Too Many Factors on Hand?

Efficient as it is, even factorial design can get choked with too many treatments in industrial experiments, where it is not uncommon to face as many as ten to fifteen factors threatening to act simultaneously on the outcome.

Consider an experiment in which there are six factors—this is not too many in several industrial contexts—and where it is the intention to find the optimum level of each. It is decided to study each factor at four levels. The number of replications to run all possible combinations is N = (4)⁶ = 1,024. Obviously, this is too many replications. Also, when a “nuisance factor” (described later in this chapter) is suspected to be influential as a cause, the rem­edy is to design the experiment to treat such a factor as yet another factor, in par with the usual factors. This, in effect, adds to the number of treatments needed, N = l^(f), exponentially!

Several means, based on statistical methods, have been devel­oped to reduce the number of replications to a lower, reasonably convenient level. A design using all combinations given by N = is known as a full factorial, whereas, designs using only a part of such combinations are often done so to reduce the number of treatments—are referred to as fractional factorials. The method of using fractional factorials in industrial manufacturing has been adapted extensively by Genichi Taguchi and others.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.