Example 7.6 Two-Level Design with Design Replication and Point Replication
[See FACTEX12 in the SAS/QC Sample Library]You can replicate a design to obtain an independent estimate of experimental error or to estimate effects more precisely. There are two ways you can replicate a design with the FACTEX procedure: you can replicate the entire design with the DESIGNREP= option, or you can replicate each point in the design with the POINTREP= option. The following example illustrates the difference.
A process engineer is conducting an experiment to study the shrinkage of an injection-molded plastic component. The engineer chooses to determine the effect of the following four factors, each at two levels: holding pressure (Pressure), molding temperature (Temperature), cooling time (Time), and injection velocity (Velocity).
The design used is a half-fraction of a 
factorial design, denoted as 
. The following statements construct the design:
proc factex; factors Pressure Temperature Time Velocity; size fraction=2; model res=max; output out=Unreplicated; run; proc print data=Unreplicated; run;
The design, saved in the data set Unreplicated), is shown in Output 7.6.1.
| Obs | Pressure | Temperature | Time | Velocity |
|---|---|---|---|---|
| 1 | -1 | -1 | -1 | -1 |
| 2 | -1 | -1 | 1 | 1 |
| 3 | -1 | 1 | -1 | 1 |
| 4 | -1 | 1 | 1 | -1 |
| 5 | 1 | -1 | -1 | 1 |
| 6 | 1 | -1 | 1 | -1 |
| 7 | 1 | 1 | -1 | -1 |
| 8 | 1 | 1 | 1 | 1 |
To obtain a more precise estimate of the experimental error, the engineer decides to replicate the entire design three times. The following statements generate a design with three replicates in 24 runs:
proc factex; factors Pressure Temperature Time Velocity; size fraction=2; model res=max; output out=Replicated designrep=3; run; proc print data=Replicated; run;
The design, saved in the data set Replicated, is displayed in Output 7.6.2.
| Obs | Pressure | Temperature | Time | Velocity |
|---|---|---|---|---|
| 1 | -1 | -1 | -1 | -1 |
| 2 | -1 | -1 | 1 | 1 |
| 3 | -1 | 1 | -1 | 1 |
| 4 | -1 | 1 | 1 | -1 |
| 5 | 1 | -1 | -1 | 1 |
| 6 | 1 | -1 | 1 | -1 |
| 7 | 1 | 1 | -1 | -1 |
| 8 | 1 | 1 | 1 | 1 |
| 9 | -1 | -1 | -1 | -1 |
| 10 | -1 | -1 | 1 | 1 |
| 11 | -1 | 1 | -1 | 1 |
| 12 | -1 | 1 | 1 | -1 |
| 13 | 1 | -1 | -1 | 1 |
| 14 | 1 | -1 | 1 | -1 |
| 15 | 1 | 1 | -1 | -1 |
| 16 | 1 | 1 | 1 | 1 |
| 17 | -1 | -1 | -1 | -1 |
| 18 | -1 | -1 | 1 | 1 |
| 19 | -1 | 1 | -1 | 1 |
| 20 | -1 | 1 | 1 | -1 |
| 21 | 1 | -1 | -1 | 1 |
| 22 | 1 | -1 | 1 | -1 |
| 23 | 1 | 1 | -1 | -1 |
| 24 | 1 | 1 | 1 | 1 |
The first replicate comprises observations 1 to 8, the second replicate comprises observations 9 to 16, and the third replicate comprises observations 17 to 24.
Now, instead of replicating the entire design, suppose the engineer decides to replicate each run in the design three times. The following statements construct a design in 24 runs with point replication:
proc factex; factors Pressure Temperature Time Velocity; size fraction=2; model res=max; output out=PointReplicated pointrep=3; run; proc print data=PointReplicated; run;
The design, saved in the data set PointReplicated, is displayed in Output 7.6.3. The first design point is replicated three times (observations 1–3), the second design point is replicated three times (observations 4–6), and so on.
| Obs | Pressure | Temperature | Time | Velocity |
|---|---|---|---|---|
| 1 | -1 | -1 | -1 | -1 |
| 2 | -1 | -1 | -1 | -1 |
| 3 | -1 | -1 | -1 | -1 |
| 4 | -1 | -1 | 1 | 1 |
| 5 | -1 | -1 | 1 | 1 |
| 6 | -1 | -1 | 1 | 1 |
| 7 | -1 | 1 | -1 | 1 |
| 8 | -1 | 1 | -1 | 1 |
| 9 | -1 | 1 | -1 | 1 |
| 10 | -1 | 1 | 1 | -1 |
| 11 | -1 | 1 | 1 | -1 |
| 12 | -1 | 1 | 1 | -1 |
| 13 | 1 | -1 | -1 | 1 |
| 14 | 1 | -1 | -1 | 1 |
| 15 | 1 | -1 | -1 | 1 |
| 16 | 1 | -1 | 1 | -1 |
| 17 | 1 | -1 | 1 | -1 |
| 18 | 1 | -1 | 1 | -1 |
| 19 | 1 | 1 | -1 | -1 |
| 20 | 1 | 1 | -1 | -1 |
| 21 | 1 | 1 | -1 | -1 |
| 22 | 1 | 1 | 1 | 1 |
| 23 | 1 | 1 | 1 | 1 |
| 24 | 1 | 1 | 1 | 1 |
Note the difference in the arrangement of the designs created by using design replication (Output 7.6.2) and point replication (Output 7.6.3). In design replication, the original design is replicated a specified number of times; but in point replication, each run in the original design is replicated a specified number of times. See the section Replication for more information on design replication.