Orthogonal Array Experimental Design

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In this work, an orthogonal array experimental design was used to optimize the synthesis of a photocatalyst. This chapter provides the reader a crucial foundation for understanding the terminology and practical use of design of experiments (DOE). The practical use of this, as will be discussed later in this work, is that wise use of DOE can drastically reduce the time and effort to optimize procedures, catalyst synthesis or otherwise. In this section, we explore some of the general procedures of experimental design, as well as several commonly-used designs. We then examine different data analysis techniques – the column effects method, and ANOVA. We also present some history on orthogonal array designs, and how they are useful at cutting cost and time investment in research.

1.1 Basic Definition of Design of Experiments

The phrase “design of experiments” refers to any orderly plan, or design, that describes four key features of an experiment, as summarized by Finney ⁠[1]⁠:

i. The set of factors to be formed into treatments.

ii. What the test subjects will be.

iii. The rules for applying treatments to the test subjects.

iv. What measurements will be taken before, during, and/or after the treatments have been applied to the test subjects.

At each step above, the experimenter should bear in mind the impact that his or her decisions will have on the cost, feasibility, and precision of the experiment [1]⁠.

1.2 An Example Chemical Engineering DOE Problem

Though good experimental design is important for producing reliable, reproducible research, many engineers are unfamiliar with DOE concepts, and many of the terms in the previous section may seem unfamiliar. For didactic purposes, we present a simple example that...

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... would need 2 × 34 = 162 observations to be able to fully explore the parameter space. Due to this “combinatorial explosion”, it is more common in scientific and industrial practice is to use a fractional-factorial experiment (FFE).

1.5 Fractional Factorial Designs and Orthogonal Arrays

Despite conveying less information than an FFD, it is possible for an FFE to capture a large amount of the variation in the data with fewer experimental trials. The justification for using FFE's comes from the sparsity of effects principle, which states that the effect of higher-order interactions, though ubiquitous, are usually insignificant [4]⁠. Though we confound the main effects with these other interactions, this confounding is probably negligible, and thus, we can justify reducing the number of required runs. An especially popular type of FFE is the orthogonal-array design.

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