1 The One-Quarter Fraction of the 2 k. 2 The One-Quarter Fraction of the 2 6-2 Complete defining relation: I = ABCE = BCDF = ADEF.

Slides:

Advertisements

Similar presentations

André L. S. de Pinho*+ Harold J. Steudel* Søren Bisgaard#

Advertisements

CSUN Engineering Management Six Sigma Quality Engineering Week 11 Improve Phase.

Statistical Analysis Professor Lynne Stokes Department of Statistical Science Lecture 15 Analysis of Data from Fractional Factorials and Other Unbalanced.

Chapter 6 The 2k Factorial Design

AB 11 22 33 44 55 66 77 88 99 10  20  19  18  17  16  15  14  13  12  11  21  22  23  24  25  26  27  28.

Design and Analysis of Experiments

Design and Analysis of Experiments Dr. Tai-Yue Wang Department of Industrial and Information Management National Cheng Kung University Tainan, TAIWAN,

II.2 Four Factors in Eight Runs Demonstrating the Effects of Confounding* Response: Conductivity (milliohm/cm), Corrected for Concentration (CC) Response:

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.

Taguchi’s Definition of Quality –or lack thereof “ The loss a product causes society after it is shipped ” Loss due to 1)Variability in function 2) Harmful.

The successful use of fractional factorial designs is based on three key ideas: 1)The sparsity of effects principle. When there are several variables,

Chapter 8 Two-Level Fractional Factorial Designs

Timed. Transects Statistics indicate that overall species Richness varies only as a function of method and that there is no difference between sites.

Stat Today: More Chapter 3. Analysis of Location and Dispersion Effects The epitaxial growth layer experiment is a 2 4 factorial design Have looked.

As with averages, researchers need to transform data into a form conducive to interpretation, comparisons, and statistical analysis measures of dispersion.

L. M. LyeDOE Course1 Design and Analysis of Multi-Factored Experiments Fractional Factorial Designs.

1 14 Design of Experiments with Several Factors 14-1 Introduction 14-2 Factorial Experiments 14-3 Two-Factor Factorial Experiments Statistical analysis.

Design of Experiments Chapter 21.

Fractional Factorial Experiments (Continued) The concept of design resolution is a useful way to categorize fractional factorial designs. The higher the.

Chapter 8Design and Analysis of Experiments 8E 2012 Montgomery 1 Design of Engineering Experiments The 2 k-p Fractional Factorial Design Text reference,

CPE 619 2k-p Factorial Design

Design-plots for factorial and fractional-factorial designs Russell R Barton Journal of Quality Technology; 30, 1 ; Jan 1998 報告者：李秦漢.

DOX 6E Montgomery1 Design of Engineering Experiments Part 7 – The 2 k-p Fractional Factorial Design Text reference, Chapter 8 Motivation for fractional.

Robust Design ME 470 Systems Design Fall Why Bother? Customers will pay for increased quality! Customers will be loyal for increased quality!

Splash Screen. Then/Now You wrote linear equations given either one point and the slope or two points. Write equations of lines in point-slope form. Write.

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.

1 Chapter 3: Screening Designs 3.1 Fractional Factorial Designs 3.2 Blocking with Screening Designs.

1 The General 2 k-p Fractional Factorial Design 2 k-1 = one-half fraction, 2 k-2 = one-quarter fraction, 2 k-3 = one-eighth fraction, …, 2 k-p = 1/ 2 p.

1 The Drilling Experiment Example 6-3, pg. 237 A = drill load, B = flow, C = speed, D = type of mud, y = advance rate of the drill.

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.

IE341 Midterm. 1. The effects of a 2 x 2 fixed effects factorial design are: A effect = 20 B effect = 10 AB effect = 16 = 35 (a) Write the fitted regression.

III.7 Blocking Two-level Designs _ Blocking _ Example _ Four Blocks _ Exercise.

Concept 1 Example 1 Write and Graph an Equation in Point-Slope Form (x 1, y 1 ) = (–2, 0) Point-slope form Answer: Write the point-slope form of an equation.

5.2 Properties of Rational Exponents

The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs The Essentials of 2-Level Design of Experiments Part I:

The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs The Essentials of 2-Level Design of Experiments Part I:

1 Prof. Indrajit Mukherjee, School of Management, IIT Bombay High (2 pounds ) Low (1pound) B=60 ( ) Ab=90 ( ) (1)=80 ( ) A=100.

Chapter 9 - Transformations. 90 degree rotation (x 1, y 1 ) 180 degree rotation (x 2, y 2 ) 270 degree rotation (x 3, y 3 )

1 Mixed and Random Effects Models 1-way ANOVA - Random Effects Model 1-way ANOVA - Random Effects Model 2-way ANOVA - Mixed Effects Model 2-way ANOVA -

L. M. LyeDOE Course1 Design and Analysis of Multi-Factored Experiments Fractional Factorials Not Based on the Powers of 2 – Irregular Designs.

Designs for Experiments with More Than One Factor When the experimenter is interested in the effect of multiple factors on a response a factorial design.

2 k factorial designs l Examine the response for all possible combinations of k factors at two levels l Are carried out as replicated or unreplicated experiments.

1 Chapter 8 Two-level Fractional Factorial Designs.

1 Chapter 8 Two-level Fractional Factorial Designs.

Diploma in Statistics Design and Analysis of Experiments Lecture 4.11 © 2010 Michael Stuart Design and Analysis of Experiments Lecture Review of.

WARM-UP PROBLEM Simplify the expression. Assume all variables are positive – 48 ANSWER 3 4.

Design of Engineering Experiments Part 5 – The 2k Factorial Design

CME Analysis: a New Method for Unraveling Aliased Effects in Two-Level Fractional Factorial Experiments C. F. Jeff Wu (Joint work with Heng Su) School.

Design and Analysis of Experiments

Regression Computer Print Out

Confounding the 2k Factorial Design in Four Blocks

Using Baseline Data in Quality Problem Solving

Design and Analysis of Multi-Factored Experiments

Special Topics In Design

Fractional Factorial Design

Construction of One-half Fractions

Exploring Partially ordered sets

Reading: ‘Washington, DC’

III.7 Blocking Two-level Designs

Text reference, Chapter 8

ENM 310 Design of Experiments and Regression Analysis Chapter 3

II.2 Four Factors in Eight Runs

The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James Lynch.

Response: Conductivity (milliohm/cm), Corrected for Concentration (CC)

Design matrix Run A B C D E

14 Design of Experiments with Several Factors CHAPTER OUTLINE

Presentation transcript:

1 The One-Quarter Fraction of the 2 k

2 The One-Quarter Fraction of the Complete defining relation: I = ABCE = BCDF = ADEF

3 The One-Quarter Fraction of the Uses of the alternate fractions E = ±ABC, F = ±BCD Projection of the design into subsets of the original six variables Any subset of 4 factors of the original 6 variables that is not a word in the complete defining relation will result in a full factorial design Any subset of 4 factors of the original 6 variables that is a word in the complete defining relation will result in a replicated one-half factorial design –Consider ABCD (full factorial) –Consider ABCE (replicated half fraction) –Consider ABCF (full factorial)

4 Design Matrix of Example 8-4 Injection molding process with six factors

5

6 Large effects: A, B, and AB (Ockham’s razor) The process is sensitive to temperature (A) if the screw speed (B) is at the high level => both A and B should be at the low level (reduce mean shrinkage) How about the part-to-part variability?

7 ŷ =  o +  1 x 1 +  2 x 2 +  12 x 1 x 2 =  +  x 1 +  x 2 +  x 1 x 2 e = y - ŷ

8 Residual plots indicate there are some dispersion effects, which can be quantified by an analysis of residuals.

9 Example 8-4 Factor C has a large dispersion effect. Its location effect is not large, so its level can be set to low to reduce variation.

10 Projection onto a cube in A, B, and C (Example 8-4) > 2 3 (n=2) B=low results in low values of average part shrinkage C=low produces low part-to-part variation => B - C - 10