Designing Engineering Experiments: Factorial Experiments & Response Surfaces, Slides of Data Analysis & Statistical Methods

Download Designing Engineering Experiments: Factorial Experiments & Response Surfaces and more Slides Data Analysis & Statistical Methods in PDF only on Docsity! Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 1 Design of Engineering Experiments – Introduction to Factorials • Text reference, Chapter 5 • General principles of factorial experiments • The two-factor factorial with fixed effects Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 2 • The ANOVA for factorials • Extensions to more than two factors • Quantitative and qualitative factors – response curves and surfaces Regression Model & The Associated Response Surface Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 5 0 1 1 2 2 12 1 2 1 2 1 2 1 2 The least squares fit is ˆ 35.5 10.5 5.5 0.5 35.5 10.5 5.5 y x x x x y x x x x x x β β β β ε= + + + + = + + + ≅ + + The Effect of Interaction on the Response Surface Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 6 Suppose that we add an interaction term to the model: 1 2 1 2 ˆ 35.5 10.5 5.5 8y x x x x= + + + Interaction is actually a form of curvature Example 5.1 The Battery Life Experiment Text reference pg. 187 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 7 A = Material type; B = Temperature (A quantitative variable) 1. What effects do material type & temperature have on life? 2. Is there a choice of material that would give long life regardless of temperature (a robust product)? Extension of the ANOVA to Factorials (Fixed Effects Case) – pg. 189 2 2 2 ... .. ... . . ... 1 1 1 1 1 2 2 . .. . . ... . ( ) ( ) ( ) ( ) ( ) a b n a b ijk i j i j k i j a b a b n ij i j ijk ij y y bn y y an y y n y y y y y y = = = = = − = − + − + − − + + − ∑∑∑ ∑ ∑ ∑∑ ∑∑∑ Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 10 1 1 1 1 1i j i j k= = = = = breakdown: 1 1 1 ( 1)( 1) ( 1) T A B AB ESS SS SS SS SS df abn a b a b ab n = + + + − = − + − + − − + − ANOVA Table – Fixed Effects Case Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 11 JMP and Design-Expert will perform the computations Text gives details of manual computing (ugh!) – see pp. 192 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 12 Residual Analysis – Example 5.1 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 15 Interaction Plot DESIGN-EXPERT P lot L i fe X = B: T em perature Y = A: M ateria l A1 A1 A2 A2 A3 A3 A: Materia l Interaction Graph L if e 104 146 188 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 16 B: Tem perature 15 70 125 20 62 2 2 2 Quantitative and Qualitative Factors • The basic ANOVA procedure treats every factor as if it were qualitative • Sometimes an experiment will involve both quantitative and qualitative factors, such as in Example 5.1 • This can be accounted for in the analysis to produce Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 17 regression models for the quantitative factors at each level (or combination of levels) of the qualitative factors • These response curves and/or response surfaces are often a considerable aid in practical interpretation of the results Regression Model Summary of Results Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 20 Regression Model Summary of Results Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 21 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 22 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 25 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 26 Chapter 5 Design & Analysis of Experiments 8E 2012 Montgomery 27