| Details of the FACTEX Procedure |
Example 15.2: Resolution IV Augmented Design
|
See RCBD in the SAS/QC Sample Library
|
Box, Hunter, and Hunter (1978)
describe an injection molding experiment
involving eight two-level factors:
mold temperature (TEMP),
moisture content (MOIST),
holding pressure (HOLDPR),
cavity thickness (THICK),
booster pressure (BOOSTPR),
cycle time (TIME),
screw speed (SPEED), and
gate size (GATE).
The design used has 16 runs and is of resolution 4; it
is often denoted as 28-4IV.
You can generate this design, shown in
Output 15.2.1,
with the following statements:
proc factex;
factors temp moist holdpr thick /* List factor names */
boostpr time speed gate;
size design=16; /* Construct 16-run design */
model resolution=4; /* of resolution 4 */
examine design aliasing; /* List points and aliasing */
run;
Output 15.2.1: A 28-4IV Design
|
| Design Points |
Experiment
Number |
temp |
moist |
holdpr |
thick |
boostpr |
time |
speed |
gate |
| 1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
-1 |
| 2 |
-1 |
-1 |
-1 |
1 |
1 |
1 |
1 |
-1 |
| 3 |
-1 |
-1 |
1 |
-1 |
1 |
1 |
-1 |
1 |
| 4 |
-1 |
-1 |
1 |
1 |
-1 |
-1 |
1 |
1 |
| 5 |
-1 |
1 |
-1 |
-1 |
1 |
-1 |
1 |
1 |
| 6 |
-1 |
1 |
-1 |
1 |
-1 |
1 |
-1 |
1 |
| 7 |
-1 |
1 |
1 |
-1 |
-1 |
1 |
1 |
-1 |
| 8 |
-1 |
1 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
| 9 |
1 |
-1 |
-1 |
-1 |
-1 |
1 |
1 |
1 |
| 10 |
1 |
-1 |
-1 |
1 |
1 |
-1 |
-1 |
1 |
| 11 |
1 |
-1 |
1 |
-1 |
1 |
-1 |
1 |
-1 |
| 12 |
1 |
-1 |
1 |
1 |
-1 |
1 |
-1 |
-1 |
| 13 |
1 |
1 |
-1 |
-1 |
1 |
1 |
-1 |
-1 |
| 14 |
1 |
1 |
-1 |
1 |
-1 |
-1 |
1 |
-1 |
| 15 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
1 |
| 16 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
The alias structure is shown in Output 15.2.2.
Output 15.2.2: Alias Structure for a 28-4IV Design
|
| Aliasing Structure |
| temp |
| moist |
| holdpr |
| thick |
| boostpr |
| time |
| speed |
| gate |
| temp*moist = holdpr*gate = thick*speed = boostpr*time |
| temp*holdpr = moist*gate = thick*time = boostpr*speed |
| temp*thick = moist*speed = holdpr*time = boostpr*gate |
| temp*boostpr = moist*time = holdpr*speed = thick*gate |
| temp*time = moist*boostpr = holdpr*thick = speed*gate |
| temp*speed = moist*thick = holdpr*boostpr = time*gate |
| temp*gate = moist*holdpr = thick*boostpr = time*speed |
|
Subsequent analysis of the data collected for the design suggests
that HOLDPR and BOOSTPR have statistically significant effects.
There
also seems to be significant effect
associated with
the sum of the aliased two-factor
interactions
TEMP*BOOSTPR,
MOIST*TIME,
HOLDPR*SPEED,
and
THICK*GATE.
This chain of confounded interactions is identified
in
Output 15.2.2.
A few runs can be added to the design
to distinguish between
the effects due to these four interactions.
You simply need a design in which any three of these
effects are estimable,
regardless of all other main effects and interactions.
For example,
the following statements generate
a suitable set of runs (see
Output 15.2.3):
proc factex;
factors temp moist holdpr thick
boostpr time speed gate;
model estimate=(moist*time
holdpr*speed
thick*gate );
size design=4;
examine design aliasing(2);
run;
Output 15.2.3: Additional Runs to Resolve Ambiguities
|
| Design Points |
Experiment
Number |
temp |
moist |
holdpr |
thick |
boostpr |
time |
speed |
gate |
| 1 |
-1 |
-1 |
1 |
1 |
1 |
1 |
-1 |
1 |
| 2 |
-1 |
1 |
-1 |
-1 |
-1 |
-1 |
-1 |
1 |
| 3 |
1 |
-1 |
-1 |
-1 |
-1 |
-1 |
1 |
1 |
| 4 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
Output 15.2.4 shows the alias structure of the additional four-run experiment.
Note that the alias link
TEMP*BOOSTPR = MOIST*TIME = HOLDPR*SPEED = THICK*GATE
found in the original design is broken.
When these four runs are added to the original 16 runs,
the
four two-factor interactions can be estimated separately with the 20 runs.
Output 15.2.4: Alias Structure of the Additional Experiment
|
| Aliasing Structure |
| 0 = gate = temp*speed = holdpr*thick = holdpr*boostprs = holdpr*time |
| = thick*boostprs = thick*time = boostprs*time |
| temp = speed = temp*gate = moist*holdpr = moist*thick = moist*boostprs |
| = moist*time = speed*gate |
| moist = temp*holdpr = temp*thick = temp*boostprs = temp*time = moist*gate |
| = holdpr*speed = thick*speed = boostprs*speed = time*speed |
| holdpr = thick = boostprs = time = temp*moist = moist*speed = holdpr*gate |
| = thick*gate = boostprs*gate = time*gate |
|
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
