Page 32 - Applied Statistics And Probability For Engineers

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1-3

Adhesive type

Old New
Temperature 100 ˚ ˚ Time 24h
70

3 1h 1
32 8
Wall thickness (in.)
Figure S1-3 A four-factorial experiment for the connector wall thick-
ness problem.

Generally, if there are k factors and they each have two levels, a factorial experimental
4
k
design will require 2 runs. For example, with k 4, the 2 design in Fig. S1-3 requires 16
tests. Clearly, as the number of factors increases, the number of trials required in a factorial
experiment increases rapidly; for instance, eight factors each at two levels would require
256 trials. This quickly becomes unfeasible from the viewpoint of time and other resources.
Fortunately, when there are four to five or more factors, it is usually unnecessary to test all
possible combinations of factor levels. A fractional factorial experiment is a variation of
the basic factorial arrangement in which only a subset of the factor combinations are actu-
ally tested. Figure S1-4 shows a fractional factorial experimental design for the four-factor
version of the connector experiment. The circled test combinations in this figure are the
only test combinations that need to be run. This experimental design requires only 8 runs in-
stead of the original 16; consequently it would be called a one-half fraction. This is an ex-
cellent experimental design in which to study all four factors. It will provide good informa-
tion about the individual effects of the four factors and some information about how these
factors interact.
Factorial and fractional factorial experiments are used extensively by engineers and sci-
entists in industrial research and development, where new technology, products, and
processes are designed and developed and where existing products and processes are im-
proved. Since so much engineering work involves testing and experimentation, it is essential
that all engineers understand the basic principles of planning efficient and effective
experiments. We discuss these principles in Chapter 13. Chapter 14 concentrates on the facto-
rial and fractional factorials that we have introduced here.

Adhesive type

Old New
Temperature 100 ˚ ˚ Time 24h

70
3 1h 1
32 8
Wall thickness (in.)
Figure S1-4 A fractional factorial experiment for the connector wall
thickness problem.