Transcript Lecture 6.1 - University of South Carolina

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

Methodology
23 Designs
 23
Means What?
– 3 Factors (Usually Labeled A, B, C)
– 2 Levels Lo (-) and Hi (+)
– Comparing 8= 23 Recipes
Methodology
23 Designs - TV with Three Adjustment Knobs
Lo Lo Hi
Picture

Knob Setting
Is At The Top
Lo
Lo
Hi
A
B
C
Hi
Hi
Lo
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
Methodology
Cube Plot
Y
Y
7
8
Y
Y
4
3
+
Y
Y
5
B
A
Lo
Hi
Lo
Hi
Lo
Hi
Lo
Hi
Factors
B
Lo
Lo
Hi
Hi
Lo
Lo
Hi
Hi
C
Lo
Lo
Lo
Lo
Hi
Hi
Hi
Hi
Response
y
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
6
+
C
_
Y
Y
1
2
_
A
+
_

Note How The Responses are
Entered into the Cube
(Lo = - and Hi =+)
Methodology
Cube Plot
Y
Y
7
8
Y
-+-
4
+
6
+
C
_
+--
--A
C
Lo
Lo
Lo
Lo
Hi
Hi
Hi
Hi
Response
y
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
Y
--+
B
_
A
Lo
Hi
Lo
Hi
Lo
Hi
Lo
Hi
Factors
B
Lo
Lo
Hi
Hi
Lo
Lo
Hi
Hi
+
_

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 (- - +)
Methodology
Cube Plot
+++
-++
++-
-++
--+
+
C
_
+--
--A
C
Lo
Lo
Lo
Lo
Hi
Hi
Hi
Hi
Response
y
Y1
Y2
Y3
Y4
Y5
Y6
Y7
Y8
+-+
B
_
A
Lo
Hi
Lo
Hi
Lo
Hi
Lo
Hi
Factors
B
Lo
Lo
Hi
Hi
Lo
Lo
Hi
Hi
+
_

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 (- + +)
Methodology
Example 1: Targeting a Process/Reducing Variation
Methodology
Example 1 - Accuracy versus Precision
Not Accu rate
bu t
Precise
Accurate
an d
Precise
x xx x
x xxxx x
x x
x
xxxxx xx
x
xxx xx
Not Accu rate
an d
Not Precise
Accurate
bu t
Not Precise
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Methodology
Example 1 - Improving a Process

Which Factors Affect
– Accuracy?
– Precision?
Methodology
Example 1 - Targeting a Process/Reducing Variation
Various Types of Significance
Statistical
 Engineering
 Economic
