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Designs for Mixture-Amount Experiments

Summary: (This paper was presented at the Journal of Quality Technology Session at the 30th Annual Fall Technical Conference of the Chemical and Process Industries Division of the American Society for Quality Control and the Section on Physical and Engineering Sciences of the American Statistical Association in Charlotte, North Carolina, October 23-24, 1986.)

A mixture experiment is one in which the response depends only on the proportions of the components present in the mixture and not on the total amount of the components. Experiments often satisfy this definitional requirement by fixing (holding constant) the total amount of the components. A mixture-amount experiment, on the other hand, is one in which the amount of the mixture varies, and hence the response may depend on the amount of the mixture as well as on the proportions of the components present in the mixture. Piepel and Cornell (1985) have discussed models for mixture-amount experiments. In this article we present and discuss ways to generate complete and fractional designs for both unconstrained and constrained mixture-amount experiments. The designs presented are also applicable to mixture-process variable experiments involving one process variable. Several examples are utilized to illustrate the design development techniques discussed.

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  • Topics: Design of Experiments
  • Keywords: Design of experiments (DOE),D-optimality,Mixture experiments,Replication
  • Author: Piepel, Gregory F.; Cornell, John A.
  • Journal: Journal of Quality Technology