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MODELS AND DESIGNS FOR EXPERIMENTS WITH MIXTURES
Author(s) -
Becker Niels
Publication year - 1978
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1978.tb01102.x
Subject(s) - simplex , component (thermodynamics) , point (geometry) , ultimate tensile strength , construct (python library) , property (philosophy) , biological system , mathematics , computer science , materials science , thermodynamics , composite material , physics , geometry , philosophy , epistemology , biology , programming language
Summary Properties such as the tensile strength of an alloy of. different metals and the freezing point of a mixture of liquid chemicals, depend on the proportions (by weight or volume) of the components present and not on the total amount of the mixture. In choosing a model to relate such a property to the proportions of the various components of the mixture, there arise intriguing difficulties due to the fact that proportions sum to unity. It is demonstrated how to construct models which allow for the possibility of inactive components (components that do not affect the property at all) or components with additive effects. The design of experiments to fit such models to data is then discussed with a view to determining whether a given component is inactive or has an additive effect. The optimal allocation of observations to simplex‐lattice designs is considered for one of these models. The construction of D ‐optimal designs for these models is an open problem.