Contributions to Mixture Experiments When Order of Addition is Important
Open Access
- Author:
- Rios, Nicholas
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 16, 2022
- Committee Members:
- Lingzhou Xue, Chair & Dissertation Advisor
Yanyuan Ma, Major Field Member
Hui Yang, Outside Unit & Field Member
Dennis Kon-Jin Lin, Special Member
Murali Haran, Major Field Member
Ephraim Mont Hanks, Professor in Charge/Director of Graduate Studies - Keywords:
- Design of Experiments
Mixture Experiments
Order of Addition
Threshold Accepting - Abstract:
- In a mixture experiment, several components are mixed to produce a response. This is a classical problem in chemical engineering, pharmaceutical, and food science fields. However, existing literature on mixture designs ignores the order of addition of the mixture components. We consider the Order-of-Addition (OofA) mixture experiment, where the response depends on the order of addition of the m components, as well as their mixture proportions. The overall goal of this experiment is to identify the addition order and mixture proportions that produce an optimal response. Full OofA Mixture designs are created which ensure orthogonality between mixture model terms and OofA effects. These designs support models with (1) typical mixture parameters, (2) order-of-addition effects, and (3) interactions between mixture and order terms. Simulations show that if interactions exist, then the optimal mixture proportions identified by traditional models may be misleading. While the full OofA Mixture designs are useful, the number of runs they require increases rapidly as m increases. We propose the use of computer algorithms to search of a subset of runs from the full OofA Mixture design that maximize an optimality criterion. In particular, a Threshold Accepting (TA) algorithm is proposed to find optimal subsets of the full design. Finally, we investigate the scenario where the set of all possible orders in a chemical experiment is restricted to those permissible on an undirected graph, such as a chemical reaction network. Sufficient conditions for estimability of the popular pariwise ordering model are derived for this scenario. Depth-First Search (DFS) is used to enumerate the set of all possible Hamiltonian paths on a graph. A fractional Depth-First Search (DFS) approach is proposed to find highly efficient fractions of the full DFS design, which are shown to have robust efficiencies under different random graphical models.