An Ideal Four-factor Components Mixture Experiment Design Based on Prominent Optimality Criteria at Level Two
Chirchir K. Emmanuel *
University of Eldoret, P.O. Box 1125-30100 Eldoret, Kenya.
Okango A. Ayubu
University of Eldoret, P.O. Box 1125-30100 Eldoret, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Aim: Mixture experiment designs are essential tools that need to be determined prior to conducting any mixture experiment in any field of study. The primary goal of these types of experiments are optimization that is either maximizing the profit/produce or minimizing the cost of production.
Study Design: Any researcher anticipating to do any research work on the mixture experiment will not evade to talk about the design that he or she is likely to use. The common of such designs being either Simplex Lattice Design (SLD) or Simplex Centroid Design (SCD).
Methodology: The choice of such design is wholly based on the optimality criteria employed. The classical of these criteria include on D-Determinant criterion, A-Average variance criterion, E- Eigen value criterion and T- Trace optimality criterion usually denoted as D-, A-, E- T- criteria. They are also known as prominent criteria.
Results: This paper considered four-factor components at order two. The penalized moment matrices obtained from the information matrices whose primary source was the design points gave the values of the criteria aforementioned. These values were ranked independently with the least average rank termed as the best design.
Conclusion: The {4,4} Simplex Lattice Design had the lowest rank value of 1.0 as compared to the other designs. This design is therefore to be used in any research work considering four factors when only two of factors are to be employed.
Keywords: Mixture experiment, optimization, design, simplex-lattice, simplex-centroid, optimality criteria, prominent, average rank value