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 803-777-7800

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

23 Means What? Methodology 23 Designs 3 Factors (Usually Labeled A, B, C) 2 Levels Lo (-) and Hi (+) Comparing 8= 23 Recipes

Methodology 23 Designs - TV with Three Adjustment Knobs The picture is the Lo Lo Hi response. Lo and Hi are factor settings Knob Setting Is At The Top

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

Methodology Cube Plot Template

Methodology Cube Plot Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Y(i) will be replaced with, e.g., Y(---) or Y(111).

Methodology Cube Plot (OVAT) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Y1 is the Response when all the Factors are Lo (- - -) Y2 corresponds to (+ - -), Y3 to (- + -) and Y5 to (- - +) Factor settings for OVAT design

Methodology Cube Plot (Full Factorial) Note How The Responses are Entered into the Cube (Lo = - and Hi =+) Y8 is the Response when all the Factors are Hi (+ + +) Y4 corresponds to (+ + -), Y6 to (+ - +) and Y7 to (- + +) Factor settings for full factorial design

Methodology Example 1: Targeting a Process/Reducing Variation

Methodology Example 1 - Accuracy versus Precision Skip

Methodology Example 1 - Improving a Process Which Factors Affect Accuracy? Precision? Skip. Slightly different picture from I.2 and I.5, but same factor effects

Statistical Engineering Economic Methodology Example 1 - Targeting a Process/Reducing Variation Various Types of Significance Statistical Engineering Economic Statistical significance may not lead to a practical difference Ted Shropshire at Becton-Dickinson often found statistical significance, but economics didn’t work out. -Sara Lee Study -No Statistical Significance Difference Between Needles -But This Was Economically Significant