Design of Experiments with MINITAB

Description

Front Matter Preface Table of Contents 1. Graphical Presentation of Data 1.1 Introduction 1.2 Types of Data 1.3 Bar Charts 1.4 Histograms 1.5 Dotplots 1.6 Stem-and-Leaf Plots 1.7 Box-and-Whisker Plots 1.8 Scatter Plots 1.9 Multi-Vari Charts 1.10 An Introduction to MINITAB 1.10.1 Starting MINITAB 1.10.2 MINITAB Windows 1.10.3 Using the Command Prompt 1.10.4 Customizing MINITAB 1.10.5 Entering Data 1.10.6 Graphing Data 1.10.7 Printing Data and Graphs 1.10.8 Saving and Retrieving Information 1.10.9 MINITAB Macros 1.10.10 Summary of MINITAB Files 2. Descriptive Statistics 2.1 Introduction 2.2 Selection of Samples 2.3 Measures of Location 2.3.1 The Median 2.3.2 The Mean 2.4 Measures of Variation 2.4.1 The Range 2.4.2 The Standard Deviation 2.4.3 Degrees of Freedom 2.4.4 The Calculating Form for the Standard Deviation 2.5 The Normal Distribution 2.6 Counting 2.6.1 Multiplication of Choices 2.6.2 Factorials 2.6.3 Permutations 2.6.4 Combinations 2.7 MINITAB Commands to Calculate Descriptive Statistics 3. Inferential Statistics 3.1 Introduction 3.2 The Distribution of Sample Means sigma Known 3.3 Confidence Interval for the Population Mean sigma Known 3.4 Hypothesis Test for One Sample Mean sigma Known 3.4.1 Hypothesis Test Rationale 3.4.2 Decision Limits Based on Measurement Units 3.4.3 Decision Limits Based on Standard z Units 3.4.4 Decision Limits Based on the p Value 3.4.5 Type 1 and Type 2 Errors 3.4.6 One-Tailed Hypothesis Tests 3.5 The Distribution of Sample Means sigma Unknown 3.5.1 Student's t Distribution 3.5.2 A One-Sample Hypothesis Test for the Population Mean sigma Unknown 3.5.3 A Confidence Interval for the Population Mean sigma Unknown 3.6 Hypothesis Tests for Two Means 3.6.1 Two Independent Samples sigma^2_1 and sigma^2_2 Known 3.6.2 Two Independent Samples sigma^2_1 and sigma^2_2 Unknown but Equal 3.6.3 Two Independent Samples sigma^2_1 and sigma^2_2 Unknown and Unequal 3.6.4 Paired Samples 3.7 Inferences about One Variance Optional 3.7.1 The Distribution of Sample Variances 3.7.2 Hypothesis Test for One Sample Variance 3.7.3 Confidence Interval for the Population Variance 3.8 Hypothesis Tests for Two Sample Variances 3.9 Quick Tests for the Two-Sample Location Problem 3.9.1 Tukey's Quick Test 3.9.2 Boxplot Slippage Tests 3.10 General Procedure for Hypothesis Testing 3.11 Testing for Normality 3.11.1 Normal Probability Plots 3.11.2 Quantitative Tests for Normality 3.12 Hypothesis Tests and Confidence Intervals with MINITAB 3.12.1 Confidence Interval for µ When sigma is Known 3.12.2 Hypothesis Tests for One Sample Mean sigma Known 3.12.3 Normal Probability Plots with MINITAB 3.13 Sample-Size Calculations 3.13.1 Sample-Size Calculations for Confidence Intervals 3.13.1.1 Confidence Interval for One Population Mean 3.13.1.2 Confidence Interval for the Difference between Two Population Means 3.13.2 Sample-Size Calculations for Hypothesis Tests 3.13.2.1 Hypothesis Test for One Population Mean 3.13.2.2 Hypothesis Test for the Difference between Two Population Means 3.13.2.3 Sample-Size Calculations for Hypothesis Tests and Confidence Intervals with MINITAB 4. DOE Language and Concepts 4.1 Introduction 4.2 Design of Experiments: Definition, Scope, and Motivation 4.3 Experiment Defined 4.4 Identification of Variables and Responses 4.5 Types of Variables 4.6 Types of Responses 4.7 Interactions 4.8 Types of Experiments 4.9 Types of Models 4.10 Selection of Variable Levels 4.10.1 Qualitative Variable Levels 4.10.2 Quantitative Variable Levels 4.11 Nested Variables 4.12 Covariates 4.13 Definition of Design in Design of Experiments 4.14 Types of Designs 4.15 Randomization 4.16 Replication and Repetition 4.17 Blocking 4.18 Confounding 4.19 Occam's Razor and Effect Heredity 4.20 Data Integrity and Ethics 4.21 General Procedure for Experimentation 4.21.1 Step 1: Cause-and-Effect Analysis 4.21.2 Step 2: Document the Process 4.21.3 Step 3: Write a Detailed Problem Statement 4.21.4 Step 4: Preliminary Experimentation 4.21.5 Step 5: Design the Experiment 4.21.6 Step 6: Sample Size, Randomization, and Blocking 4.21.7 Step 7: Run the Experiment 4.21.8 Step 8: Analyze the Data 4.21.9 Step 9: Interpret the Results 4.21.10 Step 10: Run a Confirmation Experiment 4.21.11 Step 11: Report the Experiment 4.22 Experiment Documentation 4.23 Why Experiments Go Bad 5. Experiments for One-Way Classifications 5.1 Introduction 5.2 Analysis by Comparison of All Possible Pairs Means 5.3 The Graphical Approach to ANOVA 5.4 Introduction to ANOVA 5.4.1 The ANOVA Rationale 5.4.2 ANOVA Assumptions and Validation 5.4.3 The ANOVA Table 5.5 The Sum of Squares Approach to ANOVA Calculations 5.6 The Calculating Forms for the Sums of Squares 5.7 ANOVA for Unbalanced Experiments 5.8 After ANOVA: Comparing the Treatment Means 5.8.1 Introduction 5.8.2 Bonferroni's Method 5.8.3 Sidak's Method 5.8.4 Duncan's Multiple Range Test 5.8.5 Tukey's Multiple Comparisons Test 5.8.6 Dunnett's Test 5.9 ANOVA with MINITAB 5.10 The Completely Randomized Design 5.11 Analysis of Means 5.12 Response Transformations 5.12.1 Introduction 5.12.2 The Logarithmic Transform 5.12.3 Transforming Count Data 5.12.4 Transforming Fraction Data 5.12.5 The Rank Transform 5.13 Sample Size for One-Way ANOVA 5.14 Design Considerations for One-Way Classification Experiments 6. Experiments for Multi-Way Classifications 6.1 Introduction 6.2 Rationale for the Two-Way ANOVA 6.2.1 No-Way Classification 6.2.2 One-Way Classification 6.2.3 Two-Way Classification 6.3 The Sums of Squares Approach for Two-Way ANOVA One Replicate 6.4 Interactions 6.5 Interpretation of Two-Way Experiments 6.5.1 Introduction 6.5.2 The Randomized Complete Block Design 6.5.3 a × b Factorial Experiments 6.6 Factorial Designs 6.7 Multi-Way Classification ANOVA with MINITAB 6.7.1 Two-Way ANOVA with MINITAB 6.7.2 Creating and Analyzing Factorial Designs in MINITAB 6.7.2.1 Creating the Matrix of Experimental Runs 6.7.2.2 Analyzing the Data 6.8 Design Considerations for Multi-Way Classification Designs 7. Advanced ANOVA Topics 7.1 Incomplete Factorial Designs 7.2 Latin Squares and other Squares 7.3 Fixed and Random Variables 7.3.1 One-Way Classification Fixed Variable 7.3.2 Two-Way Classification Both Variables Fixed 7.3.3 One-Way Classification Random Variable 7.3.4 Two-Way Classification One Fixed and One Random Variable 7.3.5 Two-Way Classification Both Variables Random 7.4 Nested Designs 7.4.1 Nested Variables 7.4.2 Two-Stage Nested Design: BA 7.4.3 Analysis of Nested Designs in MINITAB 7.5 Power Calculations 7.5.1 Comments on Notation 7.5.2 General Introduction to Power Calculations 7.5.3 Factorial Designs with All Variables Fixed 7.5.4 Factorial Designs with Random Variables 7.5.4.1 One-Way Classification Random Variable 7.5.4.2 Two-Way Classification One Fixed and One Random Variable 7.5.4.3 Two-Way Classification Both Variables Random 7.5.5 Nested Designs 7.5.5.1 BA: Both Variables Fixed 7.5.5.2 BA: A Fixed and B Random 7.5.5.3 BA: Both Variables Random 7.5.6 General Method to Determine the Power for a Fixed Variable 7.5.7 General Method to Determine the Power for a Random Variable 8. Linear Regression 8.1 Introduction 8.2 Linear Regression Rationale 8.3 Regression Coefficients 8.4 Linear Regression Assumptions 8.5 Hypothesis Tests for Regression Coefficients 8.6 Confidence Limits for the Regression Line 8.7 Prediction Limits for the Observed Values 8.8 Correlation 8.8.1 The Coefficient of Determination 8.8.2 The Correlation Coefficient 8.8.3 Confidence Interval for the Correlation Coefficient 8.8.4 The Adjusted Correlation Coefficient 8.9 Linear Regression with MINITAB 8.10 Transformations to Linear Form 8.11 Polynomial Models 8.12 Goodness of Fit Tests 8.12.1 The Quadratic Model as a Test of Linear Goodness of Fit 8.12.2 The Linear Lack of Fit Test 8.13 Errors in Variables 8.14 Weighted Regression 8.15 Coded Variables 8.16 Multiple Regression 8.17 General Linear Models 8.18 Sample-Size Calculations for Linear Regression 8.18.1 Sample-Size to Determine the Slope with Specified Confidence 8.18.1.1 All Observations at Two Extreme Levels k = 2 8.18.1.2 Many Uniformly Distributed Observations k rarr infin 8.18.2 Sample Size to Determine the Regression Constant with Specified Confidence 8.18.3 Sample Size to Determine the Predicted Value of the Response with Specified Confidence 8.18.4 Sample Size to Detect a Slope Different from Zero 8.19 Design Considerations for Linear Regression 9. Two-Level Factorial Experiments 9.1 Introduction 9.2 The 2^1 Factorial Experiment 9.3 The 2^2 Factorial Experiment 9.4 The 2^3 Factorial Design 9.5 The Addition of Center Cells to 2^k Designs 9.6 General Procedure for Analysis of 2^k Designs 9.7 2^k Factorial Designs in MINITAB 9.7.1 Creating the 2^k Designs in MINITAB 9.7.2 Analyzing the 2^k Factorial Designs with MINITAB 9.7.2.1 Manual Analysis with Stat Regression Regression 9.7.2.2 Analysis with the mlrk.mac Macros 9.7.2.3 Analysis with MINITAB's DOE Tools Stat DOE Factorial 9.8 Extra and Missing Values 9.9 Propagation of Error 9.10 Sample Size and Power 9.10.1 Sample Size and Power to Detect Significant Effects 9.10.2 Sample Size to Quantify Effects 9.11 Design Considerations for 2^k Experiments 10. Fractional Factorial Experiments 10.1 Introduction 10.2 The 2^5-1 Half-Fractional Factorial Design 10.3 Other Fractional Factorial Designs 10.4 Design Resolution 10.5 The Consequences of Confounding 10.6 Fractional Factorial Designs in MINITAB 10.6.1 Creating Fractional Factorial Designs in MINITAB 10.6.2 Analysis of Fractional Factorial Designs with MINITAB 10.7 Interpretation of Fractional Factorial Designs 10.7.1 Resolution V Designs 10.7.2 Resolution IV Designs 10.7.3 Resolution III Designs 10.7.4 Designs of Resolution VI and Higher 10.8 Plackett-Burman Designs 10.9 Sample-Size Calculations 10.10 Design Considerations for Fractional Factorial Experiments 11. Response-Surface Experiments 11.1 Introduction 11.2 Terms in Quadratic Models 11.3 2^k Designs with Centers 11.4 3^k Factorial Designs 11.5 Box-Behnken Designs 11.6 Central Composite Designs 11.7 Comparison of the Response-Surface Designs 11.7.1 Number of Observations and Error Degrees of Freedom 11.7.2 Number of Levels of Each Variable 11.7.3 Uncertainty about the Safety of Variable Levels 11.8 Response-Surface Designs in MINITAB 11.8.1 Creating Response-Surface Designs in MINITAB 11.8.2 Analysis of Response-Surface Designs in MINITAB 11.9 Sample-Size Calculations 11.9.1 Sample Size for 2^k and 2^k-p Plus Centers Designs 11.9.1.1 Sample Size to Detect Significant Effects 11.9.1.2 Sample Size to Quantify Effects 11.9.2 Sample Size for 3^k Designs 11.9.3 Sample Size for Box-Behnken Designs 11.9.4 Sample Size for Central Composite Designs 11.10 Design Considerations for Response-Surface Experiments Bibliography Appendix A: Statistical Tables A.1 Greek Characters A.2 Normal Distribution: Values of p = Phi -infin < z < z_p A.3 Student's t Distribution: Values of t_p Where P t_p < t < infin = p A.4 chi^2 Distribution: Values of chi^2_p Where P 0 < chi^2 < chi^2_p A.5 F Distribution: Values of F_p Where P F_p < F < infin = p and F = s^2_1/s^2_2 A.6 Critical Values for Duncan's Multiple Range Test r_0.05,p,df_epsilon A.7 Critical Values of the Studentized Range Distribution Q_0.05 k A.8 Critical Values for the One-Way Analysis of Means h_0.05,k,df_epsilon A.9 Fisher's Z Transformation: Values of... Index A B C D E F G H I K L M N O P Q R S T U V W Z