Previous Table of Contents Next


16.3.3 Fractional Factorial Designs

Sometimes the number of experiments required for a full factorial design is too large. This may happen if either the number of factors or their levels is large. It may not be possible to use a full factorial design due to the expense or the time required. In such cases, one can use only a fraction of the full factorial design. Later in Chapter 19 we discuss the procedure to design a specific class of fractional factorial designs. Here, we simply give an example.

Example 16.1 Consider only four of the five factors in the workstation study. Let us ignore the number of disk drives for this example. We have four factors, each at three levels. Therefore, the number of experiments required is
n = (3 CPUs)(3 memory levels)(3 workloads)(3 educational levels)
   = 81 experiments

The full factorial design consisting of 81 experiments is the so-called 34 design. A 34-2 fractional factorial design consisting of only nine experiments is shown in Table 16.3. Notice that each of the four factors is used three times at each of its three levels.
TABLE 16.3 A Sample Fractional Factorial Design

Experiment
Number
CPU Memory
Level
Workload
Type
Educational
Level

1 68000 512K    Managerial High school
2 68000 2M    Scientific Postgraduate
3 68000 8M    Secretarial College         
4 Z80 512K    Scientific College         
5 Z9D 2M    Secretarial High school
6 Z80 8M    Managerial Postgraduate
7 8086 512K    Secretarial Postgraduate
8 8086 2M    Managerial College         
9 8086 8M    Scientific High school

For every advantage there is a corresponding disadvantage. Fractional factorial designs save time and expense when compared to full factorial designs. However, the information obtained from a fractional factorial design is less than that obtained from a full factorial design. For example, it may not be possible to get interactions among all factors. On the other hand, if some of the interactions are known to be negligible, this may not be considered a problem and the time and expense of a full factorial design may not be justified.

In the remainder of this book, we restrict our discussion to the full factorial and fractional factorial designs.

EXERCISE

16.1  The performance of a system being designed depends upon the following three factors:
a.  CPU type: 68000, 8086, 80286
b.  Operating system type: CPM, MS-DOS, UNIX
c.  Disk drive type: A, B, C
How many experiments are required to analyze the performance if
a.  There is significant interaction among factors.
b.  There is no interaction among factors.
c.  The interactions are small compared to main effects.


Previous Table of Contents Next

Copyright © John Wiley & Sons, Inc.