Design of Experiments, Mixture Designs

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    If one of the components in a mixture design must have a fixed proportion, what’s the best way of handling it?As far as I can see Minitab only accepts upper and lower bounds, and the upper must be higher than (not equal to) the lower. I can probably rig it by making the difference very small, but is there a better way?Alternatively I could convert the rest of the components to pseudo components.Any thoughts?Thanks, Glen


    Robert Butler

       If we assume when you say that one of the components in a mixture must have fixed proportion what you mean is that it would have to always make up X% of the mix then what you need to do is build a restricted mixture design where everything else has to add up to 100% – X%. 



    DOEs come in a few flavours

    Glen:DOEs come in a few flavours. The ‘Classical’ stuff taught during
    most Six Sigma training are the full and fractional designs used with either
    continuous or discrete factors. An example is the paper helicopter
    demonstration. Helicopters can be made with long/short wings, light/heavy
    paper, long/short body, etc. These are the designs you can find in Minitab12. These
    designs can also be found in Minitab14 under DOE->factorial.Minitab14 also allows mixture designs where all components
    must total 100%. The example in the help menu shows this:“The taste of lemonade depends only on the proportions of
    lemon juice, sugar, and water”You can also have an experiment that combines mixture
    components with process variables. For example:“The taste of a cake depends on the cooking time and
    cooking temperature, and the proportions of cake mix ingredients”I have heard people mistakenly talk about the latter experiments
    as “mixture” experiments because they have a mixture of two different types of
    variables.It sounds like your setup has some variables that can be arbitrarily
    fixed (like temperature) and some that must total 100% (like some additive to a
    mixture). If this is the case, set up a mixture DOE with process
    variables.If you have a component that must always be a fixed
    percentage, then it does not vary and should not be included in the
    experimental design at all. Cheers, BTDTP.S. – If you have Minitab 12 you will have to upgrade to a
    newer version to do mixture designs.

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