Engineers at an aluminum-casting company were struggling to understand why a particular part came off the line filled with inclusions. Having conducted many one-factor-at-a-time tests to no avail, they turned to statistical software and a process called design of experiments. Optimizing based on this process let the engineers reduce the defect rate to zero.
A somewhat different version of this article appeared in Modern Paint and Coatings.
What would you do it confronted with an "opportunity" to make a major change, involving many factors, but you need to do it quickly? The traditional approach to experimentation requires you to change only one factor at a time (OFAT). However, the OFAT approach doesn’t provide data on interactions of factors, a likely occurrence with chemical processes. An alternative approach called “two-level factorial design” can uncover critical interactions. This statistically based method involves simultaneous adjustment of experimental factors at only two levels, offering a parallel testing scheme that’s much more efficient than the serial approach of OFAT.
Powerful desktop software now makes it easy to optimize paint formulations. Coatings researchers can use the computer to apply statistically based design of experiments (DOE) for mixtures-a proven method for making breakthrough improvements in cost and performance. This paper shows the application of the latest technology of computer-aided mixture design to data from Hesler and Lofstrom's 1981 article "Application to Coatings Research." In the process the essential aspects of mixture methodology are illustrated.
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.
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.
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.
Design of experiments identifies which factors matter and which ones don't when microwaving popcorn, as well as helping find optimal settings.
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.