Design of Experiments for Coatings

168 Pages·2014·6.89 MB·English

by  Rössler, Albert

Albert Rössler
Design of Experiment for Coatings
Cover: Adler-Werk Lackfabrik GmbH & Co. KG
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Albert Rössler
Design of Experiment for Coatings
Hanover: Vincentz Network, 2014
EuropEan Coatings Library
ISBN 978-3-74860-029-9
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Contents 7
Contents
1 D esign of experiments – systematic mania? ..................................... 11
1.1 D esign of experiments as part of the challenges and criteria
of success in modern R&D ..................................................................................... 11
1.2 A typical experiment in coatings formulation .................................................. 17
1.3 F actors, Levels, etc. – some vocabulary at the beginning .............................. 18
1.4 C lassical design of experiments and the limitations ....................................... 20
1.4.1 Conventional methods – more diversity is not possible .................................. 20
1.4.2 Limits in case of the classical approach. ............................................................. 21
1.4.2.1 Number of experiments in case of many factors .............................................. 21
1.4.2.2 Non-linear effects and domain dependence ....................................................... 23
1.4.2.3 Universality of the statements .............................................................................. 25
1.4.2.4 You desire, we play – multiple responses ........................................................... 26
1.4.2.5 The gain of knowledge and new information is too slow ................................ 26
1.5 Design of experiments – what’s that? ................................................................. 27
1.5.1 Design, factors and effects ..................................................................................... 27
Albert Rössler: Design of Experiment for Coatings
© Copyright 2014 by Vincentz Network, Hanover, Germany
ISBN: 978-3-86630-885-5
Paint runs through our veins.
8 Contents
1.5.2 Interactions ................................................................................................................ 30
1.6 Where is the statistics? ........................................................................................... 32
1.7 Models – pictures of reality ................................................................................... 36
1.8 Overview, possibilities, benefits and limits ....................................................... 42
1.9 A brief history of statistical design of experiments ......................................... 45
1.10 References.................................................................................................................. 45
2 Planning is essential – a lot helps a lot ................................................... 47
2.1 General principles for setting up a DoE investigation ..................................... 47
2.1.1 Strategy of experimentation and guidelines for
pre-experimental planning ................................................................................... 47
2.1.2 Overcome experimental errors – identical replication .................................... 51
2.1.3 H ow to overcome trends – randomization and arrangement in blocks ....... 51
2.1.4 Normalization, centring, orthogonal design ...................................................... 53
2.1.5 N ot realizable, irregular combinations – the experimental region .............. 54
2.2 Factorial designs – the heart of DoE .................................................................... 55
2.2.1 Two levels, two factors – 22-design ...................................................................... 55
2.2.2 Two levels, three factors – 23-design ................................................................... 56
2.2.3 The general design with two levels – 2k-design ............................................... 61
2.2.4 Factorial designs with centre-points ................................................................... 62
2.2.5 Blocking with factorial designs ............................................................................ 63
2.3 F ractional factorial designs – to separate the wheat from the chaff ............ 66
2.3.1 Basic principle of the reduction – confounding ................................................ 66
2.3.2 Blocking – perfect suited for the 24-1-design ..................................................... 69
2.3.3 Types of fractional factorial designs .................................................................... 71
2.3.4 Plackett-Burmann designs ..................................................................................... 72
2.3.5 D oE in colour measurement of a red-metallic base coat –
2 6-1-fractional factorial design ................................................................................. 72
2.4 Non-linear effect designs ....................................................................................... 76
2.4.1 C entral composite designs ..................................................................................... 77
2.4.2 Three- and higher level designs ........................................................................... 80
2.4.3 Mixed designs........................................................................................................... 80
2.4.4 Box-Behnken designs .............................................................................................. 84
2.4.5 D-optimal designs – egg-laying wool-milk-sow ................................................ 85
2.5 Mixture design – a huge area ............................................................................... 85
2.6 Qualitative classification ........................................................................................ 88
2.7 References.................................................................................................................. 93
3 Number-crunching –
nothing ventured, nothing gained in data analysis .............................. 94
3.1 Evaluation of raw data ............................................................................................. 94
3.1.1 Transformation ......................................................................................................... 94
3.1.2 Outliers ....................................................................................................................... 95
3.2 Confidence intervals – where are the limits? .................................................... 95
3.3 Regression – the best model .................................................................................. 95
3.3.1 Basic principles ........................................................................................................ 95
3.3.2 Confidence intervals for the model parameters ................................................ 99
3.3.3 Basic principles and standard assumptions for regression analysis ........... 101
3.4 Residual diagnostic – what does the deviations mean? .................................. 103
3.5 Analysis of variance – how certain we can feel? .................................................. 105
3.5.1 Introduction ............................................................................................................... 105
Contents 9
3.5.2 Example: Colour measurement of a base coat – ANOVA ................................ 111
3.6 References.................................................................................................................. 114
4 Parametric optimization and sensitivity analysis –
finding a needle in the haystack ........................................................ 116
4.1 S trategies for optimization – how we can do it better ..................................... 116
4.1.1 Method of the steepest ascent/descent ............................................................... 117
4.1.2 Box-Wilson's method .............................................................................................. 117
4.1.3 EVOP-Method (evolutionary operations) ............................................................. 117
4.1.4 Simplex-method ....................................................................................................... 118
4.1.5 Further optimization methods .............................................................................. 118
4.2 Multiple responses ................................................................................................... 118
Example: Multiple optimization of blocking and film formation
in a clear coat ............................................................................................................ 119
Example: Optimization of an indoor paint .......................................................... 121
4.3.1 Qualitative analysis of the response surface ..................................................... 125
Example: Disturbance in levelling of a pigmented base coat ........................ 125
4.3.2 Quantitative analysis of the regression model .................................................. 129
4.3.3 Taguchi-method ........................................................................................................ 129
Example: Micro foam in a thick-coat glaze finish ............................................ 130
4.4 References.................................................................................................................. 132
5 DoE-Software – do not develop the wheel once more ........................ 134
Autonomous commercial software-packages for DoE: .................................... 134
Statistic packages .................................................................................................... 135
EXCEL-based Software ........................................................................................... 135
Appendix 1 – Precision, trueness and accuracy ............................................... 136
Appendix 2 – Location and spread parameters ................................................. 137
Example: pH-value of a lime paint ....................................................................... 138
Example: pH-value of lime paints ........................................................................ 139
Appendix 3 – Normal distribution ..................................................................... 141
Example: pH-value of a lime paint ....................................................................... 143
References.................................................................................................................. 145
Appendix 4 – Confidence intervals .................................................................... 146
Example: pH-value of lime paints – continuation ............................................. 148
Appendix 5 – Hypothesis, tests and conclusions – statistical tests ................. 149
Example: Picking mushrooms .............................................................................. 150
Example: Comparison of two standard deviations ........................................... 153
Example: ANOVA – comparison of two square sums ...................................... 153
References.................................................................................................................. 153
Appendix 6 – Three-component diagrams ........................................................ 154
Appendix 7 – Linear regression ......................................................................... 155
Example: Estimation of the glass transition temperature via DSC ............. 156
References.................................................................................................................. 156
10 Contents
Appendix 8 – Failure mode and effect analysis, FMEA .................................... 157
References.................................................................................................................. 158
Appendix 9 – General references ....................................................................... 159
Acknowledgements ............................................................................. 160
Author .................................................................................................. 161
Index .................................................................................................... 163
Preface
For sure you have experience with such problems: the complex production process or the
demanded coating properties are affected by several factors (grinding time, binder content,
amount of additives, drying time, etc.). You would like to improve the system and do not
know which are the most dominant factors. No wonder, as long as your formulation is assem-
bled by 10 components. The experimental setup get out of hand, results are unintelligible
and the documentation is fragmentary at the end. In this situation you might got already
the advice to try the statistical approach by design of experiment (abbreviated DoE). Nice,
but what is that? Beside, statistics sounds like mathematics and at the moment you are too
busy for such things?
Well, time and some distance from the daily business will be necessary, if you read this
book. However, the aim is a short and generally understandable overview regarding the
effects und benefits of DoE by examples in step with actual practice. The examples are based
on real-world applications in coatings formulation. This adds the important strong applica-
tion flavour to this book, makes it useful as a reference tool and show that statistics doesn’t
have to be that dry and difficult mathematics. In addition, requirements for the approach
are illustrated, which are quite often general principles in experimental design and project
management. It is not possible to describe the topic without any statistics or mathematics,
but formulas and derivations are at the least possible amount in this book. So, the prerequi-
sites are relatively modest. In addition, there is no claim to be complete, because the topic
and connected mathematic methods as well as tools for data analysis are too extensive. Due
to this, the textbook familiarize first-time user and already practicing laboratory assistants,
engineers and chemists with possible applications and high potential of the method. It is
important to succeed the entrance and to get a feeling of success by try and error. It’s no
problem, if not everything is clear in the first run. Experience about useful applications
and limits will be generated in the course of time. After that, this technique will attend you
for sure as valuable providing tool for a long time. The skills acquired in dealing with this
method can also be employed in other applications, such as adhesives and sealants as well
as all other engineering and scientific issues.
Chapter 1 introduces the method and shows especially the difference to the classical
approach. With an example directly out of the “coating-formulation kitchen” it will be help-
fully shown, how the systematic method DoE can reduce the daily mania in the research
laboratory. Derived from today’s criteria of success in R&D, also general principles of project
management and design of experiments are illuminated.
Chapter 2 reflects the design methods and introduce into the important preliminary step
of drawing up a strategy of experimentation. State of the art experimental designs are
presented together with their properties. This should help for precise selections later on in
practice. Planning as preliminary step is the basic for all further details and the potential
savings are naturally enormous. Therefore, planning is of much higher importance as the
subsequent data analysis. A lot helps a lot in this context!
Chapter 3 is devoted to the data analysis and interpretation. During this period the basic
principle „nothing ventured, nothing gained“, can be applied. Only data from perfectly
planned and designed experiments ends up in reasonable interpretations. On the other
hand, the best set of data is useless, when no interpretation and good compression is per-
formed. Where is the limit? How valid and precise are the conclusions? These are some
questions, which will be answered in Chapter 3.
Chapter 4 introduces the standard optimization processes and describes how to convert
modelling results into concrete action. The determination of cause and effect correlations
during the identification of the most dominant factors is only one part of the story. It is also
of high importance to find those operating conditions, which lead to a maximum, minimum
or a certain value (or range) of the target response. In addition, just optimizing a problem
will end up very often in results, which are sensitive against small variations in the factor
settings due to disturbances. To look on the issue in its entirety, also strategies for robust-
ness studies are described, leading to processes and products that perform better in the
field due to variability reduction. In a manner of speaking: finding a needle in the haystack.
Chapter 5 describes some DoE software solutions on the market. It is not necessary to
reinvent the wheel once more and to create all experimental designs by hand. Modern and
good designed programs assist the practitioner in the number-crunching.
Short text elements including basic principles are included in all book chapters. They sum-
marize general and essential messages regarding design of experiments and performing
experiments. These elements do not replace the rest of the book as a kind of summary,
because basic principles are not covering methodical details. Basic principles only intensify
relevant messages regarding the philosophy of the DoE-concept. Therefore, they are not
used inflationary.
Research and development in coating industry is highly affected by experience. If some-
body is working long enough in this branch, a comprehensive treasure of raw material and
formulation knowledge will be acquired. This experience is very important and is beside
the application knowledge the working basis. However, research and development underlie
today tough necessities, because innovative ideas, higher rates of success, shorter time to
market as well as lower R&D-costs should be realized in parallel. Therefore, both, a deep
understanding of the increasing international customer demands and economic mentality
becomes more and more important in research laboratories. In addition, knowledge about
the correlations – independent if the recipes, the production or the application process are in
focus – is essential for creating innovative, stable, robust, cost-optimized and high-quality
products very rapid today. Thus, methods which support purposefully and efficiently work-
ing are crucial to be successful.
Design of experiments is one possibility, to reply the challenges of today and to manage the
important free space for creativity due to higher efficiency. This book can assist you in this
challenging task and shows how coating formulators can benefit from DoE.
Innsbruck, Austria, Mai 2014
Albert Rössler