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 Full Factorial Designs Developed by Don Edwards, John Grego and James Lynch Center for Reliability and Quality Sciences Department of Statistics University of South Carolina

Part I.3 The Essentials of 2-Cubed Designs Methodology Methodology –Cube Plots – Estimating Main Effects – Estimating Interactions (Interaction Tables and Graphs) Statistical Significance (Effects Probability Plots) Statistical Significance (Effects Probability Plots) Example With Interactions Example With Interactions A U-Do-It Case Study A U-Do-It Case Study

Methodology 2 3 Designs 2 3 Means What? 2 3 Means What? –3 Factors (Usually Labeled A, B, C) –2 Levels Lo (-) and Hi (+) –Comparing 8= 2 3 Recipes

Methodology 2 3 Designs - TV with Three Adjustment Knobs Knob Setting Is At The Top Knob Setting Is At The Top

Methodology Tabular and Graphical Methodology Cube Plots To See Relationships Between The Response and Factor Effects Cube Plots To See Relationships Between The Response and Factor Effects Sign Tables To Estimate Factor Effects Sign Tables To Estimate Factor Effects Probability Plots To Determine Statistically Significant Factor Effects Probability Plots To Determine Statistically Significant Factor Effects Interaction Graphs and Tables To Interpret Interactions Interaction Graphs and Tables To Interpret Interactions ANOVA Tables ANOVA Tables

Methodology Cube Plot

Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Note How The Responses are Entered into the Cube (Lo = - and Hi =+)

Methodology Cube Plot Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) –Y 1 is the Response when all the Factors are Lo (- - -) –Y 2 corresponds to (+ - -), Y 3 to (- + -) and Y 5 to (- - +) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) –Y 1 is the Response when all the Factors are Lo (- - -) –Y 2 corresponds to (+ - -), Y 3 to (- + -) and Y 5 to (- - +)

Methodology Cube Plot Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) –Y 8 is the Response when all the Factors are Hi (+ + +) –Y 4 corresponds to (+ + -), Y 6 to (+ - +) and Y 7 to (- + +) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) –Y 8 is the Response when all the Factors are Hi (+ + +) –Y 4 corresponds to (+ + -), Y 6 to (+ - +) and Y 7 to (- + +)

Methodology Example 1: Targeting a Process/Reducing Variation

Methodology Example 1 - Accuracy versus Precision

Methodology Example 1 - Improving a Process Which Factors Affect Which Factors Affect –Accuracy? –Precision? Which Factors Affect Which Factors Affect –Accuracy? –Precision?

Methodology Example 1 - Targeting a Process/Reducing Variation Various Types of Significance Statistical Statistical Engineering Engineering Economic Economic