, 77 for factor effects, 195 for normal distribution parameters, 52, 78, 85, 92, 95 lack of fit, 506 p-value calculations, 77 regression model parameters, 484, 508 Hypothesis types, 52 Incomplete block design, 318, 357 balanced, 325 three-level factorial, 323 two-level factorial, 318 Independence, 44 Indicator variables, 461, 536 Inferences on means, 72, 86, 89 on standard deviations two samples, 81, 93 on regression models, 481, 503 Influential observations, 624 Inner array, 408 Integrated approach, 410 Integrated design model, 598 Interaction, 110, 146, 511, 541 Interaction plot, 216 Lack-of-fit error, 482, 506 test, 506 Latin-square design, 328, 364 Least significant difference, 210 interval, 218 Least squares estimation, 475, 478, 480, 497 interpretation, 478, 499 Least squares fit, 476 Least squares means, 278 Leverage values, 628 Local control, 316 Loess smoothing, 474 Masking, 115, 618 Mean, 33 Mean square, 181 Expected, 350, 366, 425 Measurement process, 401 Measurement variation, 6, 402 Median, 34 Mixed-levels designs, 254 Mixture design, 588 Model analysis of covariance, 543, 553 analysis of variance, 173 assumptions, 630 extrapolation, 463, 518 first-order, 513, 515 fixed effects, 173, 348, 429 hierarchical, 176, 272 integrated design, 587 linear, 462, 497, 536 mathematical, 25 no-intercept regression, 480, 485 nonlinear, 640 one-way classification, 184 order, 513, 515 polynomial, 514, 588726 INDEX Model (continued) random-effect, 349 regression, 462, 497, 536 respecification, 639 response surface, 588 saturated, 185 second-order, 513, 515 specification, 462, 472, 497, 634 statistical, 25 sum of squares, see Sum of squares Multi-panel conditioning, 214 Multiple comparison procedures, 196 Nested design, 378, 423 Nested factors, see Factor Noncentral composite design, 588 Nonlinear relationship, 635, 640 response function, 640 Nonorthogonal designs, 252 Normal density function, 43 Normal equations, 499 Normal probability distribution, 20, 43, 59 Null hypothesis, 52, 55 Observation, 12 Observational data, 587 studies, 4 Observed value, 11 One-Factor-at-a-Time (OFAT) Testing, 121 Operating characteristic curve, 59, 80 Optimum response, 573, 576 Orthogonal arrays, 252, 407, 414 Orthogonal contrast, see Contrast Orthogonal polynomials, 207 Outer array, 408 Outliers, 70 accommodation, 615 detection, 614 in predictor variables, 626 in response variables, 619 Parameter, 19 analysis of variance model, 174 constraints, 174 estimation, 186 interaction, 174 main-effect, 174 Parsimony, 516 Partial regression coefficient estimate, 499 Pearson’s r, 468 Pick the winner, 437, 457 PISEAS, 470 Plackett–Burman design, 256 analysis, 293 Plots boxplot, 70 contour, 122, 571 cube, 213 factor effects, 158 interaction, 150, 216 labeled scatterplot, 148 least significant interval, 218 normal quantile-quantile, 159, 630 overlaying, 575 partial-regression, 637 partial-residual, 635 point, 39 residual, 634 scatter, 6, 148 studentized deleted residual, 644 trellis, 214 Pooled standard deviation estimate, 90 Population, 10 Power, 56 Precision, 127 Prediction equation, 475, 498 interval, 485 Probability concepts, 42 Product array design, 594 Process, 10 capability, 404 Pure error, 506 p-value, 55, 77 Quadratic model, 515, 588 Quality control procedures, 128 Quality loss function, 407 Quantile, 159 Quartile, 37 Random sample, 14 Randomization, 128, 142, 391 restricted, 391 Randomized complete block (RCB) design, 317, 552 Range, 35INDEX 727 Reduction in error sum of squares, 273 Reexpression, 642, 647 Regression analysis assumptions, 463, 481 common uses and misuses, 462 analysis linear, 470 local fit, 473 strategy, 470 sum of squares, 481, 503 Regression coefficient, 462, 497 beta-weight, 502, 519 standardized, 502, 519 Regression fallacy, 480 Repeat test, 110, 144, 312 Repeatability, 315, 402, 434 Replication, 110, 312 Reproducibility, 315, 402, 434 Residuals, 475, 498 partial, 635 studentized deleted, 623 Response dispersion, 130 location, 130 predicted, 475, 498 variable, 120 Response surface designs, 129, 410, 568, 580 Box–Behnken, 413, 585 central composite, 413, 582 Rising ridge, 572 Robust design, 401 parameter design, 587, 594 Robustness, 401 Rotatable design, 581 Ruggedness tests, 267, 293 Saddle, 572 Sample correlation coefficient, 468 Sample, 13 mean 34 sampling distribution of, 45 median, 34 size, 56, 79 standard deviation, 36, 73 types of, 13 variance, 46 Sampling distribution, 21, 45, 73 Saturated designs, 253 Scatterplot 6; smoothing, 473 Screening design, 144, 256 analysis, 293 Screening experiments, 129, 158, 256 Semi-interquartile range, 37, 70 Sequential experimentation, 255, 331 Shapiro–Wilk test for normality, 633 Signal-to-noise ratio, 436 Significance level, 55 Significance probability, 55 Simplex design, 588 Small composite design, 588 Smoothing, 473 Span, 473 Split plot, 384, 388 Split-plot design, 384, 388, 428 Stable process, 404 Staggered nested design, 382, 427 Standard deviation, 36, 81 Standard error, 45 Standard normal variate, 44 Standard process, 404 Standardized predictor variable, 519, 591 Stationary point, 593 Stationary ridge, 571 Statistic, 4, 19 Steepest ascent method, 602 Stepwise variable selection techniques, 665 collinear effects, 672 Student t distribution, 46, 60 approximate, 91 Sum of squares contrast, 200 error, 180, 481, 498 interaction effect, 178 main effect, 178 model, 177 partitioned, 177 regression, 481, 503 total, 177, 481 Supersaturated design analysis, 297 Taguchi approach, 129, 406 Taguchi design, 406, 436 t-distribution, 46 Test run, 110 Tolerance intervals, 50 Transformation Box–Cox, 642 logarithmic, 640 power-family, 642 Transmitted variation, 411 t-statistic, 73, 209728 INDEX Tukey’s significant difference, 212 Type I error, 55, 202 Type II error, 55, 202 Unbalanced design analysis, 272 Variable 11 categorical, 536 collinear, 518 continuous, 42 indicator, 461, 536 predictor, 461, 462, 497 response, 12, 110 selection techniques, 659 standardized, 579 Variance component, 350, 434 Variance inflation factors, 673 Variation assignable cause, 173 measurement, 402 random, 173 sources of, 173 transmitted, 411 Whole plots, 388
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