PNNL

Abstract

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 multiple-component constraints (MCCs), and a nonlinear MCC. Traditional methods and software for designing constrained mixture experiments with SCCs and linear MCCs are not directly applicable because of the nonlinear MCC. A modification of existing methodology to account for the nonlinear MCC was developed and is described in this article. The case study involves a 15-component nuclear waste glass example in which SO3 is one of the components. SO3 has a solubility limit in glass that depends on the composition of the balance of the glass. A goal was to design the experiment so that SO3 would not exceed its predicted solubility limit for any of the experimental glasses. The SO3 solubility limit had previously been modeled by a partial quadratic mixture (PQM) model expressed in the relative proportions of the 14 other components. The PQM model was used to construct a nonlinear MCC in terms of all 15 components. In addition, there were SCCs and linear MCCs. This article discusses the waste glass example and how a layered design was generated to (i) account for the SCCs, linear MCCs, and nonlinear MCC and (ii) meet the goals of the study.