Construction of Saturated Designs for Mixture Experiments

Mixture Experiments are very common in real life experiments. Designing a mixture experiment involves selection of the proportion of the mixture components in a fashion such that a mathematical model can be fitted adequately and the parameters could be estimated. In agricultural experiments, the mixture components may be several sources of the input applied or input may be applied at different crop growth stages in splits such that total quantity applied to the crop is constant. Efficient designs for mixture experiments are useful when the response is assumed to depend on the relative proportions of the ingredients present in the mixture. A number of algorithms and heuristics are available in literature; however, a limited work has been done in the use of algorithms for mixture experiments. There is a need to develop designs for mixture experiments in smaller number of runs for a specific model for varying proportions using algorithmic approach. In this study we have developed algorithms to construct saturated designs fort mixture experiments. The algorithm provides a greater flexibility in design construction in comparison to the traditional approach in terms of models to be fitted; number of runs to be requited etc. These designs are very well suited in real life experiments. The use of algorithms in construction of designs for mixture experiments not only reduces the computational cost but also results in a more efficient search of the design in a continuous design space.

Mixture Designs Generated by Orthogonal Arrays Developed Using Difference Schemes

This paper presents an algorithm for constructing mixture designs based on orthogonal arrays developed using difference schemes. The algorithm can also be applied to constrained mixture experiments. The algorithm allows the generation of efficient mixture designs for Scheffé canonical polynomials.