Remarks on Experiments with Two-Level Factors

In multifactor experiments, particularly when the number of fac­tors is high, testing at two levels of factors is quite adequate to decide (1) if one or more of the factors is ineffective, (2) the rela­tive extent of effectiveness of each factor, and (3) if two or more of the factors interact, meaning that their combined effect is not merely cumulative. We have seen that the number of trials for three factors at two levels in full-factorial experiments is given by 2³ = 8. If the number of factors is increased to four, the total number of trials is 2⁴ = 16, which is a big jump from eight. There are several situations in which close to a dozen or so factors can be identified as likely to be influential. In such cases, a full-facto­rial experiment, even with only two levels per factor, can become unmanageable.

A well-known method for dealing with problems in industrial manufacturing is popularly known as the Taguchi method. It consists of listing for a specified response all the possible factors; this is done by a whole team of experts drawn from all fields— not just engineering—involved in the product. Then, in a brain­storming session—this is important—in which people of diverse ranks and job specialties participate, each of the factors is scruti­nized, some are rejected by joint discretion, and the list of factors is considerably shortened. Using only these final factors, a full- factorial, two-level experiment is carried out. After analyzing the response and identifying and rejecting those factors determined to have marginal influence, the list of factors is further shortened. With the remaining short list of factors, a partial-factorial, multi­level-multifactor experiment is scheduled.

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