Experiment!: Planning, Implementing and Interpreting

9.5 Factor Screening: Fractional Factorial Designs

At the beginning of a study it is often possible to think of a large number of factors that could be important for the response. Initially, we may only be interested in finding out which of these candidates – if any – have a substantial effect. This process of separating the vital few factors from the trivial many is called screening. The purpose is to find out which factors to keep for the real experiment, which is to be conducted later.

Equation 9.2 shows that the number of runs in a full factorial experiment increases exponentially with the number of factors. This is why it is convenient to use special screening designs to reduce the number of runs. We will soon see that this is done by “mixing effects together” and focusing on main effects and low order interactions. These designs typically fall into two categories: fractional factorial designs and Plackett–Burman designs. We will concentrate on the first category and only briefly mention some characteristics of the latter.

Exercise 9.5: Use Equation 9.2 to determine the number of runs needed in a full factorial experiment as the number of factors, n, increases from two to eight. The number of levels, l, should be two. What can be said about how the number of runs increases when factors are added?

The 23 design in Table 9.3 tests three factors in eight runs (replicates have been left out for simplicity). Imagine that you are interested in four factors but are only allowed ...