Designing a mixture experiment when the components are subject to a nonlinear multiple-component constraint

摘要

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 SO_3 is one of the components. SO_3 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 SO_3 would not exceed its predicted solubility limit for any of the experimental glasses. A partial quadratic mixture model expressed in the relative proportions of the 14 other components 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 (1) account for the SCCs, linear MCCs, and nonlinear MCC and (2) meet the goals of the study.