What You Should Know about 2^{k} Experimentation for Six Sigma
2^{k} full factorial experiments give you a powerful jumpstart into the world of improvement through DOE for Six Sigma projects. But really, they’re just the tip of the iceberg. As you gain experience, you want to discover how to address more advanced topics.

Curvature: The assumption of 2^{k}^{ }experiments is that the effects of your experimental factors are linear. Although this idea is often a good first approximation, a line often doesn’t fit your process or system. For those cases, you need to design your experiment to reveal the curved nature of the reality of your situation. This redesign usually involves including more than two levels for each of your experimental factors.

Replications: If you repeat your experiment, you get slightly different results. Variation, as always, is a part of everything — including your experiment. Repeating runs of your experiment (called replications) allows you to estimate how much of the observed variation in your process or system is explained by Y = f(X) and how much remains unexplained, the ε.

Analysis of variance (ANOVA): Almost all experiments involve exploring, investigating, and comparing the sources of observed variations. ANOVA is an advanced method that allows you to categorize and quantify all the various sources of variation.

Robustness: The ability of a process or system to perform consistently in the face of variation is called robustness. Taguchi and other experiment designs allow you to investigate and optimize your process or system so that it’s as immune as possible to the ravages of variation.

Response surface methods (RSM) and optimization: The purpose of many experiments is to find out the best values to set the input variables at. A whole branch of the field of DOE focuses on designing and analyzing experiments to find the local or global optimal operation settings.

Fractional factorial experiments: You can adapt 2^{k} full factorial experiments to more efficiently search through a large number of experimental factors. What you give up in increasing the number of experimental factors is analytical accuracy. Fractional factorial experiments teach how and where to adapt your experiment to get the most out of your search efforts.