Apply powerful design of experiments (DOE) tools to make your system more robust to variations in component levels and processing factors.
This article shows how to do a comprehensive experiment that combines mixture components with process factors in one crossed design, thus revealing interactions that would remain hidden by not combining all the variables in one study.
The latest versions of dedicated DOE software exhibit more versatility than ever before to create optimal designs that handle any combination of mixture components, processing factors (such as time or temperature) and categorical variables (such as supplier and material type). These computer programs easily manipulate almost any number of responses in powerful optimization routine that reveal "sweet spots" - the operating windows that meet all specifications at minimal cost. In this paper, we review the basic principles of mixture design. Then we apply state-of-the-art tools for optimal design to the formulation of a coating.
See how statistically-based mixture design of experiments (DOE) make breakthrough improvements in cost and performance of paints and coatings. Dedicated DOE software exhibit make it easy to create optimal designs that handle any combination of mixture components, processing factors (such as time or temperature) and categorical variables (such as supplier and material type). They easily manipulate almost any number of responses in powerful optimization tools that reveal "sweet spots" - the operating windows meeting all specifications at minimal cost.
Statistical tools, especially design of experiments (DOE), provides the means for quality improvement of diammonium phosphate (DAP) and related fertilizer products. Depletion of high grade phosphate ores in Florida and elsewhere makes it increasingly difficult to meet customer specifications for nitrogen content of DAP. Urea or ammonia can be used as nitrogen supplements, but this adds cost to the final product. This paper lays out a special form of DOE, called two-level factorial design, which helped to maximize nitrogen content in DAP and make it less susceptible to impurities in lower grade phosphates.
Design of experiment (DOE) tools provide an efficient means for you to optimize your process. But, you shouldn't restrict your studies only to process factors. Adjustments in the formulation may prove to be beneficial, as well. A simple but effective strategy of experimentation involves: 1. Optimizing the formulation via mixture design; and 2. Optimizing the process with factorial design and response surface methods. This article shows you how to apply DOE methods to your formulation. A case study gives you a template for action.
A version of this article appeared in Chemical Engineering Progress. (chem-2.pdf 56KB) April 1998.
(Click on http://www.statease.com/pubs/ital-favform.pdf for an Italian translation 435KB.
Also see a PDF of this article as published in Ric-Mach Chimica News, http://www.statease.com/pubs/sixsigma.pdf . (sixsigma.pdf 129KB) June 2004.)
The traditional approach to experimentation requires changing only one factor at a time (OFAT). However, the OFAT approach does not provide data on the interactions of factors, a likely occurrence with processes. This white paper lays out the tried-and-true "SCO" strategy of screening and characterization via two-level factorial design of experiments (DOE), followed, if needed, by response surface methods (RSM) for process optimization.
This paper discusses supplementing Lenth's method by combining his estimate of error variance from small factorial effects with the pure error variance from replicate observations or (possibly) other estimates of error variance. Presented at the Fall Technical Conference.
With the latest computer software, today's formulators can take advantage of a powerful tool: design of experiments (DOE) for mixtures. DOE methods use test arrays that produce maximum information from minimal runs. Industrial experimenters typically turn to two-level factorials as their first attempt at DOE. However, mixture design accounts for the dependence of response on proportionality of ingredients where factorial design does not. If you formulate chemicals, food or other products, consider using mixture design rather than factorials or related optimization methods. To show you how, follow along as we conduct a kitchen chemistry experiment on pound cake.