Statistical Design and Analysis of Experiments

Автор(ы):Mason Robert L.
06.10.2007
Год изд.:2003
Описание: Statistical Design and Analysis of Experiments is intended to be a practitioner's guide to statistical methods for designing and analyzing experiments. The topics selected for inclusion in this book represent statistical techniques that we feel are most useful to experimenters and data analysts who must either collect, analyze, or interpret data. The material included in this book also was selected to be of value to managers, supervisors, and other administrators who must make decisions based in part on the analyses of data that may have been performed by others.
Оглавление:
Statistical Design and Analysis of Experiments — обложка книги.
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]
  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 [132]
  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 f-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 [239]
      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 [325]
    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 [418]
  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 [510]
    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. Receding 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 [606]
  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 [702]
  8. Upper-Tail Critical Values for the F-Max Test [703]
  9. Orthogonal Polynomial Coefficients [705]
  10. Critical Values for Outlier Test Using (?) and (?) [709]
  11. Critical Values for Outlier Test Using (?) [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 723
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