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Design of Experiments for Coatings PDF

168 Pages·2014·6.89 MB·English
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Albert Rössler Design of Experiment for Coatings Cover: Adler-Werk Lackfabrik GmbH & Co. KG Bibliographische Information der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliographie; detaillierte bibliographische Daten sind im Internet über http://dnb.ddb.de abrufbar. Albert Rössler Design of Experiment for Coatings Hanover: Vincentz Network, 2014 EuropEan Coatings Library ISBN 978-3-74860-029-9 © 2014 Vincentz Network GmbH & Co. KG, Hanover Vincentz Network, P.O. Box 6247, 30062 Hanover, Germany This work is copyrighted, including the individual contributions and figures. Any usage outside the strict limits of copyright law without the consent of the publisher is prohibited and punish- able by law. This especially pertains to reproduction, translation, microfilming and the storage and processing in electronic systems. The information on formulations is based on testing performed to the best of our knowledge. The appearance of commercial names, product designations and trade names in this book should not be taken as an indication that these can be used at will by anybody. They are often registered names which can only be used under certain conditions. Please ask for our book catalogue Vincentz Network, Plathnerstr. 4c, 30175 Hanover, Germany T +49 511 9910-033, F +49 511 9910-029 [email protected], www.european-coatings.com Satz: Vincentz Network, Hanover, Germany ISBN 978-3-74860-029-9 EuropEan Coatings Library Albert Rössler Design of Experiment for Coatings European Coatings Library >> There‘s more! Discover our other bestsellers: Thomas G. Mezger The Rheology Handbook 4th Edition Already in its 4th edition, this standard work describes the principles of rheology clearly, vividly, and in practical terms. With its practical instruc- tions and illustrative examples, it enables the reader to perform tests with rotational and oscillatory rheometers and interpret the results correctly. > 2014, 432 pages, hardcover · 139,- €, order-no. 552, eBook: 552_PDF Artur Goldschmidt, Jochen Winkler Bodo Müller, Ulrich Poth Hans-Joachim Streitberger Titanium Dioxide Coatings Formulation BASF Handbook: Production, Properties and Effective 2nd Revised Edition Basics of Coating Technology Usage/2nd Revised Edition This reference work provides laboratory as- 2nd Edition A great source of information on the proper- sistants, engineers and chemists with de- This well-known standard work describes the ties and use of titanium dioxide pigments: tailed insights into coatings formulation: latest developments and tendencies in coat- this completely revised edition provides the opening with a look at the composition of ing technology. Special emphasis is placed on reader with a comprehensive overview of the coatings, it then gives advice on specific for- coating applications like automobile produc- working mechanisms and possible applica- mulations before formulation guidelines are tion coating, coil coating, automobile repair tions of titanium dioxide. analysed. coating, and industrial coating in general. > 2013, 154 pages, hardcover > 2011, 287 pages, hardcover > 2007, 792 pages, hardcover 99,- €, order-no. 656, eBook: PDF_656 139,- €, order-no. 285, eBook: 285_PDF 116,- €, order-no. 166, eBook: 166_PDF www.european-coatings.com/shop 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

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