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Modifying the Experimental Design After Experiment

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  • #55478

    J.P.
    Participant

    Hello everybody,

    I’m using response surface design (Box-Behnken) to figure out how print paramerers (4) affect the printing resolution. The design had 54 runs alltogether and these were separated into six blocks. After doing the experiment I noticed that there is extra variation in one of the factors (the print height) depending on the block. However, I was able to measure how much this extra variation is for each specific block.

    So my question is, can i correct the factor ‘print height’ using the measured values and re-analyze the design? Or will this ‘corrupt’ the design because one factor takes more values than was specified in the original design (instead of three different values of print height it would have 3*6=18 values)?

    If somebody could help me out with this, it would be really awesome.

    Best regards,
    J.P.

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    #200135

    Chris Seider
    Participant

    I suspect you went straight to a RSD (response surface design) instead of using a basic factorial analysis.

    This finding if yours may show why many of us don’t say rush into a RSD.

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    #200136

    Robert Butler
    Participant

    I suppose you could take the view that one factor has more than three levels or you could also take the view that for the one factor, the ability to control the low, medium, and high levels was something less than your ability to control for the other three variables.

    If you have the ability to at least run VIF’s (Variance Inflation Factors) you should do the following:

    Take the idealized design with the levels expressed as -1’s, 0’s, and 1’s and then take the design you have actually run and, for the 4th factor do the following:

    1. Identify the overall minimum and maximum value for the 4th variable across all of the blocks.
    2. Compute the following:
    A1 = (Max Value + Min Value)/2
    A2 = (Max Value – Min Value)/2
    3. For each actual value of the 4th variable compute the following:
    Adjusted 4th = (Actual Value – A1)/A2
    This will scale the 4th value to a -1 to 1 range but it will involve more than three levels.

    Run a VIF analysis on the idealized matrix and then do the same on the actual matrix and look at the VIF terms for each of the 4 factors. The VIF’s for the idealized will tell you what you should have had and the VIF’s for the actual will tell you what you do have. If none of the VIF’s are greater than 10 then the variables in your matrix will still have exhibited sufficient independence from one another to permit their inclusion in a multivariable analysis.

    If you don’t have this capability – put your planned matrix of the X’s (no need for actual names and no need for any Y response values) and your actual matrix of the X’s in an Excel spread sheet and post it on this forum. I’ll take a look at it and let you know where you stand.

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    #200139

    J.P.
    Participant

    Hi,

    @ Chris Seider: Tell me about it! Next time I’m sure to do a proper parameter screening before running a full rsd. This is what happens when you assume too much and know too little…

    @ Robert Budler: Thanks for the advice! I now calculated the VIF using regression analysis (as explained in http://blog.minitab.com/blog/starting-out-with-statistical-software/what-in-the-world-is-a-vif). I used the other factors as predictors (levels expressed as -1, 0, 1) and adjusted print height as response (also normalized between -1 and 1). According to the returned R-sq value (O%), i then calculated that VIF=1. The planned matrix gave me also VIF=1. Can it be this low in both cases? Or have I made mistake somewhere? I’ve attached the planned and actual matrix as excel file. A-C are the “other” factors and D the print height. Thanks again!

    Best regards,
    J.P.

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    #200140

    J.P.
    Participant

    *Butler

    Now that I think about it, it’s really obvious that the VIF for the planned design should be 1. But how about the actual design, shouldn’t it gain some multicollinearity when one of the factors is chosen (almost) randomly? Just wondering.

    Best regards,
    J.P.

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    #200141

    Robert Butler
    Participant

    I checked both of the designs and the VIF’s for the various terms are well below 10. The term-by-term assessment is in the attachment. As you can see, not all of the terms have a VIF = 1. I also checked the condition indices. They too should be less than 10 and they are. What is interesting is that, in this case, the imprecision associated with the assignment of values to D actually results in smaller VIF’s for the squared terms and a smaller condition index for the overall design (these differences are numeric only and are of no concern).

    To your question concerning VIF’s = 1 for a planned design – it depends. If you are using one of the standard designs – factorial, composite, Box-Behnken, Plackett-Burman, then for most of the variables in those designs the VIF’s will be 1. If you are running a computer generated design such as a D-Optimal then very often the VIF’s will not be equal to 1 for any of the terms in the model.

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    #200142

    Chris Seider
    Participant

    @laurila6

    It’s always important to learn from our experiences. I’m still learning even thought I’ve been doing some of this quite a while….new things to tackle and learn always pop up.

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    #200143

    J.P.
    Participant

    All’s well that ends well. Thanks for the help!

    Br,
    J.P.

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    #200144

    J.P.
    Participant

    @rbutler

    Hi again,

    I’m getting different VIF values in the minitab DoE analysis depending on if I use the normalized factor levels or the actual values (screen captures as attachment). Is this normal? There must be some reasonable explanation for this, but i just cant see it…

    Br,
    J.P.

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    #200145

    Robert Butler
    Participant

    That is correct – VIF and the eignevalue/condition index, like regression analysis, are sensitive to magnitude differences in the variables. That’s why you run the test and you should run the regression with the variables scaled from -1 to 1 – it puts everyone on a level playing field.

    As far as regression is concerned this issue is somewhat alleviated by the double precision methods employed in most regression packages but even that aspect will not cover all cases and you will have situations where term significance in the regression is driven by magnitude instead of correlation significance.

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