Mixture Experiment Design When the Upper Bound of a Component Is Constrained by a Nonlinear Function of the Relative Proportions of the Other Components

• Activity Number: 298
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Greg Piepel*+ and Scott Cooley and John Vienna
• Companies: Pacific Northwest National Laboratory and Pacific Northwest National Laboratory and Pacific Northwest National Laboratory
• Keywords: Mixture experiment ; Experimental design ; Solubility constraint

Abstract

A method is presented for designing a mixture experiment when the upper bound of one component is constrained by a nonlinear function of the relative proportions of the remaining components. For this situation, traditional methods for designing constrained mixture experiments with single component constraints (SCCs) and multiple component constraints (MCCs) are not applicable. Alternative methods were considered and one method was selected. The new method is illustrated for a 15-component nuclear waste glass example, where one of the components is SO3. SO3 has a solubility limit in glass that depends on the glass composition. The percentage of SO3 that is soluble in a glass had previously been modeled by a partial quadratic mixture experiment model in the relative proportions of the remaining 14 components. In addition, there were traditional SCCs and MCCs. The presentation discusses the waste glass example, and how the SCCs, MCCs, and non-traditional constraint on SO3 were used to construct a constrained mixture experiment design.