## Case Studies and White Papers

#### Mixture Design - Simple as Pound Cake

With computer software, food formulators can take advantage of a powerful statistical tool: design of experiments (DOE) for mixtures. DOE methods employ test arrays that produce maximum information from minimal runs. Industrial experimenters typically turn to two-level factorials as their first attempt at DOE. These designs consist of all combinations of each factor at its high and low levels. With large numbers of factors, only a fraction of the runs need to be completed to product estimates of main effects and simple interactions. However, when the response depends on proportions of ingredients, such as in food formulations, factorial designs may not make sense. Mark & Pat explore this concept with a pound cake recipe.

#### A Balancing Act: Optimizing a Product's Properties

G.C. Derringer provides an easy-to-read explanation of the commonly used optimization function called desirability. When used as the final step in DOE, this function allows simultaneous optimization of multiple responses, resulting in the discovery of a group of optimal factor settings.

#### Optimizing Formulation Performance with Desirability Functions

Formulators often must make tradeoffs between conflicting performance measures. This paper illustrates how multiple response measures can be combined into one objective function, called "desirability", which can then be optimized by univariate techniques. The methodology consists of several basic steps: - Develop predictive models for each response - Transform each response to a desirability scale - Mathematically combine the individual desirability measures in to one overall index - Use numerical optimization methods to find the formulation that produces maximum overall desirability. By way of a case study on material used to make pipe, the paper shows how to generate models from statistically designed mixture experiments. Then by application of desirability functions, the optimum combinations of ingredients become apparent. Two and three dimensional surface maps, generated from commercially available personal computer software, will be illustrated.

#### Applying DOE to Microwave Popcorn

Design of experiments identifies which factors matter and which ones don't when microwaving popcorn, as well as helping find optimal settings.

#### Optimizing Plasma Sprayed Alumina-Titania Coatings Using Statistical Methods

A statistical design of experiment study of the plasma spraying of alumina-titania powder is presented. In this study, the coating design has been optimized starting with classical experiments, progressing through fractional and full-factorial experiments, and concluding with response surface methodologies. The alumina-titania powder system in this study is being used in the fabrication of heater tubes that emulate nuclear fuel tubes for use in thermal-hydraulic testing. A substantial range of plasma processing conditions and their effect on the resultant coating are presented. The coatings were characterized by hardness tests, electrical tests, and optical metallography (i.e., image analysis). Coating qualities are discussed with respect to dielectric strength, hardness, porosity, surface roughness, deposition efficiency, and microstructure. Attributes of the coatings are correlated with the changes in operating parameters. An optimized coating design is presented for this specific application.

#### Analyzing Two-Level Factorials Having Missing Data

This presentation details and demonstrates a procedure that, despite missing data, allows the use of user-friendly, normal-probability plots for two-level-factorial effect selection.

#### A Simple Comparative Experiment with Paper Clips

Details and demonstrates a fun experiment to do at home or in class to build understanding of variation and how it can be handled with simple comparative designs. For teaching purposes it works best if each student breaks two brands of clips, thus providing data for a paired t-test, which blocks out variability due to the tester.

An updated version of paper-clip experiment is provided in the June 2009 Stat-Teaser posted at https://cdnm.statease.com/news/news0906.pdf.

#### DOE It Yourself

Fun science projects.

#### The Role of Pure Error on Normal Probability Plots

A look at augmenting the usual probability plot effects with points representing pure error.

#### Experiments Uncover Source of Valve Failures

Company engineers at Fluoroware Ind. chose to use Design-Expert software to troubleshoot customer complaints that their plastic components were failing prematurely. In the past, doing this sort of test could be very complicated; however, using DOE to test multiple factors at once significantly simplified the process.