Lecture 38: Center Points
Bread Wrapper Experiment
Current Operating Conditions
A company currently makes
material that goes into bread
wrappers. In order to improve
the strength of the seals made
with the wrapper material it
decides to do an experiment.
The current process uses 1.1% of
polyethylene in the material.
Pieces of the material are sealed
using a seal temperature of 255o
F and a cooling bar temperature
of 55o F.
1
Factors at 2 levels
2
Comment
A: Seal Temperature
225o F and 285o F
Note that the current
operating conditions are in
the center of levels for each
of the experimental factors.
B: Cooling Bar Temperature
46o F and 64o F
C: % Polyethylene
0.5% and 1.7%
3
Treatment Combinations
There are 23 = 8 treatment
combinations.
Each run produces a whole
roll of material. If the roll is
not usable, the experiment
becomes very expensive.
4
Replication
Because each run of the
experiment can be
expensive replicating the
treatment combinations may
not be practical.
5
6
1
Lecture 38: Center Points
Replication
Completely Randomized
Instead of replicating the
treatment combinations,
replicate the current
operating conditions (center
points).
The experiment will consist
of 8 treatment combinations
and 4 center point
replications in a completely
randomized design.
7
Treatment Combinations
8
Center Points
Use the data at the center
points to quantify the
random error variation, i.e.
variation in material treated
the same.
Use the data at the
treatment combinations to
estimate the effects of the
factors and interactions.
9
10
11
12
Informal Analysis
A: Seal Temperature
225o F (–1): Mean = 8.525
g/in
285o F(+1): Mean = 6.775
g/in
2
Lecture 38: Center Points
Informal Analysis
B: Cooling Bar Temperature
 46o F (–1): Mean = 7.375
g/in
 64o F (+1): Mean = 7.925
g/in
13
14
15
16
17
18
Informal Analysis
C: % Polyethylene
 0.5 % (–1): Mean = 6.875
g/in
 1.7 % (+1): Mean = 8.425
g/in
Summary
Increasing seal temperature
tends to decrease strength a lot.
Increasing cooling bar
temperature tends to increase
strength a little.
Increasing the % polyethylene
tends to increase strength a lot.
3
Lecture 38: Center Points
Seal Temp and Bar Temp
When seal temperature is 225o F,
increasing the bar temperature
tends to increase the strength.
When seal temperature is 285o F,
increasing the bar temperature
has little effect on the strength.
19
20
21
22
Seal Temp and % Poly
When seal temperature is 225o F,
increasing the % polyethylene
tends to increase the strength a
lot.
When seal temperature is 285o F,
increasing the % polyethylene
tends to increase the strength a
little.
Bar Temp and % Poly
Other Interactions
When bar temperature is
46o F or 64o F, increasing
the % polyethylene tends to
increase the strength.
The only other interaction is
a 3-way interaction
involving all three factors.
23
24
4