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 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

 The FACTEX Procedure

 Design Points ExperimentNumber 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

 The FACTEX Procedure

 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

 The FACTEX Procedure

 Design Points ExperimentNumber 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

 The FACTEX Procedure

 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

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