Client, Enterprise

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CUSTOMER COMPETITIVE INTELLIGENCE
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FOR SYSTEMS INNOVATION DESIGN
DEPARTMENT OF STATISTICS
REDGEMAN_at_UIDAHO.EDU
OFFICE 1-208-885-4410
DR. RICK EDGEMAN, PROFESSOR CHAIR SIX SIGMA
BLACK BELT
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Design of Experimentsand2k Factorial Designs
DEPARTMENT OF STATISTICS
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a highly structured strategy for acquiring,
assessing, and applying customer, competitor, and
enterprise intelligence for the purposes of
product, system or enterprise innovation and
design.
DEPARTMENT OF STATISTICS
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The Scientific Method Informed
Observation Data Driven Decision
Making Directed Experimentation 2k Factorial
Experiments, Interaction and Scree Plots 2k-p
Fractional Factorial Designs Central Composite
Designs Response Surface Methods Process
Optimization - Selecting Your Settings.
The Scientific Context of Quality Improvement
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Sin
Design of Experiments
The Scientific Method of Informed Observation
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Soliciting, Hearing Acting Upon theVoice of
the Process
DATA! You are DRIVEN!
Thank you Dr. Freud. It is key to
effective DECISION-MAKING!
Data-Driven Decision Making
In God we trust. ... all others must bring
data.
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Where and What Do We Measure
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Directed Experimentation
Regression data is commonly observational in
nature, having arisen simply from observing the
response variable, Y, and noting the values of
the driver variables which led to the
response. In contrast, data in an experimental
design setting usually arise from planning or
setting the values of interest of the driver
variables and then observing the response
variable.
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Experimental Designs
The scheme used to determine the settings of the
driver variables and of collecting the data is
referred to as an experimental design. Three
very useful classes of experimental designs
are 2k factorial designs, 2k-p fractional
factorial designs, and Central Composite Designs
(CCD)
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2k Factorial Designs
2k factorial designs are experimental designs for
which there are k factors (or driver variables)
and each of these factors will be investigated
at 2 levels, high and low or, symbolically,
and -. All possible combinations of factor
levels are used in the investigation. That is,
if there are k three driver variables, then the
data that would be collected would be represented
as follows
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X1 X2 X3 Y - - - Y1 - - Y2
- - Y3 - Y4 - - Y5
- Y6 - Y7 Y8
23 Factorial Design Data
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The full factorial model when k 3 is given
by Y ?0 ?1X1 ?2X2 ?3X3 ?12X1X2
?13X1X3 ?23X2X3 ?123X1X2X3 ? It is rare to
investigate the three-factor interaction term.
A replicated 2k design (r2k) would gather r
observations under each of the 2k (factorial)
combinations previously listed.
The 23 Full Factorial Model
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X1 X2 X3 X1X2 X1X3 X2X3 X1X2X3 Y -
- - - Y1 - -
- - Y2 - - -
- Y3 - - - - Y4
- - - Y5 - -
- - Y6 - - - - Y7
Y8
Modified 23 Full Factorial Data Set
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ExampleOptimization of aFlexible Packaging
Material Process
DEPARTMENT OF STATISTICS
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A key characteristic of a flexible packaging
material is its seal strength, measured in grams
/ square inch. This is the force required to
separate the seal once it has been made. A
flexible packaging material manufacturer has
identified four variables which are believed to
influence the seal strength (Y) of a particular
material and has specified operating ranges for
these variables which, it is thought, are broad
enough to identify the impact of the variable if,
in fact, there is an impact. These variables
follow.
A 24 Factorial Design ExampleSeal Strength of
Flexible Packaging Material
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Flexible Packaging Material Variables
Response Variable Y Seal Strength
(gm/si) Driver Variables High 1
Low -1 Temperature in Degrees
300 250 Pressure psi 100 80 Material
Thickness (inch) .03 .02 Dwell in
Seconds .20 .10
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Degrees Pressure Gage Dwell
Strength -1 -1 -1 -1
150 -1 -1 -1 1
158 -1 -1 1 -1
141 -1 -1 1 1
163 -1 1 -1 -1
160 -1 1 -1 1
164 -1 1 1 -1
147 -1 1 1 1
168 1 -1 -1 -1
153 1 -1 -1 1
159 1 -1 1 -1
149 1 -1 1 1
160 1 1 -1 -1
170 1 1 -1 1
163 1 1 1 -1
171 1 1 1 1
178
Flexible Packaging Material Data
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Factor Main Effects for Seal Strength of
aFlexible Packaging Material
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Graphic Representation Flexible Packaging
Material Example
Degrees Low -1
High 1
163 168
160 178
158 164
159 163
141 147
149 171
150 160
153 170
High 1 Dwell Low -1
High 1 Gage Low
-1
Pressure Low -1
High 1
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Main Effect for Degrees
Degrees Low -1
High 1
163 168
160 178
158 164
159 163
141 147
149 171
150 160
153 170
High 1 Dwell Low -1
High 1 Gage Low
-1
Pressure Low -1
High 1
Right Cube vs. Left Cube (153 149 178)/8
- (150 141 168)/8 1303/8 - 1251/8
162.875 - 156.375 6.50
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Main Effect for Pressure
Degrees Low -1
High 1
163 168
160 178
158 164
159 163
141 147
149 171
150 160
153 170
High 1 Dwell Low -1
High 1 Gage Low
-1
Pressure Low -1
High 1
Right Faces vs. Left Faces (160
168 170 178)/8 - (150 163 153
160)/8 165.125 - 154.125
11.0
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Main Effect for Gage
Degrees Low -1
High 1
163 168
160 178
158 164
159 163
141 147
149 171
150 160
153 170
High 1 Dwell Low -1
High 1 Gage Low
-1
Pressure Low -1
High 1
Back Faces vs. Front Faces (141 163 ..
178)/8 - (150 158 .. 163)/8
159.625 - 159.625 0.0
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Main Effect for Dwell
Degrees Low -1
High 1
163 168
160 178
158 164
159 163
141 147
149 171
150 160
153 170
High 1 Dwell Low -1
High 1 Gage Low
-1
Pressure Low -1
High 1
Top Faces vs. Bottom Faces (158 163 .
163 178)/8 - (150 141 170 171)/8
164.125 - 155.125 9.0
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Interaction Effects for Seal Strength of
aFlexible Packaging Material
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Interaction Effect for Dwell with Degrees
Degrees Low -1
High 1
163 168
160
178 158 164
159
163 141
147 149
171 150
160 153
170
High 1 Dwell Low -1
High 1 Gage
Low -1
Pressure Low -1
High 1
(150 141 160 147 159 160 163
178)/8 - (158 163 164 168 153 149 170
171)/8 157.25 - 162.00
-4.75
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Analysis of Variance for Seal Strength Source
DF SS MS Fcalc Pvalue Degrees
1 169.00 169.00 12.95
0.016 Pressure 1 484.00
484.00 37.09 0.002 Gage 1
0.00 0.00 0.00
1.000 Dwell 1 324.00
324.00 24.83 0.004 DegreesPressure 1
72.25 72.25 5.54
0.065 DegreesGage 1 42.25
42.25 3.24 0.132 DegreesDwell 1
90.25 90.25 6.92
0.047 PressureGage 1 12.25
12.25 0.94 0.377 PressureDwell 1
30.25 30.25 2.32
0.188 GageDwell 1 156.25
156.25 11.97 0.018 Error 5
65.25 13.05 Total
15 1445.75
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Which Terms are Important?An Application of
Scree Plots
Sums of Squares Above the Line May be Associated
with Active Effects and Interactions.
SS Below the Line May be Associated with
Inactive Effects Interactions.
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Regression
Analysis Strength 160 3.25 Degrees 5.50
Pressure 0.000 Gage 4.50 Dwell
2.12 temppr 1.62 tempgag - 2.38 tempdw
0.875 presgag - 1.37 presdw
3.13 gagedw Predictor Coefficient Effect Std.
Dev. Tcalc Pvalue Constant 159.625
----- 0.9031 176.75 0.000 Degrees
3.250 6.500 0.9031 3.60
0.016 Pressure 5.500
11.000 0.9031 6.09 0.002 Gage
0.000 0.000 0.9031 0.00
1.000 Dwell 4.500 9.000 0.9031
4.98 0.004 temppr 2.125
4.250 0.9031 2.35 0.065
tempgag 1.625 3.250 0.9031
1.80 0.132 tempdw -2.375
-4.750 0.9031 -2.63 0.047 presgag
0.875 1.750 0.9031 0.97
0.377 presdw -1.375
-2.750 0.9031 -1.52 0.188 gagedw
3.125 6.250 0.9031 3.46
0.018 S 3.612 R2
95.5 R2adj 86.5
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Analysis of VarianceOverall Model
Source DF SS MS Fcalc
Pvalue Regression 10 1380.50 138.05
10.58 0.009 Error 5
65.25 13.05 Total 15 1445.75
Unusual
Observations Obs Degrees Strength Fit
StDev Fit Residual St Resid 10
1.00 159.000 154.875 2.995
4.125 2.04 R R denotes an observation
with a large standardized residual
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End of Session
DEPARTMENT OF STATISTICS