Based on real-world applications in coatings formulation, he shows that statistics don’ t have to be that dry and difficult mathematics. Essential for everyone who wants to dive into the topic quickly and start using DoE straight away.

**Contents of Design of Experiments for Coatings**

1 Design of experiments – systematic mania?

1.1 Design of experiments as part of the challenges and criteria of success in modern R&D

1.2 A typical experiment in coatings formulation

1.3 Factors, Levels, etc. – some vocabulary at the beginning

1.4 Classical design of experiments and the limitations

1.4.1 Conventional methods – more diversity is not possible

1.4.2 Limits in case of the classical approach

1.4.2.1 Number of experiments in case of many factors

1.4.2.2 Non-linear effects and domain dependence

1.4.2.3 Universality of the statements.

1.4.2.4 You desire, we play – multiple responses

1.4.2.5 The gain of knowledge and new information is too slow

1.5 Design of experiments – what’s that?

1.5.1 Design, factors and effects.

1.5.2 Interactions

1.6 Where is the statistics?

1.7 Models – pictures of reality

1.8 Overview, possibilities, benefits and limits

1.9 A brief history of statistical design of experiments

1.10 References

2 Planning is essential – a lot helps a lot

2.1 General principles for setting up a DoE investigation

2.1.1 Strategy of experimentation and guidelines for pre-experimental planning

2.1.2 Overcome experimental errors – identical replication.

2.1.3 How to overcome trends – randomization and arrangement in blocks.

2.1.4 Normalization, centring, orthogonal design

2.1.5 Not realizable, irregular combinations – the experimental region

2.2 Factorial designs – the heart of DoE

2.2.1 Two levels, two factors – 22-design

2.2.2 Two levels, three factors – 23-design

2.2.3 The general design with two levels – 2k-design

2.2.4 Factorial designs with centre-points

2.2.5 Blocking with factorial designs

2.3 Fractional factorial designs – to separate the wheat from the chaff

2.3.1 Basic principle of the reduction – confounding

2.3.2 Blocking – perfect suited for the 24-1-design

2.3.3 Types of fractional factorial designs

2.3.4 Plackett-Burmann designs.

2.3.5 DoE in colour measurement of a red-metallic base coat –

2 6-1-fractional factorial design

2.4 Non-linear effect designs

2.4.1 Central composite designs.

2.4.2 Three- and higher level designs

2.4.3 Mixed designs

2.4.4 Box-Behnken designs

2.4.5 D-optimal designs – egg-laying wool-milk-sow

2.5 Mixture design – a huge area

2.6 Qualitative classification

2.7 References

3 Number-crunching – nothing ventured, nothing gained in data analysis

3.1 Evaluation of raw data

3.1.1 Transformation

3.1.2 Outliers

3.2 Confidence intervals – where are the limits?

3.3 Regression – the best model

3.3.1 Basic principles

3.3.2 Confidence intervals for the model parameters

3.3.3 Basic principles and standard assumptions for regression analysis

3.4 Residual diagnostic – what does the deviations mean?.

3.5 Analysis of variance – how certain we can feel?

3.5.1 Introduction

3.5.2 Example: Colour measurement of a base coat – ANOVA.

3.6 References

4 Parametric optimization and sensitivity analysis – finding a needle in the haystack

4.1 Strategies for optimization – how we can do it better

4.1.1 Method of the steepest ascent/descent

4.1.2 Box-Wilson's method

4.1.3 EVOP-Method (evolutionary operations)

4.1.4 Simplex-method

4.1.5 Further optimization methods

4.2 Multiple responses

Example: Multiple optimization of blocking and film formation in a clear coat

Example: Optimization of an indoor paint

4.3.1 Qualitative analysis of the response surface

Example: Disturbance in levelling of a pigmented base coat

4.3.2 Quantitative analysis of the regression model

4.3.3 Taguchi-method

Example: Micro foam in a thick-coat glaze finish

4.4 References

5 DoE-Software – do not develop the wheel once more

Autonomous commercial software-packages for DoE:

Statistic packages

EXCEL-based Software

Appendix 1 – Precision, trueness and accuracy

Appendix 2 – Location and spread parameters

Example: pH-value of a lime paint

Example: pH-value of lime paints

Appendix 3 – Normal distribution

Example: pH-value of a lime paint

References

Appendix 4 – Confidence intervals

Example: pH-value of lime paints – continuation

Appendix 5 – Hypothesis, tests and conclusions – statistical tests

Example: Picking mushrooms.

Example: Comparison of two standard deviations

Example: ANOVA – comparison of two square sums

References

Appendix 6 – Three-component diagrams

Appendix 7 – Linear regression

Example: Estimation of the glass transition temperature via DSC

References

Appendix 8 – Failure mode and effect analysis, FMEA

References

Appendix 9 – General references

Acknowledgements

Author

Index

1.1 Design of experiments as part of the challenges and criteria of success in modern R&D

1.2 A typical experiment in coatings formulation

1.3 Factors, Levels, etc. – some vocabulary at the beginning

1.4 Classical design of experiments and the limitations

1.4.1 Conventional methods – more diversity is not possible

1.4.2 Limits in case of the classical approach

1.4.2.1 Number of experiments in case of many factors

1.4.2.2 Non-linear effects and domain dependence

1.4.2.3 Universality of the statements.

1.4.2.4 You desire, we play – multiple responses

1.4.2.5 The gain of knowledge and new information is too slow

1.5 Design of experiments – what’s that?

1.5.1 Design, factors and effects.

1.5.2 Interactions

1.6 Where is the statistics?

1.7 Models – pictures of reality

1.8 Overview, possibilities, benefits and limits

1.9 A brief history of statistical design of experiments

1.10 References

2 Planning is essential – a lot helps a lot

2.1 General principles for setting up a DoE investigation

2.1.1 Strategy of experimentation and guidelines for pre-experimental planning

2.1.2 Overcome experimental errors – identical replication.

2.1.3 How to overcome trends – randomization and arrangement in blocks.

2.1.4 Normalization, centring, orthogonal design

2.1.5 Not realizable, irregular combinations – the experimental region

2.2 Factorial designs – the heart of DoE

2.2.1 Two levels, two factors – 22-design

2.2.2 Two levels, three factors – 23-design

2.2.3 The general design with two levels – 2k-design

2.2.4 Factorial designs with centre-points

2.2.5 Blocking with factorial designs

2.3 Fractional factorial designs – to separate the wheat from the chaff

2.3.1 Basic principle of the reduction – confounding

2.3.2 Blocking – perfect suited for the 24-1-design

2.3.3 Types of fractional factorial designs

2.3.4 Plackett-Burmann designs.

2.3.5 DoE in colour measurement of a red-metallic base coat –

2 6-1-fractional factorial design

2.4 Non-linear effect designs

2.4.1 Central composite designs.

2.4.2 Three- and higher level designs

2.4.3 Mixed designs

2.4.4 Box-Behnken designs

2.4.5 D-optimal designs – egg-laying wool-milk-sow

2.5 Mixture design – a huge area

2.6 Qualitative classification

2.7 References

3 Number-crunching – nothing ventured, nothing gained in data analysis

3.1 Evaluation of raw data

3.1.1 Transformation

3.1.2 Outliers

3.2 Confidence intervals – where are the limits?

3.3 Regression – the best model

3.3.1 Basic principles

3.3.2 Confidence intervals for the model parameters

3.3.3 Basic principles and standard assumptions for regression analysis

3.4 Residual diagnostic – what does the deviations mean?.

3.5 Analysis of variance – how certain we can feel?

3.5.1 Introduction

3.5.2 Example: Colour measurement of a base coat – ANOVA.

3.6 References

4 Parametric optimization and sensitivity analysis – finding a needle in the haystack

4.1 Strategies for optimization – how we can do it better

4.1.1 Method of the steepest ascent/descent

4.1.2 Box-Wilson's method

4.1.3 EVOP-Method (evolutionary operations)

4.1.4 Simplex-method

4.1.5 Further optimization methods

4.2 Multiple responses

Example: Multiple optimization of blocking and film formation in a clear coat

Example: Optimization of an indoor paint

4.3.1 Qualitative analysis of the response surface

Example: Disturbance in levelling of a pigmented base coat

4.3.2 Quantitative analysis of the regression model

4.3.3 Taguchi-method

Example: Micro foam in a thick-coat glaze finish

4.4 References

5 DoE-Software – do not develop the wheel once more

Autonomous commercial software-packages for DoE:

Statistic packages

EXCEL-based Software

Appendix 1 – Precision, trueness and accuracy

Appendix 2 – Location and spread parameters

Example: pH-value of a lime paint

Example: pH-value of lime paints

Appendix 3 – Normal distribution

Example: pH-value of a lime paint

References

Appendix 4 – Confidence intervals

Example: pH-value of lime paints – continuation

Appendix 5 – Hypothesis, tests and conclusions – statistical tests

Example: Picking mushrooms.

Example: Comparison of two standard deviations

Example: ANOVA – comparison of two square sums

References

Appendix 6 – Three-component diagrams

Appendix 7 – Linear regression

Example: Estimation of the glass transition temperature via DSC

References

Appendix 8 – Failure mode and effect analysis, FMEA

References

Appendix 9 – General references

Acknowledgements

Author

Index

**Design of Experiments for Coatings Hardcover**

by Albert Roessler (Author)