the essentials of 2-level design of experiments part i: the essentials of full factorial designs
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
The Essentials of 2-Level Design of The Essentials of 2-Level Design of ExperimentsExperiments
Part I: The Essentials of Full Factorial DesignsPart I: The Essentials of Full Factorial Designs
Developed by Don Edwards, John Grego and James Developed by Don Edwards, John Grego and James LynchLynch
Center for Reliability and Quality SciencesCenter for Reliability and Quality SciencesDepartment of StatisticsDepartment of Statistics
University of South CarolinaUniversity of South Carolina803-777-7800803-777-7800
Part I.3 The Essentials of 2-Cubed DesignsPart I.3 The Essentials of 2-Cubed Designs
MethodologyMethodology– Cube PlotsCube Plots– Estimating Main EffectsEstimating Main Effects– Estimating Interactions (Interaction Tables and Graphs)Estimating Interactions (Interaction Tables and Graphs)
Statistical Significance (Effects Probability Plots)Statistical Significance (Effects Probability Plots) Example With InteractionsExample With Interactions A U-Do-It Case StudyA U-Do-It Case Study
MethodologyMethodology 2233 Designs Designs
2233 Means What? Means What?– 3 Factors (Usually Labeled A, B, C)3 Factors (Usually Labeled A, B, C)– 2 Levels Lo (-) and Hi (+)2 Levels Lo (-) and Hi (+)– Comparing 8= 2Comparing 8= 233 Recipes Recipes
MethodologyMethodology 2233 Designs - TV with Three Adjustment Designs - TV with Three Adjustment
KnobsKnobs
A B C
Hi
Lo
Hi
Lo Hi
Lo
Lo Lo Hi Picture
Knob SettingKnob SettingIs At The TopIs At The Top
Knob SettingKnob SettingIs At The TopIs At The Top
MethodologyMethodology Tabular and Graphical MethodologyTabular and Graphical Methodology
Cube Plots To See Relationships Cube Plots To See Relationships Between The Response and Factor Between The Response and Factor EffectsEffects
Sign Tables To Estimate Factor EffectsSign Tables To Estimate Factor Effects Probability Plots To Determine Probability Plots To Determine
Statistically Significant Factor EffectsStatistically Significant Factor Effects Interaction Graphs and Tables To Interaction Graphs and Tables To
Interpret InteractionsInterpret Interactions ANOVA TablesANOVA Tables
MethodologyMethodologyCube PlotCube Plot
MethodologyMethodologyCube PlotCube Plot
Note How The Responses Note How The Responses are Entered into the Cubeare Entered into the Cube (Lo = - and Hi =+) (Lo = - and Hi =+)
Note How The Responses Note How The Responses are Entered into the Cubeare Entered into the Cube (Lo = - and Hi =+) (Lo = - and Hi =+)
Factors ResponseA B C yLo Lo Lo Y1
Hi Lo Lo Y2
Lo Hi Lo Y3
Hi Hi Lo Y4
Lo Lo Hi Y5
Hi Lo Hi Y6
Lo Hi Hi Y7
Hi Hi Hi Y8
Factors ResponseA B C yLo Lo Lo Y1
Hi Lo Lo Y2
Lo Hi Lo Y3
Hi Hi Lo Y4
Lo Lo Hi Y5
Hi Lo Hi Y6
Lo Hi Hi Y7
Hi Hi Hi Y8
C
B
A
+
+
+
_
_
_
Y1Y2
Y3Y4
Y5 Y6
Y7 Y8
C
B
A
+
+
+
_
_
_
Y1Y2
Y3Y4
Y5 Y6
Y7 Y8
MethodologyMethodologyCube PlotCube Plot
Note How The Responses Note How The Responses are Entered into the Cubeare Entered into the Cube (Lo = - and Hi =+) (Lo = - and Hi =+)– YY11 is the Response when all is the Response when all
the Factors are Lo (- - -)the Factors are Lo (- - -)
– YY2 2 corresponds to (+ - -),corresponds to (+ - -),YY33 to (- + -) and Y to (- + -) and Y55 to (- - +) to (- - +)
Note How The Responses Note How The Responses are Entered into the Cubeare Entered into the Cube (Lo = - and Hi =+) (Lo = - and Hi =+)– YY11 is the Response when all is the Response when all
the Factors are Lo (- - -)the Factors are Lo (- - -)
– YY2 2 corresponds to (+ - -),corresponds to (+ - -),YY33 to (- + -) and Y to (- + -) and Y55 to (- - +) to (- - +)
Factors ResponseA B C yLo Lo Lo Y1
Hi Lo Lo Y2
Lo Hi Lo Y3
Hi Hi Lo Y4
Lo Lo Hi Y5
Hi Lo Hi Y6
Lo Hi Hi Y7
Hi Hi Hi Y8
Factors ResponseA B C yLo Lo Lo Y1
Hi Lo Lo Y2
Lo Hi Lo Y3
Hi Hi Lo Y4
Lo Lo Hi Y5
Hi Lo Hi Y6
Lo Hi Hi Y7
Hi Hi Hi Y8
C
B
A
+
+
+
_
_
_
Y4
Y6
Y7 Y8
- - - + - -
- - +
- + -
C
B
A
+
+
+
_
_
_
Y4
Y6
Y7 Y8
- - - + - -
- - +
- + -
MethodologyMethodologyCube PlotCube Plot
Note How The Responses Note How The Responses are Entered into the Cubeare Entered into the Cube (Lo = - and Hi =+) (Lo = - and Hi =+)– YY88 is the Response when all the is the Response when all the
Factors are Hi (+ + +)Factors are Hi (+ + +)
– YY4 4 corresponds to (+ + -),corresponds to (+ + -),YY66 to (+ - +) and Y to (+ - +) and Y77 to (- + +) to (- + +)
Note How The Responses Note How The Responses are Entered into the Cubeare Entered into the Cube (Lo = - and Hi =+) (Lo = - and Hi =+)– YY88 is the Response when all the is the Response when all the
Factors are Hi (+ + +)Factors are Hi (+ + +)
– YY4 4 corresponds to (+ + -),corresponds to (+ + -),YY66 to (+ - +) and Y to (+ - +) and Y77 to (- + +) to (- + +)
Factors ResponseA B C yLo Lo Lo Y1
Hi Lo Lo Y2
Lo Hi Lo Y3
Hi Hi Lo Y4
Lo Lo Hi Y5
Hi Lo Hi Y6
Lo Hi Hi Y7
Hi Hi Hi Y8
Factors ResponseA B C yLo Lo Lo Y1
Hi Lo Lo Y2
Lo Hi Lo Y3
Hi Hi Lo Y4
Lo Lo Hi Y5
Hi Lo Hi Y6
Lo Hi Hi Y7
Hi Hi Hi Y8
C
B
A
+
+
+
_
_
_
- - - + - -
- - +
- + -
+ + +
+ + -
+ - +
- + +
C
B
A
+
+
+
_
_
_
- - - + - -
- - +
- + -
+ + +
+ + -
+ - +
- + +
MethodologyMethodologyExample 1: Targeting a Process/Reducing VariationExample 1: Targeting a Process/Reducing Variation
MethodologyMethodology Example 1 - Accuracy versus PrecisionExample 1 - Accuracy versus Precision
xx
xxxxxx
Accurate and
Precise
Not Accurate but
Precise
x xx
x xxx xx
x xx
x xxx xx
Accurate but
Not Precise
x x
x
xxx
x
xx
x xxx
x
x
xx
xxx x
x
x x
x
xxx
x
xx
x xxx
x
x
x
xxx x
x
Not Accurate and
Not Precise
MethodologyMethodologyExample 1 - Improving a ProcessExample 1 - Improving a Process
Which Factors AffectWhich Factors Affect– Accuracy?Accuracy?– Precision?Precision?
Which Factors AffectWhich Factors Affect– Accuracy?Accuracy?– Precision?Precision?
F a c t o r B
+
+
+
--
-
Factor C
Factor A
F a c t o r B
+
+
+
--
-
Factor C
Factor A
MethodologyMethodology Example 1 - Targeting a Process/Reducing VariationExample 1 - Targeting a Process/Reducing Variation
Various Types of SignificanceVarious Types of Significance StatisticalStatistical EngineeringEngineering EconomicEconomic