I always prefer a DOE to a multiple regression, because the analysis is stronger and the factors are completely independent of each other. However, there are two specific instances when you must use a multiple regression over a DOE. The first is when someone hands you a stack of data and asks if there are any relationships between the variables. In this case, you have no power to set up the study the way you want--the data is already collected and is ready to analyze. The second is when you have the ability to set up the study, but you find out that controlling each of the potential factors is not as easy as you think. I always ask the question "Can I specify that each of the factors be set to a given value that I demand, in any combination I want?" If that answer is yes, then a DOE is the way to go. If the answer is no, then multiple regression is the way to go. There haven been a handful of cases where I ran into the second situation. The most recent example was with some work I was doing with the United States Bowling Congress. We wanted to predict certain characteristics of ball motion based on properties of the ball. The problem was that I could not manufacture a ball with all the combinations of specific properties I wanted at will. We ran the multiple regression, and it still turned out very successful. You can learn about this study by visiting bowl.com
and browsing to the Equipment Specifications and Certification Department.
Scott C. Sterbenz, P.E.
ASQ Six Sigma Forum