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### Summary

### Summary

Most books cover the subject from a statistical or theoretical point of view. Ideal for working engineers, this book uses real-world examples and boils statistical theory and analysis down to its simplest form.

∗ Features new and updated material, including cases and a larger focus on multivariate analysis.

∗ Uses simple analysis tools for practical implementation on the job.

∗ Targets experiment planning as the groundwork for quality experiments.

### Author Notes

William J. Diamond is a consulting engineer based in Riverview, Florida

### Table of Contents

Preface | p. xiii |

Acknowledgments | p. xvi |

Part 1 Fundamentals of Experiment Design | p. 1 |

1 Introduction to Experiment Design: Fundamental Concepts | p. 3 |

Origin of Bad Experiments | p. 3 |

Philosophy for Good Experiments | p. 5 |

Project Strategy | p. 5 |

Experiment Strategy | p. 6 |

Perceptions of Reality | p. 7 |

Theology for Experimenters | p. 7 |

Populations | p. 10 |

Distributions | p. 11 |

Means and Variances | p. 14 |

2 Introduction to Experiment Design: Elements of Decision Making | p. 18 |

Stating the Alternative Decisions | p. 18 |

Defining the Risks | p. 20 |

Establishing an Objective Criterion | p. 23 |

One Population Sampled | p. 24 |

Two Populations Sampled | p. 27 |

Computing the Sample Size | p. 28 |

Importance of N | p. 31 |

Choosing [alpha], [beta], and [delta] | p. 34 |

Operating Characteristic Curves | p. 39 |

Power Curves | p. 41 |

3 Simple Comparative Experiments: Decisions About Population Means | p. 44 |

Cases 1-3 Variance or Variances Are Known | p. 46 |

Case 1. H[subscript 0]:[mu subscript 1] = [mu subscript 0]; Variance is Known | p. 46 |

Case 2. H[subscript 0]:[mu subscript 1] = [mu subscript 2]; Variances Are Equal and Known | p. 48 |

Case 3. H[subscript 0]:[mu subscript 1] = [mu subscript 2]; Variances Are Not Equal and Both Are Known | p. 50 |

Cases 4-6 Variance or Variances Are Unknown | p. 51 |

Case 4. H[subscript 0]:[mu subscript 1] = [mu subscript 0]; Variance is Unknown | p. 52 |

Case 5. H[subscript 0]:[mu subscript 1] = [mu subscript 2]; Variances Are Equal and Unknown | p. 56 |

Case 6. H[subscript 0]:[mu subscript 1] = [mu subscript 2]; Variances Are Not Equal and Are Unknown | p. 58 |

Cases 7-9 Sample Estimate of Variance Is Known | p. 61 |

Case 7. H[subscript 0]:[mu subscript A] = [mu subscript 0]; S[superscript 2] Is Known | p. 62 |

Case 8. H[subscript 0]:[mu subscript A] = [mu subscript B]; S[superscript 2] Is Known and [sigma superscript 2 subscript A] = [sigma superscript 2 subscript B] | p. 63 |

Case 9. H[subscript 0]:[mu subscript A] = [mu subscript B]; S[superscript 2 subscript A] and S[superscript 2 subscript B] Are Known and [sigma superscript 2 subscript A] = [sigma superscript 2 subscript B] | p. 64 |

Special Cases | p. 65 |

Special Case 1 (Paired Comparisons) | p. 65 |

Special Case 2 (Some Data Lost) | p. 67 |

4 Simple Comparative Experiments: Decisions About Population Variances | p. 71 |

Sample Size | p. 71 |

Criterion Values | p. 73 |

Case 1. H[subscript 0]:[sigma superscript 2 subscript 1] = [sigma superscript 2 subscript 0]; H[subscript a]:[sigma superscript 2 subscript 1] [ [sigma superscript 2 subscript 0] | p. 74 |

Case 2. H[subscript 0]:[sigma superscript 2 subscript 1] = [sigma superscript 2 subscript 0]; H[subscript a]:[sigma superscript 2 subscript 1] ] [sigma superscript 2 subscript 0] | p. 75 |

Case 3. H[subscript 0]:[sigma superscript 2 subscript 1] = [sigma superscript 2 subscript 2]; H[subscript a]:[sigma superscript 2 subscript 1] [not equal] [sigma superscript 2 subscript 2] | p. 76 |

Case 4. Combined Problem: H[subscript a1]:[mu subscript A] [not equal] [mu subscript B]; H[subscript a2]:[sigma superscript 2 subscript A] [not equal] [sigma superscript 2 subscript B] | p. 77 |

Case 5. H[subscript 0]:[mu subscript A] = [mu subscript B]; Assumed [sigma superscript 2 subscript A] = [sigma superscript 2 subscript B] | p. 78 |

5 Sequential Experiments | p. 82 |

Case 1. [sigma superscript 2] Is Known; H[subscript a]:[mu subscript 1] ] [mu subscript 0] | p. 83 |

Case 2. [sigma superscript 2] Is Known; H[subscript a]:[mu subscript 1] [not equal] [mu subscript 0] | p. 85 |

Case 3. [sigma superscript 2] Is Unknown; H[subscript a]:[mu subscript 1] ] [mu subscript 0] | p. 87 |

Part 2 Two-Level Multivariable Experiments | p. 91 |

6 Two-Level Multivariable Experiments: Eight-Trial Hadamard Matrix Designs | p. 93 |

Introduction to Matrix Experiments | p. 93 |

Other Advantages of Matrix Experiment Design | p. 97 |

Construction of Hadamard Matrices | p. 98 |

Use of the 8 x 8 Hadamard Matrix | p. 100 |

One Variable, Each Treatment Combination Replicated Four Times | p. 101 |

Two Variables, Each Treatment Combination Replicated Twice | p. 103 |

Three Variables | p. 109 |

Four Variables (Resolution IV Design) | p. 115 |

Five, Six, or Seven Variables (Resolution III Designs) | p. 121 |

7 Two-Level Multivariable Experiments: Hadamard Matrices Greater Than Order 8 | p. 130 |

16-Trial Designs | p. 132 |

32-Trial Designs | p. 134 |

64-Trial Designs | p. 135 |

128-Trial Designs | p. 136 |

Smoak Modified Designs for Resolution IV Designs | p. 136 |

Other Hadamard Matrices Not of Order 2[superscript n] | p. 139 |

Summary | p. 148 |

8 John's Three-Quarter Fractional Factorials | p. 150 |

Resolution V Designs | p. 150 |

Four Variables in 12 Trials | p. 151 |

Seven and Eight Variables in 48 Trials | p. 158 |

Nine to 11 Variables in 96 Trials | p. 162 |

Resolution IV Designs | p. 163 |

Three Variables in Six Trials | p. 163 |

Five or Six Variables in 12 Trials | p. 164 |

Nine to 12 Variables in 24 Trials | p. 166 |

Seventeen to 24 Variables in 48 Trials | p. 167 |

Thirty-Three to 48 Variables in 96 Trials | p. 167 |

9 Unbalanced Resolution V Designs | p. 175 |

Class A Designs | p. 176 |

Six-Variable, 28-Trial Design | p. 176 |

Seven-Variable, 36-Trial Design | p. 181 |

Eight-Variable, 44-Trial Design | p. 183 |

Nine- to 11-Variable Designs | p. 185 |

Class B Designs | p. 185 |

Seven-Variable, 38-Trial Design | p. 185 |

Eight-Variable, 46-Trial Design | p. 188 |

Nine-Variable, 71-Trial Design | p. 189 |

Twelve-Variable, 143-Trial Design | p. 190 |

Class AB Designs | p. 191 |

10 Resolution V Designs with Efficiency = 1 | p. 195 |

Three-Variable Designs | p. 196 |

Four-Variable Designs | p. 197 |

Five-Variable Designs | p. 197 |

Six and Higher Numbers of Variables | p. 198 |

11 Hadamard Matrix Designs for Binomial and Poisson Responses | p. 200 |

Binomial | p. 200 |

Poisson | p. 204 |

12 Summary of Two-Level Matrix Designs | p. 208 |

13 A Computer Program for Generating Hadamard Matrix Designs and Analyzing the Data from Such Designs | p. 215 |

Designing the Experiment | p. 216 |

Example of Saturated Resolution III Designs: 15 Variables in 16 Trials, Not Using the START Program, and Coding the Levels of the Variables as 0 or 1 | p. 217 |

Example of Saturated Resolution IV Designs: John's Three-Quarter Fractional Factorial with Six Variables in 12 Trials, Not Using the START Program, and Coding the Levels of the Variables as 0 or 1 | p. 218 |

Example of Resolution IV Designs: John's Three-Quarter Fractional Factorial with Nine Variables in 24 Trials, Using the START Program, and Using the Actual Levels of the Variables | p. 219 |

Example of Saturated Resolution III Designs: 15 Variables in 16 Trials, Not Using the START Program, and Using the Actual Levels of the Variables | p. 220 |

Analyzing the Data | p. 221 |

Example of Resolution V Designs: Four Variables in 16 Trials | p. 221 |

Example of Saturated Resolution IV Designs: Eight Variables in 16 Trials | p. 222 |

Example of Resolution III Designs: 13 Variables in 16 Trials | p. 223 |

Example of John's Three-Quarter Fractional Factorial: Nine Variables in 24 Trials | p. 224 |

Appendix 1 APL Computer Program Coding | p. 226 |

Appendix 2 Confounding of Two-Factor Interactions in Resolution IV Design | p. 234 |

14 Analysis of Goodness | p. 243 |

15 Alternative Methods of Analysis | p. 251 |

Part 3 Multilevel Multivariable Experiments | p. 261 |

16 Multilevel Experiments with Qualitative Variables | p. 263 |

Use of ANOVA | p. 264 |

Latin and Greco-Latin Squares | p. 272 |

17 Multilevel Experiments with Quantitative Variables | p. 281 |

Central Composite Rotatable Designs | p. 282 |

Designs for Experiments Where the Levels of Some of the Variables Are Different | p. 288 |

16-Trial Experiment Designs with Variables at Two Levels and Three Levels | p. 295 |

Two Variables at Two Levels and One Variable at Three Levels | p. 295 |

Three Variables at Two Levels and One Variable at Three Levels | p. 295 |

Main Effects | p. 296 |

Interactions | p. 297 |

Two Variables at Two Levels and Two Variables at Three Levels | p. 297 |

Four Variables at Two Levels and One Variable at Three Levels | p. 298 |

32-Trial Experiment Designs with Variables at Two Levels and Three Levels | p. 298 |

64-Trial Experiment Designs with Variables at Two Levels and Three Levels | p. 303 |

Other Multilevel Experiment Designs | p. 306 |

18 Experiment Designs for Chemical Composition Experiments | p. 309 |

Extreme-Vertices Designs | p. 309 |

Simplex Designs | p. 315 |

19 Random-Strategy Experiments | p. 322 |

Part 4 Related Topics | p. 327 |

20 Blocking an Experiment | p. 329 |

21 Validation of Test Methods | p. 335 |

22 Concepts for a Complete Project Strategy | p. 348 |

Project Definition | p. 353 |

Planning the Project | p. 353 |

Design of the First Experiment | p. 355 |

Design of the Second Experiment | p. 357 |

Design of the Third Experiment | p. 362 |

Design of the Fourth Experiment | p. 367 |

23 Project Engineer's Game | p. 369 |

Project Assignment | p. 370 |

Use of the Computer Program | p. 370 |

Playing the Game | p. 371 |

Other Project Engineer Games | p. 372 |

Appendix Computer Program and Response Equation for Project Engineer's Game | p. 373 |

Instructions for Game Director | p. 376 |

Min and Max Values of Variables | p. 376 |

Response Equations | p. 376 |

24 Estimation of Variance | p. 378 |

25 Testing Distributions | p. 384 |

Case 1. One Population | p. 384 |

Case 2. Two Populations | p. 386 |

Part 5 General References, Symbols, Tables, and Answers to Exercises | p. 389 |

General References | p. 391 |

Symbols | p. 397 |

Tables | p. 399 |

Answers to Exercises | p. 414 |

Index | p. 419 |