Statistical Robust Design (eBook)

Magnus Arnér, Tetra Pak Packaging Solutions, Sweden

Preface

1 What is Robust Design?

1.1 The Importance of Small Variation

1.2 Variance Reduction

1.3 Variation Propagation

1.4 Discussion

1.4.1 Limitations

1.4.2 The outline of this book

Exercises

2 DOE for Robust Design, Part 1

2.1 Combined Arrays: An Example

2.2 Dispersion Effects

Exercises

References

3 Noise and Control Factors

3.1 Introduction to Noise Factors

3.2 Finding the Important Noise Factors

3.2.1 Reducing the number of noise factors

3.3 How to Include Noise in a Designed Experiment

3.3.1 How to include noise in experimentation

3.4 Control Factors

Exercises

References

4 Response, Signal, and P diagrams

4.1 The Idea of Signal and Response

4.2 Ideal Functions and P Diagrams

4.3 The Signal

Exercises

5 DOE for Robust Design, Part 2

5.1 Combined and Crossed Arrays

5.2 Including a Signal in a Designed Experiment

5.2.1 Combined arrays with a signal

5.2.2 Inner and outer arrays with a signal

5.3 Crossed Arrays versus Combined Arrays

5.3.1 Differences in factor aliasing

5.4 Crossed Arrays and Split-Plot Designs

5.4.1 Limits of randomization

5.4.2 Split-plot designs

Exercises

References

6 Smaller-the-Better and Larger-the-Better

6.1 Different Types of Responses

6.2 Failure Modes and Smaller-the-Better

6.3 Larger-the-Better

6.4 OperatingWindow

Exercises

References

7 Regression for Robust Design

7.1 Graphical Techniques

7.2 Analytical Minimization of (g0(z))2

7.3 Regression and Crossed Arrays

Exercises

8 Mathematics of Robust Design

8.1 Notational System

8.2 The Objective Function

8.2.1 Multidimensional problems

8.2.2 Pareto optimality

8.3 ANOVA for Robust Design

8.3.1 Traditional ANOVA

8.3.2 Functional ANOVA

Exercises

References

9 Design and Analysis of Computer Experiments

9.1 Overview of Computer Experiments

9.2 Experimental Arrays for Computer Experiments

9.2.1 Screening designs

9.2.2 Space filling designs

9.3 Response Surfaces

9.4 Optimization

Exercises

References

10 Monte Carlo Methods for Robust Design

10.1 Geometry Variation

10.2 Geometry Variation in Two Dimensions

10.3 Crossed Arrays

11 Taguchi and His Ideas on Robust Design

11.1 The Experimental Arrays

11.1.1 The nature of inner arrays

11.1.2 Crossing the arrays

11.2 Signal to Noise Ratios

11.3 Some Other Ideas

Exercises

References

Appendix A Loss Functions

Exercises

References

Appendix B Data to chapter 2

Appendix C Data to chapter 5

Appendix D Data to chapter 6

Index