# Doubt in DOE

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• #30207

RC
Participant

Hello to all:
Somebody could help me, I am performing a design of experiments, but I have a doubt, the study is to minimize the length or the size of a weld, it is a design 2³, it is to say are 8 experiments, but with some of the parametros the weld cannot be made, thus cannot be measured. could somebody help me to know that value I must put for these cases?
thanks in advance for your help

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#78448

Opey
Participant

Well RC, you’ve learned a valuable lesson the hard way.  A mis-estimation like this can completely invalidate a designed experiment…what you’re left with is either redoing the experiment with realistic factor settings, or making guesses as to what those unrealistic points would have been, had you been able to make a measurement.  Obviously, this latter option is trouble.  (If you’re just going to guess what the factors do, why do a designed experiment in the first place?)
Something you could try, if your 3 factors account for 95%+ of the variation, is to identify the factor that is limiting you, along with the setting.  (If factor B is limiting you, at its high setting, for example…)  Trim the setting closer to its partner, and you’ll just be rerunning 4 points.  Again, this is best if your 3 factors account for 95%+ of the variation.  Otherwise (if it’s only 80% or lower, or so), it’s probably better to rerun the whole experiment – making sure that each point is practicable.
Hope this helped,
Opey

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#78449

Robert Butler
Participant

There are a number of things you could do.  If we assume that you have not yet run the design and that your problem is that of looking at the proposed combinations and realizing that one or more cannot be run because, as you said, a weld cannot be made, then you can do any of the following:
1. Change the high and low limits of one or more of the parameters so that the resulting design can be run.
Possible problem with this-The ranges become so narrow that the region of interest is not the region you wish to investigate.
2. Choose a RANGE of low values and a RANGE of high values for each of the variables in your design.  Take ONLY those design points that cannot be run and check to see if by substituting a different low or high value in for one or more of the variables in that particular combination you can convert the design point into something that can be run.
Possible problem with this- your design will no longer be perfectly orthogonal.  In many cases this is more of a theoretical concern than anything else-most designs when they are actually run will not be perfectly orthogonal.  In order to check for trouble make up a dummy response to the resulting design and run it and check the values for the variance inflation factors and also for any ill conditioning warnings that your particular package may issue.  If the design checks out, set it up and run it.
3. Find a degreed statistician and have him/her build you a restricted design using one of the many optimality criteria (A,G,D etc.)  There are a number of packages on the market that will do this for you but unless you know how to check the resulting design and how to trick the package into doing what you want instead of what it thinks you want you can go wrong with great assurance.
If  we assume that you have already run the design then your question becomes one of analysis.  For those cases where the horses died just indicate missing data.  Run the full model through you statistics package.  If it is any good it will come back and tell you that one or more of the terms in your model cannot be estimated.  Drop these terms from the initial model and submit the reduced model for consideration.  Keep doing this until you get a series of terms that can be examined.
For a 2^3 design the dead horses will probably translate into the inability to estimate one or more of the interaction terms. The power of factorial designs is that they are robust-they can really take a beating and still deliver main effect estimates.

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#78450

aush
Participant

RC
Did you try to fit in factorial design . Your experiment is a full factorial .It may be posible that a factorial design may just fit in.

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#78453

RC
Participant

The experiment already was made, but with limited results, but now I’m going run it again with the advice that you have given me.Thank you very much for your help

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#78505

Carl H
Participant

1.  Try a fractional factorial (4 runs) design avinding the “bad” settings in the four runs.  If you can only afford 8 total runs, make 2 replicates.  This can give you info on main effects and potentially some on an interaction (with planning).
or
2.  You may want to consider using a simplex optimization method of testing.  Although this method is typically used for optimizing or “hill climbing” response surfaces, it also could be applied to your testing.
Basically, you setup an initial simplex by picking four test points or vertices.  Set them to be the four adjacent “cube points” of a 2^3 full factorial design and not include the 1 or more points which gave you bad data inteh first DOE.  After you test these first 4 points (vertices), you “determine” which one gave the “worst” response to the “best” response.  You project away from the worst vertex “through” the other 3 “better” ones.  This gives you the next (5th) vertex to test.  From there, you follow “simplex rules” to progress to 6-8th or more vertexes to test.  If one of the vertices is a “bad”place to run (from DOE #1 info), then treat it a s the worst and the simplex will move away from this reguion.  Eventually you “spiral or hover” around a vertex which consistantly give the best response.  This may be where your optimum settings are.
Pros to this approcah are that you can avoid “bad” settings, potentially find and optimum and possibly even get some main and interaction effects with some accuracy.
Cons to this method is that data is not orthogonal, you may require more runs/replicates to counter measurement noise.
The book Sequential Simplex Optimization by Walters et all is a good reference.  Some software suppliers on the WEB for this.
Good Luck,
Carl

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#78567

Dixit
Member

In your screening experiment, what are the 3 factors and how many of them are independent?  I can be of more help if you can share this info.  Also for the response you are trying to measure (length of weld), what are the units?

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#78607

Eoin
Participant

Try 0.

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#78608

Robert Butler
Participant

I wouldn’t recommend substituting 0 for missing values in a design.  If you do this you will drastically alter the model resulting from the analysis.  To check this take the simple 2^3 design below and just assign as a response the numbers 1-8  and build the model. Next set the values 2 and 6 to missing. Your regression diagnostics on the reduced set will show that you cannot estimate the effect of the v1xv2 interaction.  Put all of the other main and two way interactions back in the model expression and, using backward elimination, run the model again. Finally, substitute “0” for those points that you set to missing and run the model the third time.
v1 v2 v3    resp1   resp2   resp3
-1  -1  -1       1           1          1
1  -1  -1       2           –           0
-1  1  -1        3           3          3
1  1  -1        4           4          4
-1 -1  1         5          5           5
1 -1  1         6          –            0
-1  1  1         7          7           7
1  1  1         8          8            8
For the first response v1 v2 v3 v1xv2 v1xv3 and v2xv3 are all significant when running a backward elimination with a selection of .1.  In the second case the v1xv2 interaction cannot be estimated but all others can (zero df for error of course) and the coeffieicnts for the remaining terms are the same as those in the first case.  In the last case, all of the terms except v2 and v3 are eliminated because inserting “0” for missing has altered the “measured” responses of the experiments.

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#78609

RC
Participant

vijay The 3 parameters are distance, preassure and voltage.
How many of them are independent? I don’t know I’m traying to find it.
and the length of the weld is in milimeters
Thanks for your help.

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#78613

Robert Butler
Participant

RC,
What Vijay is asking for is your design matrix with some indication as to which experiments gave a result and which did not. Since I wrote out the complete 2^3 matrix in my second post just indicate which of the eight experiments actually gave you some kind of measureable result.  For example, if 1,2,4,6,7 had measureable results just list them in this order.  Armed with that information we can tell you what you can and cannot estimate with the results from your first experimental effort.

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