Interactions

In practice, it is often found that only two-factor interactions have a significant effect. The effect of quadratic terms (A2, B2, etc.) depends on the process. Some processes are inherently nonlinear with respect to the factor values used in the model. If the data can be fitted only by using many higher-order terms or are not well fitted even with all possible linear and quadratic terms, it may indicate that the process is oscillating over the range of one or more factors. It also may mean that the factor levels or the response should be transformed. Quadratic terms for qualitative factors are often very difficult to interpret and generally should be avoided.

The decision to include or exclude interactions between main factors is extremely important. A screening experiment, which allows for no interactions, may be useful when there is little understanding of the process and no interactions are believed to exist. During the analysis of a screening experiment, it may be found that some main factors are unimportant. If that is the case, the effect of some unplanned interactions may be estimated. There is, however, no assurance that important interactions will not remain confounded with main factors. A better choice is to use a Resolution IV design instead of the Screening (Resolution III) design. The R-IV design will assure no confounding between main effects and two-factor interactions, although the two-factor interactions cannot be estimated.

During the analysis of an experiment planned with interactions, it is often possible to eliminate one or more main factors and to add unplanned interactions to the analysis. See Factorial Designs

Learn more about the DOE tools for designed experiments in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Intro. to DOE short course (only $99) or online Advanced Topics in DOE short course (only $139), or his online Black Belt certification training course ($875).