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DoE – Main Effects and 2F-Interactions in Screenings

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  • #243711

    osmio
    Participant

    Hello,

    I have a general question about a DoE problem. In the software I am using right now I can choose between screening and characterization (and optimization of course). It is well known that screening is for many factors and to determine the most important ones. In the software the difference between them is basically less runs + a linear model for screening and more runs + e.g. a 2FI model for characterization (this is a special case with numeric and categorical factors for which I should use a optimal custom design).

    Here is the issue I am dealing with right now. This is a hypothetical question and no real life example:

    A) Assume I do a DoE with Factors A-F. I do a screening with only few runs and a linear model. I find that A,B,C are most significant, D may or may not be, and E,F are not significant. Due to the linear model I have no information about interaction like AB. So I select A,B,C, maybe D, and start a RSM.

    B) Assume I do the same DoE but with more runs and a 2FI model. I find that A,B,AF,BD, B,C are most significant, D may or may not be, and E,F are not significant. So I select A,B,C, also D and F due to the interaction, and start a RSM.

    I hope you will see the issue I can’t grasp fully: For screening I have read that you are interested in the main effects only and to reduce the factors. However, is it possible that an interaction between a high signifikant and a medium/low significant factor (AD/AF) can be itself high significant? In that case you would dismiss D or F and lose important factors? Is there a way how you can deal with this, or maybe is this not possible at all?

    Thank you very much!

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    #243712

    Robert Butler
    Participant

    I’m not trying to be mean spirited or snarky but it’s called “experimental” design and not “infallible” design for a reason.  :-) Seriously, this is a standard problem and one every engineer/scientist/MD faces.  Your choices of variables to examine are, of necessity, based on what you know or think you know about a process and the number of experiments you run are usually determined by factors such as time/money/effort required.

    The approach I use when building designs for my engineers/scientists/MD’s etc. is to first spend time looking over what data they might have (this is usually a sit down meeting) with respect to the issue at hand and discuss not only what we can see from plots and simple univariate analysis of the data but also what they, as professionals, think might need addressing.

    In the majority of cases the final first design I build for them will be a modified screen with enough runs added to allow for a check for specific two-way interactions their experience suggests might be present.  In addition, if they think one or more of the variables might result in curvilinear behavior I’ll make sure to include enough design points to check that as well.

    Oh yes, one additional item – from time-to-time someone (or a group of someone’s) will have in mind an experiment that they are just positive is really the answer to the problem.  Usually these “sure-fire” experiments are few in number (the sure-fire counts  of 1 and 2 are quite popular) so if they fall inside the variable matrix I will add them to the list of experiments to be run as well (and if they don’t fall inside then my first question is: Why haven’t we extended the ranges of the variables of interest to make sure we have covered the region of the sure-fire experiments?).

    As for building a modified screen of this type my usual procedure is to use D-optimal methods to identify the experimental runs.  What you need to do is build a full matrix for all mains, two-way, and curvilinear effects, force the machine to accept a highly fractionated design for the mains, and then tell the machine to augment this design with the minimum number of points needed for the specific two-way and curvilinear effects of interest.  After you have this design then you can toss in the sure-fire points (if they exist) and you will be ready to start experimenting.

    • This reply was modified 1 week ago by Robert Butler. Reason: typo
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    #243716

    osmio
    Participant

    Thank you very much for the reply and for sharing your experience! As a beginner, this helped me to understand some aspects a lot better. To use only specific interactions is of course a good idea, I was also playing around with this. I just came around this hypothetical issue I have written above and was hoping someone will come and say: “Of course it is well known (from mathematics /  statistics) that a very insignificant factor will never produce a significant interaction, so you can easily remove it for further study!” :-)

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    #243809

    Robert Butler
    Participant

    In re-reading your comments it occurred to me there is an often overlooked but critical aspect to the issue of variable assessment using the methods of experimental design which should be mentioned.

    In my experience, the worry that one might miss an important interaction when making choices concerning experiments to be included in a design is very often countered by the kind of people for whom the design was run. You should remember, for the most part, the people you are working with are the best your company/organization could get their hands on and they are very good at what they do.  When you give people of this caliber designed data you are presenting them with the following:

    1. Because the data is design data they are guaranteed correlations between the variables and the outcomes actually reflect correlations which are independent of one another.  This means they do not have to worry about the inter-correlation relationships between the independent variables because they do not exist.

    2. Because the data is design data they do not have to worry about some hidden/lurking/unknown variable showing up in the guise of one of the variables that were included in the study (you did randomize the runs – right?).

    3. Because the data is design data if a variable does not exhibit a significant correlation with an outcome they are guaranteed, for the the range of the variable examined, the odds of that variable mattering are very low.

    Given the above, and the insight these people have with respect to whatever process is under consideration, what you have is a variation on the saying about card playing – “a peek is as good as a trump.”  In other words the results of the analysis of this kind of data coupled with the knowledge your people bring to the table will very often make up for any shortcomings that were, of necessity, built into the original design.

    What this means is if there is an interaction that was overlooked in the design construction their prior knowledge, coupled with design data will often result in the discovery of the untested interaction.  This kind of a finding will usually occur during the discussion of the design analysis when the results of the analysis get paired with their knowledge about process performance.  If and when this happens it has been often been the case that I was able to take the original design matrix and augment the runs with a couple of additional experiments. These experiments, when added to what was already run, allowed an investigation of the original terms along with an investigation of the “overlooked” interaction.

    Note: If you run an augmentation to an existing design you will want to include one or two design points from the original as a check to make sure things haven’t changed substantially since the time of the initial design run.

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