L^k Factorial Experiments with Hard-To-Change and Easy-To-Change Factors

Abstract

Experimental factors, especially when they are hard-to-change, are often not independently reset on each run. For example, it would be very costly to let a mold cool down between runs and then reheat it when the same mold temperature is required on successive runs. Therefore, even when the experiment is run using a random run order, a “completely randomized design” requiring a single error term is not obtained. There is a restriction on randomization that causes the experiment to require more than one error term in the model. The analysis of the experiment with restricted randomization often proceeds, however, as if a completely randomized design were run. This ignores the fact that the experiment inherently has a “split plot” structure. We examine properties of experiments run in this very common manner and investigate L^k experiments using two error terms. One error term is associated with setting the “hard-to-change factors” and the other represents the remaining error. We develop the expected covariance matrices for observations and for the estimated regression coefficients in experiments using a random run order and using run orders that restrict randomization partially or completely. We compare the precision of the estimators of the regression coefficients for the various run order scenarios and show that classical split-plot blocking is superior to a random run order.

• Blocking
• Restricted Randomization
• Split-Plot Designs

Additional information

Notes on contributors

Huey L. Ju

Dr. Ju is Vice President. Her email address is [email protected].

James M. Lucas

Dr. Lucas is the Principal. He is a Fellow of the ASQ. His e-mail address is [email protected].