Design of Experiments - Dynacentrix · “Design of Experiments: ... 11 Analysis of factorial...
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How to Optimize Products and Processes “Which combination of factors will give the best car engine at low cost, with low fuel consump- tion and minimal pollution?” A usually complex and costly experimental situation is easily resolved with Design of Experi- ments (DOE). All factors are considered in a minimal number of experiments, and the results are verified with recognized statistical methods. The book describes the method in its simple basis and adds valuable examples from a variety of application areas. The authors provide their detailed analyses and offer solutions, with the graphical presentation that is the trademark of Umetrics software MODDE. “Design of Experiments: Principles and Appli- cations” is 329 pages and the contents range from beginner’s level with initial screening all the way up to complex mixtures. The authors are experts in Design of Experiments and have a vast experience of application areas from years of consulting and lecturing at Umetrics. Design of Experiments Principles and Applications L. Eriksson, E. Johansson, N. Kettaneh-Wold, C. Wikström, and S. Wold ISBN 91-973730-0-1 “For newcomers in the field of experimental design the book is very useful.” “The book gives a detailed introduction to the princi- ples of experimental design and gives excellent illus- trations of the use of the MODDE software as an in- tegrated tool in design and analysis of experiments.” Rolf Carlson in Journal of Chemometrics, 15, 2001, 495-496
Transcript of Design of Experiments - Dynacentrix · “Design of Experiments: ... 11 Analysis of factorial...
How to Optimize Products and Processes“Which combination of factors will give the best car engine at low cost, with low fuel consump-tion and minimal pollution?”
A usually complex and costly experimental situation is easily resolved with Design of Experi-ments (DOE). All factors are considered in a minimal number of experiments, and the resultsare verified with recognized statistical methods. The book describes the method in its simplebasis and adds valuable examples from a variety of application areas. The authors provide theirdetailed analyses and offer solutions, with the graphical presentation that is the trademark ofUmetrics software MODDE.
“Design of Experiments: Principles and Appli-cations” is 329 pages and the contents rangefrom beginner’s level with initial screening allthe way up to complex mixtures. The authors areexperts in Design of Experiments and have avast experience of application areas from yearsof consulting and lecturing at Umetrics.
Design of ExperimentsPrinciples and Applications
L. Eriksson, E. Johansson, N. Kettaneh-Wold, C. Wikström, and S. Wold
ISBN 91-973730-0-1
“For newcomers in the field of experimental designthe book is very useful.”
“The book gives a detailed introduction to the princi-ples of experimental design and gives excellent illus-trations of the use of the MODDE software as an in-tegrated tool in design and analysis of experiments.”
Rolf Carlson in Journal of Chemometrics, 15, 2001,495-496
Content of “Design of Experiments: Principles and Applications”
specification/Significant modelFourth limiting case – Outsidespecification/Non-significantmodel
18 D-optimal designD-optimal designWhen to use D-optimal designFeatures of the D-optimalapproachEvaluation criteria
19 Mixture designA working strategy for mixturedesignAdvanced mixture designs
20 Multi-Level qualitativefactorsExample – Cotton cultivationRegression analysis of Cottonapplication – Coefficient plotRegression analysis of Cottonapplication – Interaction plot
21 Taguchi approach torobust designThe Taguchi approach –IntroductionArranging factors in inner andouter arraysThe classical analysis approach
22 Models of variability:DistributionsModels of variability - DistributionsThe normal distributionThe t-distributionConfidence intervals
23 Analysis of variance,ANOVAIntroduction to ANOVAANOVA – Regression modelsignificance testANOVA – Lack of fit test
24 PLSWhen to use PLSThe LOWARP applicationPLS model interpretation
Statistical AppendixReferences
Computation of main effects in the22 caseA second method of understandingmain effectsA quicker by-hand method forcomputing effectsPlotting of main and interactioneffectsInterpretation of main andinteraction effects in the 23 caseComputation of effects using leastsquares fit
9 Factorial designs (Part 3)Introduction to least squaresanalysisLeast squares analysis applied tothe CakeMix dataThe proper way of expressingregression coefficientsUse of coefficient and effect plots
10 Analysis of factorialdesigns (Part 1)Introduction to the analysis offactorial designsEvaluation of raw data – ReplicateplotRegression analysis – The R2 /Q2
diagnostic toolR2 /Q2 pointing to a poor modelModel interpretation – CoefficientplotUse of model – Response contourplotModel interpretation and use inthe case of several responses
11 Analysis of factorialdesigns (Part 2)Evaluation of raw data – ConditionnumberEvaluation of raw data – ScatterplotEvaluation of raw data – Histogramof responseEvaluation of raw data –Descriptive statistics of responseRegression analysis – Analysis ofvariance (ANOVA)Regression analysis – Normalprobability plot of residualsUse of model – Making predictions
12 Analysis of factorialdesigns (Part 3)Cause of poor model. 1. Skewresponse distribution
0 Preface 1Why Design of Experiments (DOE)is usedSectors where DOE is usedThree primary experimentalobjectives
1 Introduction (Part 1)When and where DOE is usefulWhat is DOE?General Example 1: ScreeningGeneral Example 2: OptimizationGeneral Example 3: RobustnesstestingThe Cake Mix application
2 Introduction (Part 2)VariabilityReacting to noiseFocusing on effectsIllustration: Cake MixConsequence of variability
3 Introduction (Part 3)The model conceptConceptual basis of semi-empiricalmodeling
4 Problem formulation (Part 1)Stages in the experimental processSpecification of factorsSpecification of responsesSelection of modelGeneration of designCreation of experimental worksheet
5 Problem formulation (Part 2)Qualitative factors at two levelsQualitative factors at many levelsRegular and irregular experimentalregionsMetric of factorsMetric of responses
6 Problem formulation (Part 3)Overview of modelsGeometry of models
7 Factorial designs (Part 1)Introduction to full factorialdesignsThe 22 full factorial design –construction & geometryThe 23 full factorial design –construction & geometryThe 24 and 25 full factorial designsPros and cons of two-level fullfactorial designs
8 Factorial designs (Part 2)Main effect of a factor
Benefits of responsetransformationCause of poor model. 2. CurvatureCause of poor model. 3. BadreplicatesCause of poor model. 4. DeviatingexperimentsIntroduction to PLS regression
13 Screening (Part 1)Selection of experimental objectiveFractional Factorial DesignsA geometric representation offractional factorial designsResolution of fractional factorialdesignsLaser welding application IWhat to do after screeningGradient techniquesGradient techniques applied to thelaser welding applicationAutomatic search for an optimalpoint
14 Screening (Part 2)Confounding patternGeneratorsDefining relationResolutionPlackett-Burman designs
15 Optimization (Part 1)Background to General Example 2Introduction to response surfacemethodology (RSM) designsOverview of composite designsTruck engine applicationWhat to do after RSMAutomatic search for an optimalpointMODDE optimizer applied to thetruck engine data
16 Optimization (Part 2)Three-Part full factorial designsBox-Behnken designsA comparison of Composite, Three-Part factorial, and Box-BehnkendesignsProperties of classical RSMdesigns
17 Robustness testingIntroduction to robustness testingHPLC applicationFirst limiting case – Insidespecification/Significant modelSecond limiting case – Insidespecification/Non-significantmodelThird limiting case – Outside
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