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DOE Mixture Questions

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  • #52615

    Saherngu
    Participant

    I’m trying to set up a mixture DOE in which I have a combination of mixtures, amounts, and factors.- 3 factors compose the mixture. So it seems that I will start with creating a mixture DOE and work in the amount and factors.- The 4th factor is the amount that the mixture takes up in the overall volume (either 7.5% or 30.0%).
    – For the 5th and 6th factors (which are size and density of the mixture particles), I figure that I can call them “process factors” in the mixture DOE.This seems to be the way it could be done via Minatab.  I inquired and their response was that Minitab does not allow for a design with both process variables and multiple amounts, but that I could set up the “amount” as a third process variable.
    QUESTION: is it really allowed to include the “amount” as a 3rd process variable?  With all I’ve seen regarding mixture designs, it seems that people discuss adding in either process variables or mixture amounts (but not both?).  It seems fine – in fact, the 1st two “process variables” are not process variables – they’re actually material properties (particle density, particle size). Also – if a test matrix was created with the “amount” as the 3rd process variable, could a D-optimal algorithm then be used to decrease the size of the test matrix?  I assume so.
    I appreciate any input on this issue.  Thank you.

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    #185258

    Saherngu
    Participant

    Would appreciate any response to the previous note.  Thank you.

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    #185261

    Putnam
    Participant

    It’s difficult to tell from your post, but it sounds more like a mixture study with four materials than anything else.  You have the three materials you originally mention, which are blended. Then that mixture goes into a final blend (obviously with something else) so that the original mixture represents two different volumes in the final mixture. If this is correct, just set a mixture design up with four factors and you should be OK.
    You’d need to provide more information on how particle size and density are going to play into your design.  I’m assuming you can actually control these two independently in the starting material. 

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    #185262

    Robert Butler
    Participant

      Designs involving mixture and process variables are common. If you don’t have one of the more advanced design packages the simplest design, although not the most efficient in terms of number of experiments, would be a 3 parameter mixture design coupled with a 3 parameter factorial.
     
    The three ingredients that go into making up the mixture will always have to add to 100 percent.  This mix, in turn, is added to something else at either 7.5% or 30% of the final volume of whatever it is you are making.
     
     If, as your post suggests, you really have control over particle density and size and these can be varied independently of the ratios making up the initial mix then you can treat these, and the final volume percents as three process variables.  In that case you could run the usual 3 variables in 4 experiments fractionated factorial design and at each of the points in that design you could run the basic 4 point mixture (three corner points and a center) for a total of 16 experiments.  If you were to replicate a couple of the design points you could do everything in 18 experiments.  As noted, a design package that allowed you to program restrictions might be able to reduce this number.  
     
     Of course, if any assumptions mentioned above are violated you will need to provide more information before anyone can offer suggestions.

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    #185263

    Saherngu
    Participant

    Mike,
    Thanks for the response.  I think that you make a good point.  The 3 materials (actually sand, metal, and rock) are combined in a mix at different proportions.  For each run, this mix is put into a liquid solution.  The liquid solution really should be the 4th part of the overall mix.  So, it does sound like a 4 factor mixture DOE.  The 4 factors would be controlled by % volume.
    Particle size and density can be controlled independently for each material (sand, metal, rock) in the mix.  Would you agree that these factors can be considered “process factors”?
    Thanks again.

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    #185264

    Putnam
    Participant

    James,
    I don’t think I’d call your material particle size and density “process” factors, although these characteristics could be design factors.  This may be just semantics on my part. 
    My experience with solids (mostly bulk pharamceuticals) has been that density and particle size vary directly for a single material.  Large, dense particles can be milled into smaller, lower density ones.  Likewise, powder denstiy increases as you increase the average particle size.
    If you can actually control both the material particle size and density, and if the two characteristics are truely independent (you can really get a small particle, high density material), then you’d need to do a much larger design (similar to the other suggestion on this thread) with density and particle size used as factors for each material. 
    Mike

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    #185265

    Saherngu
    Participant

    Thank you, Robert.
    Sorry if my previous post was not clear.  The mixture is made of 3 solids (sand, metal, rock) and a liquid solution.  As Mike had suggested, maybe the best way to create the test matrix is with a mixture of 4 factors (sand, metal, rock, and liquid solution) – with the %’s defined by volume.  Which do you think is best?
    If the two other factors (density, particle size) can be applied to all 3 mixture components simultaneously (the solution not included) for each experimental run, then I think I can use your strategy of running the 2×2 factorial design (density, particle size) for each mixture design point.  I need to verify if this simultaneous classification is correct.  If it is not, then it sounds like different process factors will need to be run for each mixture factor, which would make the test matrix much bigger.
    I hope this is clear – I’m on the run, just stopping for a few minutes at a Starbucks with wireless to respond.

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    #185266

    Saherngu
    Participant

    Mike,
    All good points.  I’m calling them “process factors”, but they’re really environmental conditions if anything – noise in the real world, but chosen to be controlled for this experiment.  “Process factors” is Minitab language.
    Particle size and density should can be independent, if chosen to be.  I need to verify if the levels chosen for particle size and density will be applicable to each of the mixture components simultaneously – that would make things easier.  If the process variable levels would be different for each mix component within an experimental run, that would make the matrix much bigger as you said.
    Particle density and size, though, should be independent.
    James

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    #185280

    Robert Butler
    Participant

      We need to back up a bit here.
      1. Your most recent post indicates the percent of addition of the mix of sand, metal, and rock can vary between 7.5 and 30% as opposed to just being limited to these two levels.  If this is the case then the “liquid” in the mix could vary between 92.5% and 70%. 
       a. If true is this liquid a single substance or is it too comprised of some combination of additives?
     2. If sand, metal, and rock are the three solids unless you have different kinds of metals and rocks I don’t see how you are going to vary density and particle size – density is mass per unit volume and for any given metal or rock type it is going to be constant.  As for sand – unless you are using some kind of sand pellets comprised of sand and different binders and levels of inert filler I don’t see how you could change its density at all.
      3. With these ingredients, you would want to build a restricted mixture design which specifically avoids the corners of the triangle or, if you include liquid, the pyramid.
      I’ll wait to read your response to this and the other posts to the thread before attempting to offer anything more.
     

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    #185292

    Saherngu
    Participant

    The 4th factor is the amount that the mixture takes up in the overall volume (either 7.5% or 30.0%).
    Robert,
    I’ll try to clear up my description.  My initial description was per the 1st way I thought of creating the test matrix (with a mixture of 3 items – sand, rock, and metal; and then adding another factor for the % volume that this 3 solids mix occupies in the overall volume).  The mixture of these 3 items (sand, rock, metal) will occupy either 7.5% or 30.0% of the overall volume.  The remaining volume (either 92.5% or 70.0%) will be occupied by either water or a brine liquid.  This liquid is to be considered as a single substance. 
    For the sand, rock, and metal, each will be at one of 3 levels in the mixture matrix (-1, 0, or 1).
    For varying density and particle size, there are standard sand, rock, amd metal to purchase.  Particle Size and Density will be at two levels each.  For each experimental run, the level of the density and particle size will be applied to all three solids (sand, rock, and metal).  So, if the Density is at the “high” level and the Particle Size is at the “low” level for a particular experimental run, then these density and Particle Sizes would be applied to each of the the 3 solids in the mixture (sand, rock, metal).  Because of this setup, it seems plausible to consider both Particle Size and Density as Process Factors and cross the 4 factor mixture design against a 2×2 factorial (composed of Particle Size and Density).  You had suggested this yesterday and it sounds like a good way to go.  Do you still think this is the best way to go?  About 25 runs is our maximum.
    Question: why avoid the corners of the pyramid?  Would the VIF’s be better this way?
    Hope this is more clear.  I very much appreciate your help and look forward to hearing back.
    James

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    #185293

    Saherngu
    Participant

    Robert – please ignore the 1st line in the last post.  I checked the posting and noticed the 1st line, which shouldn’t be there.
    Just to clarify:  the 3 solids will, by volume, occupy either 7.5% of the overall volume or 30.0% of the overall volume.  The remainder is occupied by liquid.
    James

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    #185310

    Robert Butler
    Participant

      If you can only put the sand,rock, metal mix into the product at only two different percentages it would be much easier to treat the percentage as a variable in the standard factorial design which would include particle size and density.
       As for the three component mixture – the levels would be between 0 and 1 – you don’t get to put -1 in a mixture design.  The reason you would stay away from the corner points of the mixture is because these correspond to the “pure” combinations (i.e. 100% of either sand, rock or metal) and unless you have a very curious process I doubt these design points would be of much value.
      I’d recommend reading Chapter 5 – The Inclusion of Process Variables in Mixture Experiments in Volume 5 of the ASQC series of Basic References in Quality Control. The title of the volume is How to Run Mixture Experiments for Product Quality by John Cornell.  My copy (there may have been revisions since) is 88 pages in length and it is an excellent primer on mixture experiments.

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    #185319

    Saherngu
    Participant

    Robert,
    Thank you for the DOE advice and the references.  Much appreciated.

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