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Design of Experiment - Mixture Design

Designed experiments refer to the analysis of data collected when cause factors have been varied in a deliberate, planned manner. When performing a designed experiment, the quality of the results is determined primarily before the experiment is actually performed. A particular type of designed experiments is termed mixture designs and is used when the objective is to formulate a recipe from a mixture of ingredients. Design points based on proportional combinations of the ingredients are determined in such a way to map the experimental region. At each design point, the appropriate recipe is mixed and measured responses are recorded. The responses may be highly quantitative and physical in nature, such as cost, viscosity, or immiscibility or may be more qualitative in nature, such as preference ratings for color, smell, or texture. When the design point combination responses are recorded, models are derived that plot contour maps showing optimal areas for analyzed responses. In the mixture region picture, 4 ingredients (X1, X2, X3, X4) are combined at design points that map the light gray area. The yellow contour lines show values of the response, for example smell preference. The yellow oval designates the area where the response is the highest value. At the selected point, designated by the cross-hairs, the model predicts the smell preference of the recipe of X1=53.5%, X2=22.1%, X3=16.3%, X4=8%, to be the highest at 397.5. The red circled points are the design points. From a small number of experiments (in the case of this example, 17) an optimal value may be obtained extremely efficiently. The guesswork of formulation is removed! No more is the laboratory testing a recipe and then deciding which way to experiment next based on the results of the last run. One of our clients estimates he saved 9 months of laboratory work by using this modeling process. Call Alexandria today to save valuable product development time.

Figure 1 : Mixture Design/Design of Experiments

Design of Experiment - Factorial Design

Factorial Designed Experiments are used when independent or causal variables are tested for effect on dependent variables or responses. Causal variables have multiple levels and are varied in deliberate combinations with each other whereupon responses are measured. Factorial designs predict individual variable effects as well as interacting effects. Experimentation without the use of factorial designs is typically a “one factor at a time “ or FAT approach and can consume your research and development budget quickly. Consider the researcher who wants to find which of 8 factors, each of 2 levels, are effecting response values of interest. With a one factor at a time approach, the researcher would set all 8 factors at the first level, measure the responses, then move the first factor to the second level while fixing all other factors and measure the responses. Proceeding with this method, the researcher would need 16 consecutive runs of the material to measure the differences in factor effects and would have no information on the interaction effects. With a factorial design, varying all 8 factors in a planned method, simultaneously, 16 runs would not only separate the 8 factor effects but would also determine 7 interaction effects, something that cannot be measured with a one at a time approach. The efficient use of planned experimentation can accelerate the researcher up the knowledge curve. Termed DOE, design of experiment saves time and money in product design and product failure evaluation.

    Figure 2: Factorial Design/Design of Experiments
FAT Approach
DOE Approach

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Revision Date June 5, 2008