Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 1 Factorial Experiments Text reference, Chapter 5 General principles of factorial experiments.

Slides:



Advertisements
Similar presentations
Randomized Complete Block and Repeated Measures (Each Subject Receives Each Treatment) Designs KNNL – Chapters 21,
Advertisements

Multiple Comparisons in Factorial Experiments
Chapter 6 The 2k Factorial Design
Chapter 4Design & Analysis of Experiments 7E 2009 Montgomery 1 Experiments with Blocking Factors Text Reference, Chapter 4 Blocking and nuisance factors.
DOX 6E Montgomery1 Design of Engineering Experiments Part 3 – The Blocking Principle Text Reference, Chapter 4 Blocking and nuisance factors The randomized.
1 Design of Engineering Experiments Part 3 – The Blocking Principle Text Reference, Chapter 4 Blocking and nuisance factors The randomized complete block.
Chapter 3Design & Analysis of Experiments 7E 2009 Montgomery 1.
Experiments with both nested and “crossed” or factorial factors
Designing experiments with several factors
STT 511-STT411: DESIGN OF EXPERIMENTS AND ANALYSIS OF VARIANCE Dr. Cuixian Chen Chapter 14: Nested and Split-Plot Designs Design & Analysis of Experiments.
Chapter 14Design and Analysis of Experiments 8E 2012 Montgomery 1.
Experimental Design, Response Surface Analysis, and Optimization
1.Basic Principles & Definitions 2.The Advantage 3.Two-Factorial Design 4.Number of Replicates 5.General Factorial Design 6.Response Surfaces & Contour.
Design and Analysis of Experiments Dr. Tai-Yue Wang Department of Industrial and Information Management National Cheng Kung University Tainan, TAIWAN,
Design of Engineering Experiments - Experiments with Random Factors
Chapter 5 Introduction to Factorial Designs
1 Chapter 6 The 2 k Factorial Design Introduction The special cases of the general factorial design (Chapter 5) k factors and each factor has only.
14-1 Introduction An experiment is a test or series of tests. The design of an experiment plays a major role in the eventual solution of the problem.
Lecture 8 Last day: 3.1 Today: Next day: , Assignment #2: Chapter 2: 6, 15 (treat tape speed and laser power as qualitative factors),
1 Chapter 5 Introduction to Factorial Designs Basic Definitions and Principles Study the effects of two or more factors. Factorial designs Crossed:
Analysis of Variance Chapter 3Design & Analysis of Experiments 7E 2009 Montgomery 1.
8. ANALYSIS OF VARIANCE 8.1 Elements of a Designed Experiment
13-1 Designing Engineering Experiments Every experiment involves a sequence of activities: Conjecture – the original hypothesis that motivates the.
13 Design and Analysis of Single-Factor Experiments:
1 14 Design of Experiments with Several Factors 14-1 Introduction 14-2 Factorial Experiments 14-3 Two-Factor Factorial Experiments Statistical analysis.
Text reference, Chapter 14, Pg. 525
Chapter 8Design and Analysis of Experiments 8E 2012 Montgomery 1 Design of Engineering Experiments The 2 k-p Fractional Factorial Design Text reference,
Chapter 13Design & Analysis of Experiments 8E 2012 Montgomery 1.
DOX 6E Montgomery1 Design of Engineering Experiments Part 7 – The 2 k-p Fractional Factorial Design Text reference, Chapter 8 Motivation for fractional.
Design of Engineering Experiments Part 4 – Introduction to Factorials
1 The General Factorial Design Two-factor factorial design General case: Factor A – a levels Factor B – b levels … n replicate (n  2) Total observations:
Design of Engineering Experiments Part 5 – The 2k Factorial Design
1 The General 2 k Factorial Design Section 6-4, pg. 224, Table 6-9, pg. 225 There will be k main effects, and.
14-1 Introduction An experiment is a test or series of tests. The design of an experiment plays a major role in the eventual solution of the problem.
Chapter 6Based on Design & Analysis of Experiments 7E 2009 Montgomery 1 Design and Analysis of Engineering Experiments Ali Ahmad, PhD.
DOX 6E Montgomery1 Design of Engineering Experiments Part 4 – Introduction to Factorials Text reference, Chapter 5 General principles of factorial experiments.
Then click the box for Normal probability plot. In the box labeled Standardized Residual Plots, first click the checkbox for Histogram, Multiple Linear.
DOX 6E Montgomery1 Unreplicated 2 k Factorial Designs These are 2 k factorial designs with one observation at each corner of the “cube” An unreplicated.
Chapter 6Design & Analysis of Experiments 8E 2012 Montgomery 1 Design of Engineering Experiments Part 5 – The 2 k Factorial Design Text reference, Chapter.
DOX 6E Montgomery1 Design of Engineering Experiments Part 9 – Experiments with Random Factors Text reference, Chapter 13, Pg. 484 Previous chapters have.
Design Of Experiments With Several Factors
Chapter 6Design & Analysis of Experiments 7E 2009 Montgomery 1 Design of Engineering Experiments Two-Level Factorial Designs Text reference, Chapter 6.
1 The 2 k-p Fractional Factorial Design Text reference, Chapter 8 Motivation for fractional factorials is obvious; as the number of factors becomes large.
Analysis of Covariance Combines linear regression and ANOVA Can be used to compare g treatments, after controlling for quantitative factor believed to.
Chapter 15Design & Analysis of Experiments 8E 2012 Montgomery 1.
DOX 6E Montgomery1 Design of Engineering Experiments Part 2 – Basic Statistical Concepts Simple comparative experiments –The hypothesis testing framework.
Single-Factor Studies KNNL – Chapter 16. Single-Factor Models Independent Variable can be qualitative or quantitative If Quantitative, we typically assume.
28. Multiple regression The Practice of Statistics in the Life Sciences Second Edition.
Chapter 13 Design of Experiments. Introduction “Listening” or passive statistical tools: control charts. “Conversational” or active tools: Experimental.
Copyright © 2010 Pearson Addison-Wesley. All rights reserved. Chapter 14 Factorial Experiments (Two or More Factors)
1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay Some Basic Definitions Definition of a factor effect: The change in the mean response when.
1 Design of Engineering Experiments – The 2 k Factorial Design Text reference, Chapter 6 Special case of the general factorial design; k factors, all at.
Statistics 3502/6304 Prof. Eric A. Suess Chapter 3.
Engineering Statistics Design of Engineering Experiments.
Design and Analysis of Experiments
Design of Engineering Experiments Part 5 – The 2k Factorial Design
Two-way ANOVA problems
Chapter 5 Introduction to Factorial Designs
Prof. Eric A. Suess Chapter 3
Design & Analysis of Experiments 8E 2012 Montgomery
Randomized Complete Block and Repeated Measures (Each Subject Receives Each Treatment) Designs KNNL – Chapters 21,
Simple Linear Regression
ENM 310 Design of Experiments and Regression Analysis Chapter 3
Regression and Categorical Predictors
Chapter 5: Introduction to Factorial Designs
14 Design of Experiments with Several Factors CHAPTER OUTLINE
Two-way ANOVA problems
Presentation transcript:

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 1 Factorial Experiments Text reference, Chapter 5 General principles of factorial experiments The two-factor factorial with fixed effects The ANOVA for factorials Extensions to more than two factors Quantitative and qualitative factors – response curves and surfaces

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 2 Some Basic Definitions Definition of a factor effect: The change in the mean response when the factor is changed from low to high

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 3 The Case of Interaction:

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 4 Regression Model & The Associated Response Surface

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 5 The Effect of Interaction on the Response Surface Suppose that we add an interaction term to the model: Interaction is actually a form of curvature

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 6 Example 5.1 The Battery Life Experiment Text reference pg. 167 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)?

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 7 The General Two-Factor Factorial Experiment a levels of factor A; b levels of factor B; n replicates This is a completely randomized design

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 8 Statistical (effects) model: Other models (means model, regression models) can be useful

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 9 Extension of the ANOVA to Factorials (Fixed Effects Case) – pg. 168

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 10 ANOVA Table – Fixed Effects Case Design-Expert will perform the computations Text gives details of manual computing (ugh!) – see pp. 171

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 11

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 12 Design-Expert Output – Example 5.1

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 13 JMP output – Example 5.1

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 14 Residual Analysis – Example 5.1

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 15 Residual Analysis – Example 5.1

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 16 Interaction Plot

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 17 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 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

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 18 Quantitative and Qualitative Factors Candidate model terms from Design- Expert: Intercept A B B 2 AB B 3 AB 2 A = Material type B = Linear effect of Temperature B 2 = Quadratic effect of Temperature AB = Material type – Temp Linear AB 2 = Material type - Temp Quad B 3 = Cubic effect of Temperature (Aliased)

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 19 Quantitative and Qualitative Factors

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 20 Regression Model Summary of Results

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 21 Regression Model Summary of Results

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 22

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 23

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 24

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 25

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 26

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 27

Chapter 5Design & Analysis of Experiments 7E 2009 Montgomery 28 Factorials with More Than Two Factors Basic procedure is similar to the two-factor case; all abc…kn treatment combinations are run in random order ANOVA identity is also similar: Complete three-factor example in text, Example 5.5

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com. Inc. All rights reserved.