Factorial Experiments When Factor Levels are Not Necessarily Reset

Abstract

In industry, the run order of experiments is often randomized, but this does not guarantee that all factor levels are reset from one run to the next. When this happens and the levels of factors are the same in successive runs, the assumption of independent observations from run to run may be violated or incorrect. In this case, an ordinary least squares analysis can produce biased estimates of the coefficients in the model, which leads to erroneous test results and inferences.

In this paper we describe how not resetting the levels of one or more factors in successive runs can result in less precision in parameter estimates and a larger than expected prediction variance. We present formulas for the prediction variance and the expected prediction variance for this situation. These quantities are important because they allow us to compare the prediction properties of experiments that are completely randomized to experiments where the levels of one or more factors are not reset. We give an analysis of an industrial experiment of this type and recommendations for carrying out factorial experiments where the levels of one or more factors are not reset.

• Design of Experiments
• Prediction Variance
• Randomization
• Split-Plot Designs

Additional information

Notes on contributors

Derek F. Webb

Dr. Webb is an Assistant Professor of Mathematics and Statistics in the Department of Mathematics and Computer Science. He is a Member of ASQ. His email address is [email protected].

James M. Lucas

Dr. Lucas is a Consultant and a Member of the Editorial Review Board for the Journal of Quality Technology. He is a Fellow of ASQ. His email address is [email protected].

John J. Borkowski

Dr. Borkowski is an Associate Professor of Statistics in the Department of Mathematical Sciences. He is a Member of ASQ. His email address is [email protected].