ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

Order-of-Addition Experiments

5 September 2018, 09:30 – 10:00

Abstract

Submitted by
Joseph Voelkel
Authors
Joseph Voelkel (Rochester Institute of Technology)
Abstract
The order in which components are added in a chemical batch, film, food product, or in a study of protein transport may be a primary consideration in an experiment, especially in the earliest stages of studying a process.

Little investigation has been done for the design of such order-of-addition (OofA) experiments until our recent work. Based on an idea from Van Nostrand (1995), we define and explain a reference standard of OofA experiments by extending the idea of orthogonal arrays. (We try to show this and other ideas as simply as possible.) For strength 2 designs, we find that OofA orthogonal arrays require that the number of runs N is divisible by 12 when the number m of components exceeds 3. (For m = 3, the full design requires only 6 runs.) We consider a chi-square criterion to measure the balance of an OofA array, and show that for strength 2 designs, OofA OA’s appear to be equivalent to D-optimal designs. In many situations, a number of non-isomorphic (distinct) designs exist; in such cases we use secondary measures to determine an optimal design. We have found OofA orthogonal arrays for m = 4 and 5 when N = 12, for m = 5, 6, and (near-optimal) 7 when N = 24.

We also extend these optimal OofA designs to incorporate standard process variables so that, for example, temperature or mixing speeds may be included. Our methods can also take into account natural restrictions that the experimenter may have, such as requiring that one component is always added before another. Finally, we show and analyze examples of some recent experiments in m = 4, 5, and 6 components.
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