Case Studies and White Papers

Mixture Design - Simple as Pound Cake

Published: December 1995
Authors: Mark Anderson, Patrick Whitcomb

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

Published: June 1994
Author: George Derringer

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.

Publication: Quality Progress

Optimizing Formulation Performance with Desirability Functions

Published: August 1993
Authors: Mark Anderson, Patrick Whitcomb

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.

Publication: Quebec Metalurgical Conference

Applying DOE to Microwave Popcorn

Published: July 1993
Authors: Mark Anderson, Hank Anderson

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

Publication: Process Industries Quality

Optimizing Plasma Sprayed Alumina-Titania Coatings Using Statistical Methods

Published: June 1993
Authors: T.J. Steeper, W.L. Riggs II, A.J. Rotolico, J.E. Nerz, D.J. Varacalle, Jr., G.C. Wilson, Mark Anderson, Patrick Whitcomb

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.

Publication: Thermal Spray Coatings: Research, Design and Applications

Analyzing Two-Level Factorials Having Missing Data

Published: January 1993
Authors: Kinley Larntz, Patrick Whitcomb

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.

Publication: Fall Technical Conference, St. Louis

A Simple Comparative Experiment with Paper Clips

Published: January 1992
Author: Mark Anderson

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

Publication: Stat-Ease, Inc.

DOE It Yourself

Published: January 1992
Author: Mark Anderson

Fun science projects.

Publication: Stat-Ease, Inc.

Published: January 1992
Authors: Patrick Whitcomb, Kinley Larntz

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

Publication: Conference

Experiments Uncover Source of Valve Failures

Published: June 1988
Authors: Nancy Chase, Dan Selness

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.

Publication: Quality Magazine