Case Studies and White Papers
How to Design and Analyze Mixture Designs that Include Process Factors and/or Categorical Variables
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.
Computer-Aided Tools for Optimal Mixture Design
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.
Quality managers who understand how to apply statistical tools for design of experiments (DOE) are better able to support use of DOE in their organizations. Ultimately, this can lead to breakthrough improvements in product quality and process efficiency.
Revealing Interactions From Fractional DOEs
Fractional two-level factorials are a powerful tool for making significant improvements to product quality and process efficiency. Unfortunately, this approach to design of experiments (DOE) may alias the main effects with their interactions. Then it is no longer clear which factors truly influence the process. In part 1, this paper illustrates the use of graphical technique for the viewing alternative aliased interactions. The graphical procedure enhances, but does not remove, the guesswork required when a highly-fractional design produces significant effects. The only sure way to pin down the actual effects will be to perform follow up experiments, which will be discussed in Part 2. A technique called "foldover" is tailor-made for de-aliasing effects. This sequential approach to DOE offers a great deal of flexibility to the quality engineer.
Find The Most Favorable Formulations
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.)
Statistical Design of Experiments for Quality Improvements of Fertilizer Products
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.
Inspirational examples of DOE being applied in non-manufacturing, including sales and marketing (particularly for web-page development), but also billing, education of medical patients and many other business processes that can be quickly improved (and most effectively!) via multifactor testing methods.
Design of Experiments Strategies
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.
Mixing it up with Computer-Aided Design
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.