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A mixture experiment (ME) combines components in various proportions and observes the values of one or more responses for each mixture. The proportions of the q components in each mixture must sum ...

This article presents a case study of developing a space-filling design (SFD) for a constrained mixture experiment when the experimental region is specified by single-component constraints (SCCs), ...

This article presents a case study of developing an experimental design for a constrained mixture experiment when the experimental region is defined by single-component constraints (SCCs), linear m...

In developing models for mixture experiments, the first step typically involves fitting a complete Scheffe linear mixture (SLM) model using all components varied in the experiment. It next may be desirable to reduce a complete SLM model by (i) eliminating (in a way appropriate for mixture experiments) components that have negligible effects and (ii) combining components that have similar effects. Standard methods for reducing non-mixture linear models, such as t-tests and variable-selection techniques, are not applicable for reducing SLM models. In the mixture experiment literature, a time-consuming, manual iterative approach has been used to reduce SLM models.Automatic and semi-automatic versions of a method for backward reduction of SLM models are proposed to eliminate components (in a way appropriate for mixture experiments) or combine components. The method uses associated partial F-tests to guide the model reduction steps. The method allows for specifying (i) components that must remain in th...

In many product-quality situations, it must be shown with high confidence (X%) that a high percentage (at least Y%) of the product made during the production period has true values of property below a calculated value. This can be done using an X%/Y% u..

This article describes the solution to a unique and challenging mixture experiment design problem involving (1) 19 and 21 components for two different parts of the design, (2) many single-component and multicomponent constraints, (3) augmentation of existing data, (4) a layered design developed in stages, and (5) a no-candidate-point optimal design approach. The problem involved studying the liquidus temperature of spinel crystals as a function of nuclear waste glass composition. A D-optimal approach was used to augment existing glasses with new nonradioactive and radioactive glasses chosen to cover the designated nonradioactive and radioactive experimental regions. The traditional approach to building D-optimal mixture experiment designs is to generate a set of candidate points from which design points are D-optimally selected. The large number of mixture components (19 or 21) and many constraints defining each layer of the waste glass experimental region made it impossible to generate and store the huge...

A glass composition variation study (CVS) for high-level waste (HLW) stored in Idaho is being statistically designed and performed in phases over several years. The purpose of the CVS is to investigate and model how HLW-glass properties depend on glass composition. The resulting glass property–composition models will be used to develop desirable glass formulations and for other purposes. Phases 1 and 2 of the CVS have been completed and are briefly described. This paper focuses on the CVS Phase 3 experimental design, which was chosen to augment the Phase 1 and 2 data with additional data points, as well as to account for additional glass components not studied in Phases 1 and/or 2. In total, 16 glass components were varied in the Phase 3 experimental design. The paper describes how these Phase 3 experimental design augmentation challenges were addressed using the previous data, preliminary property–composition models, and statistical mixture experiment and optimal experimental design methods and software....