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DoE Design For Multi Level Factors?

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  • #32232

    Brad M.
    Participant

    I need some input on what type of DoE model I should use.  We are conducting a DoE on a solderability defect.  Our experiment involves two (2) factors.  One (1) factor will be varied over three (3) levels and the other factor will be varied over four (4) levels.  What recommendations do you have?  Should a screening experiment be done first or is there a design that can provide valid response data with factors varied over multiple/differing levels?  Thanks for any feedback you may provide.

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    #85853

    Mikel
    Member

    If you have prior knowledge that these factors are significant and that the levels are legit – run the 3 x 4 (12 unique treatment combination) experiment.

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    #85875

    Brad M.
    Participant

    Stan,
    Thanks for the reply.  What specific DoE design would you recommend?

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    #86680

    J Andell
    Participant

    If the two factors are continuously variable in nature, you might want to consider either a simple 2-level factorial, or a response surface design (central composite may be the best for a 2-factor, but there can be reasons to favor others). If the factor levels are basically fixed (such as with categorical data, or with fixed commercial formulations), then a 3×4 full factor experiment is called for.

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    #86681

    Mike Nellis
    Participant

    Hello Brad M.,
    Run the factors at the level combinations below and record your response(s) after each run.  Generate your summar data, charts, and graphs.  Re-run the test to confirm any conclusions you made from the first experiments.
    Hope this helps.
    -Mike 
             A  B  Response

    2  1  .003 (example)
    1  2
    2  2
    1  1
    3  1
    1  4
    1  3
    3  3
    2  4
    2  3
    3  2
    3  4
     
     

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    #86687

    Ljubomir Lazic
    Participant

    First of all you should tel us a priory knowledge about outcome?
    If Second order model of outcome is satisfactory then you should apply CENTRAL COMPOSITE ROTATABLE DESIGNS (CCRD) for k=2 with 5 replica at NULL factor level, which design plan is:

    TABLE 2.147 CCRD

     

    Design of experiment
    matrix

    No of
    exper.

    X1 (factor
    level)

    X2 (factor
    level)

    1

    +

    +

    2

    +

    3

    +

    4

    5

    -1,414

    0

    6

    +1,414

    0

    7

    0

    -1,414

    8

    0

    +1,414

    9

    0

    0

    10

    0

    0

    11

    0

    0

    12

    0

    0

    13

    0

    0

     

     

     
     
    So yu should have 13 experiments in order to get second order regression model for outcam with high confidence. The question is :
    – ar you restricted with number of experiment ( time, expenses etc.)?
    if answer is no then I propose CENTRAL COMPOSITE ROTATABLE DESIGNS (CCRD) for k=2 with 5 replica at NULL factor level.

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    #86688

    rams
    Participant

    Maybe this is an alternative:
    If in case you are not really sure if there are quadratic effects, then try a 2×2 using the low and high levels of your factors.
    Check for lack of fit or validate runs on the midpoints to check for curvature.
    If no significant curvature, then the experiment is OK.
    Else, augment the design to form a central composite design (face-centered).
    This is assuming your factors are continuous.
     

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    #86699

    N
    Participant

    Brad,
    I used a General Full Factorial DOE in Minitab for a 2 x 2 x 2 x 3.  This should work for what you have too.

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    #86719

    jediblackbelt
    Participant

    Have you looked at a balanced ANOVA?  I have done this in the past has a multistep style experiment.  Some of the other replies are better off though.  I especially like the one where you run a design with a curvature check.
     

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    #86730

    Som
    Member

    I suggest you run a full factorial experiment with 2 replicates, since you have only two factors – if you have resource constrain you can live with one replicate as with 12 data points you are left with 9 df to estimate your error.

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