(549c) Linking Measurements and Statistical Methodology through the Characterization of Polymeric Materials: Hierarchical Analysis of Gel Permeation Chromatography Data

As future chemical engineers, it is important that students be able to identify and quantify sources of error. A statistical analysis technique that is often overlooked is hierarchical design methodology, which allows for the separation of overall variance into several related components. While hierarchical methodology is relevant to many fields, we have demonstrated that it can be taught through the synthesis and characterization of polymeric materials.

Hierarchical or nested design methodology helps engineers to identify different sources of variation within their data. Essentially, the methodology can be viewed as a variance decomposition technique, where the overall variance is separated into several components; the goal is to locate the most significant sources of variance. For any process with multiple steps or stages, it can be useful to know whether the variance is equally a result of all operating stages, or if select process steps are contributing most of the variance.

The hierarchical design methodology and subsequent analysis is very general and can be applied to many fields of study. However, it is often overlooked in the chemical engineering undergraduate curriculum. We would suggest that it is a valuable tool for students to add to their background, and that it can be taught alongside other chemical engineering concepts to make good use of precious teaching time. In addition to expanding their knowledge base, students can also develop improved problem analysis and investigation skills, gain laboratory experience, and advance their communication skills.

The general concept can be introduced to students with a straightforward thought experiment: consider synthesizing some material and then analyzing the material using a property characterization technique in the lab. If we replicate the synthesis process and the characterization technique several times, we will not always obtain exactly the same outcome! Common sense dictates that there will be variability observed between genuine, independent replicates. Variability can be imparted to the measured property from several possible sources of error; students can likely identify most of these themselves. Sources of error may include random fluctuations in the operating conditions between batches/reactors, heterogeneity in the reactor as samples are collected, inconsistencies in the analytical technique, and so on.

The original motivation for integrating chemical engineering concepts (specifically polymer reaction engineering concepts) and the hierarchical design methodology came about during experimental design and data analysis in graduate student research. Each experimental stage of polymer synthesis and characterization can introduce new sources of error, and this provides a very tangible way for students to identify and quantify potential variability. Gradually and progressively, the same methodology was introduced in other settings including undergraduate student research projects, senior design projects, and lab data analysis in statistics courses. The most recent iteration of this project was in the context of an independent research project course. As such, there was additional flexibility to shift between the academic/theoretical side and the experimental/laboratory side of the project.

This background is intended to provide some historical context, but the approaches used thus far should by no means be seen as the only methods of delivery. In fact, the hierarchical design methodology is extremely versatile; it could be used as part of an undergraduate laboratory course, a lecture-based statistics course, a senior undergraduate research project, or with graduate students. Of course, individual instructors could adapt the project at their discretion, especially given the diversity of student backgrounds, laboratory capabilities and course timelines.

We can encourage students to explore the power of hierarchical design methodology through statistical design of experiments, synthesis of polymeric materials, and/or subsequent characterization steps. The real-world application of a seemingly complicated statistical analysis methodology can help students to understand the relevance of the approach, to recognize the methodical simplicity of the analysis steps, and (more importantly) to appreciate inherent variability in experimental work. It is our hope that sharing our experience and several case studies will inspire other instructors to integrate these important topics into their own undergraduate chemical engineering courses.

Based on the recent publication: N. Filipovic, A. J. Scott, A. Penlidis (2021). "Hierarchical Data Analysis for the Characterization of Polymeric Materials: Linking Measurements and Statistical Methodology." Chemical Engineering Education, 55(1): 11-22.