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DOE – How to Design Experiment with Multiple Levels

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This topic contains 10 replies, has 6 voices, and was last updated by  Robert Butler 1 week, 1 day ago.

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  • #54226

    Lucas Xu
    Participant

    As I know, we usually design our experiment with 2 levels with multiple factors, which is typical DOE format.But how about we design with multiple levels, can we do that? For example, I want to design 4 levels with 5 factors, how can I operate in Mintab? Hope someone could help me.

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    #194308

    Robert Butler
    Participant

    Two level designs are “typical” because they are the lowest level designs that meet the basic criteria of designs – efficiency with respect to number of runs and ability to identify significant effects. A central concept of design is that if an effect is going to be observed your best chance of seeing it will be by contrasting responses recorded at the extremes of the variables of interest.

    The main drawback to two level designs is that they can only describe linear (straight line) trends. The next step up from a two level design would be a two level design with center points. The design will still only be able to describe straight line trends with respect to the variables of interest but it will also allow for an overall check for the existence of curvilinear behavior somewhere in the design space. It won’t be able to assign the curvilinear response to any one variable but it will tell the researcher if one exists.

    After we pass 2 level designs we come to a fork in the road. We can go after 3 level designs or we can go after composite designs. Both of these will allow for a check of main effects curvilinear behavior (straight line and single bend curvature), however, 3 level designs will also allow for the examination of interaction terms involving squares of the factors of interest.

    If you are going to try for something beyond 3 level designs or composites with specific 5 level settings you will have to build them yourself. However, before you do you really need to think about what it is that you are doing.

    If you want 4 levels what you are saying is that you want to investigate CUBIC response trends. I’m sure there are some processes around somewhere where cubic responses are the norm but I must admit I don’t recall ever having to deal with this situation. I won’t pass judgment on what you are doing but based on what I’ve seen and done I think it is overkill – both with respect to number of experiments needed and the time and effort involved in the work.

    Ok, so much for the op ed. If you want designs above 3 levels (here we are ignoring composites) you will have to build them yourself. The easiest way to do this would be to generate the complete matrix of design points (in your case 4**5 = 1024 combinations), put them in a file, and use them as the search space for a D-optimal (or A-Optimal) design generation algorithm. For your 4 level, 5 factor design, the basic model you would need to specify to the D-optimal package would be either

    Model = A,B,C,D,E, A**2, B**2,C**2, D**2,E**2, A**3, B**3,C**3,D**3, E**3

    or

    Model = A,B,C,D,E, A**3, B**3,C**3,D**3, E**3

    which one would depend on the instructions concerning term definition for your stat package’s D-optimal routine.

    One additional thought (let me pull out the soapbox again) – if the point of having more than 3 levels is because you want to have a “better definition” of the trend of a suspected curve shape then there are two other possibilities.

    First – if the suspected curvature is the very common situation where the curvilinear response is one that is not symmetric (that is the center point and one or other of the extremes will have essentially the same values meaning that you will have missed the inflection point)and if you have some idea as to where in the design space the inflection might occur, you can take a standard 3 level design and locate the “center” values at these levels. Your matrix will no longer be a series of -1,0,1 levels. Rather you will have to “normalize” your chosen “center” values to whatever it is they scale to. (For example: if the -1,0,1 levels of the perfect space corresponded to 0,5,10 and if you actually wanted to run 0, 2,10 then the “normalized” values would be -1, -.6, 1.)

    The design will be a tad non-orthogonal but it shouldn’t matter and it will allow you to use standard 3 level designs for your investigation.

    Second – If you really just want to have more points to define a curve you can take your standard 2 level design, add a couple of center points, and then toss in some additional one-at-a-time runs to flesh out the curve shape for whatever factor(s) you are interested in.

    This would amount to augmenting a two level design with a series of ladder experiments where you vary the one variable while freezing the others as levels inside the design. This is a very cumbersome way to go and before you do it you should have some assurance that you actually need to look for curvature in the cubic and higher orders. If you choose this route you will have to give some thought to the analysis. If everything is inside the design space (it should be) then you ought to run the analysis with and without the ladder values and see what you see.

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    #194314

    Chris Seider
    Participant

    And don’t forget about EVOP.

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    #194315

    MBBinWI
    Participant

    @lucasxu83 – Besides the excellent advice provided by Robert Butler, the only other reason to perform more than a 3 level design is if you have discrete variables.

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    #194317

    Lucas Xu
    Participant

    @rbutler Thanks, maybe for linear equation, 2 level will be enough for most of case…

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    #194318

    Lucas Xu
    Participant

    @cseider what is EVOP?

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    #194319

    Chris Seider
    Participant

    See below. It’s a great technique without perturbing the process much. http://thequalityportal.com/articles/evop.htm

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    #202277

    Nur Fariha

    Which type of design experiment can be used for two factors at different levels?
    for example i have factor
    time with 21 level
    nanofluids 7 level

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    #202278

    Robert Butler
    Participant

    You’ll have to provide more information about time and the nanofluids – are we talking multiple kinds of fluids whose levels can be changed independently of one another or are we talking multiple levels of a single fluid or is it something else?

    As for time are we talking taking measurements across time or are we talking about running something for specified intervals of time or are we talking about something else?

    If it is a simple case of having both time and nanofluids at different intervals/concentrations and if you want to check curvilinear effects and two way interactions then everything I said in the earlier post concerning 3 level/composite designs and the lack of any need to go beyond 3 levels applies.

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    #236208

    ce_seek
    Participant

    @rbutler

    if the experiment is preliminary, which one is better to conduct?

    1. two level factorial with center point replicates
    2. go directly to three level factorial

    Thank you!

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    #236212

    Robert Butler
    Participant

    Which one is better depends on many things. If it is preliminary and you have no prior information concerning a possible curvilinear response over the range of variables you are examining then it comes down to a matter of time/money/effort. If we are discussing the example of your other post – 2 variables, then you would be running 6 vs 10 experiments – 2**2 + two center points vs 3**2 and a single replicate of one of the design points.

    One compromise is to run the 2**2 plus the two center points and, if the analysis indicates curvlinear behavior, augment the existing run of experiments with a couple of additional design points to test the curvature with respect to the two variables of interest. To do this you would need to use one of the computer generated design methods such as D-Optimal. You would force in the existing design and allow the program to choose additional runs from all of the possible design points in a 3**2 design.

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