Example 7.2 Resolution 4 Augmented Design

[See FACTEX17 in the SAS/QC Sample Library]Box, Hunter, and Hunter (1978) describe an injection molding experiment that involves eight 2-level factors: mold temperature (Temp), moisture content (Moisture), holding pressure (HoldPress), cavity thickness (Thick), booster pressure (BoostPress), 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 . You can generate this design, shown in Output 7.2.1, with the following statements:

proc factex;
   factors Temp        Moisture HoldPress Thick 
           BoostPress  Time     Speed     Gate;
   size design=16;                      
   model resolution=4;                 
   examine design aliasing;            
run;

The FACTORS statement lists factor names. The option DESIGN=16 of the SIZE statement specifies the design size. The RESOLUTION=4 specifies the resolution of the design. The EXAMINE statement lists points and aliasing.

Output 7.2.1 A Design

The FACTEX Procedure

Design Points
Experiment Number	Temp	Moisture	HoldPress	Thick	BoostPress	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 7.2.2.

Output 7.2.2 Alias Structure for a Design

Aliasing Structure
Temp
Moisture
HoldPress
Thick
BoostPress
Time
Speed
Gate
Temp*Moisture = HoldPress*Gate = Thick*Speed = BoostPress*Time
Temp*HoldPress = Moisture*Gate = Thick*Time = BoostPress*Speed
Temp*Thick = Moisture*Speed = HoldPress*Time = BoostPress*Gate
Temp*BoostPress = Moisture*Time = HoldPress*Speed = Thick*Gate
Temp*Time = Moisture*BoostPress = HoldPress*Thick = Speed*Gate
Temp*Speed = Moisture*Thick = HoldPress*BoostPress = Time*Gate
Temp*Gate = Moisture*HoldPress = Thick*BoostPress = Time*Speed

Subsequent analysis of the data collected for the design suggests that HoldPress and BoostPress have statistically significant effects. There also seems to be significant effect associated with the sum of the aliased two-factor interactions Temp*BoostPress, Temp*Time, Moisture*Time, HoldPress*Speed, and Thick*Gate. This chain of confounded interactions is identified in Output 7.2.2.

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 7.2.3):

proc factex;
   factors Temp        Moisture HoldPress Thick
           BoostPress  Time     Speed     Gate;
   model estimate=(Moisture*Time 
                   HoldPress*Speed 
                   Thick*Gate);
   size design=4;                    
   examine design aliasing(2);      
run;                               

Output 7.2.4 shows the alias structure of the additional four-run experiment. Note that the alias link

Temp*BoostPress=Moisture*Time=HoldPress*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.