Fractional Design Plans for Process Variables in Mixture Experiments

Summary: Many industrial processes involve the blending of ingredients to form end products. Experimenting with these processes consists of varying the proportions of the individual ingredients (i.e., varying the blends) as well as varying the conditions at which the blends are prepared and processed. The objective of the experimentation is to find those blends and conditions that produce the product of highest quality. Such experiments are known as mixture experiments with process variables.In this paper, designs for mixture experiments with process variables are presented where the emphasis is on using only a fraction of the total number of possible design points and the fitting of reduced models for measuring the effects of the mixture components and process variables. An example is given of an experiment consisting of three mixture components and three process variables to provide the background setting and the motivation for seeking a reduction in the total number of experimental runs.