# General multi level DOE (AAAARRRGGHHHHHH!!)

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• #29665

Lee Yates
Participant

Can anyone help?? I am trying to set up a DOE containing 2 factors, each factor having 6 levels. Using Power and Sample size, as I should, in Minitab does not give me an option for this (only 2 level or Placket-Burman designs). Has anyone come across this issue before, or any ideas how to get around it. Please help I do not want to compromise my proffesional integrity, but I am rapidly running out of hair!!

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#76460

Robert Butler
Participant

Two factors at 6 levels will be a 6**2 experiment for a total of 36 experiments.  I’m not aware of any package that will do this for you.  The easiest way to set this up is to take a piece of graph paper and simply plot out the 36 points that would be part of the 6×6 matrix.  Before doing any of this however, I would recommend asking some hard questions concerning the need for 6 levels.  In  the vast majority of cases this is definitely overkill.  The operating philosophy behind DOE is that if change is going to be observed it will best be seen by contrasting extremes-hence the focus on 2 and 3 level designs.
If your circumstances are such that you will not be premitted to consider less than 6 levels per factor, I’d recommend arguing for a 3 level “screening” design over the same region.  This would give you a 9 point design and with a couple of replicates you would have 11 experiments which would permit a check of all interactions and all linear and curvilinear effects.  It is true that with such a design only the corner points would correspond exactly to points from a 6 level design but I’d have a hard time believing that the small difference between the other points of a three level design and those of a 6 level design would make that much difference. Thus, if there was still some doubt you could use the 3 level design as a starting point and then fill in other areas of the design with points from the 6 level design.  Since you could use your regression equation to predict the responses at the levels of the 6 factor design. the additional design points would act as confirmation runs for the findings from your initial effort.

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#76464

mcleod
Member

Robert,
It is 2^6 not 6^2.  Therefore, he will have 64 experiments and not 36 as you had stated.  Otherwise, I agree with your assessment.

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#76465

mcleod
Member

Robert,
Forgive me.  My head is not on straight (a Monday morning thing).  You are right, it is 36 experiments, not the 64 I just suggested.
Scott

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#76550

Marz
Participant

Assuming the variables are continuous, have you considered doing a Central Composite Design.
This would require maybe 10 to 12 experiments depending how many centre point replicates you do.
Mintab can do your general full factorial at 6 levels for you.

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#76551

Steve Wang
Member

Tell me how many runs you can afford—-I will send you and DOE matrix. I have a software that can generate DOE matrix with any number of levels. It is called LHS.

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#169123

Cone
Participant

Lee, I am in the same situation – I have an 8 factor, 3 level DOE that I am trying to do – – -I can’t see how to do it in Minitab either – – -help!!

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#169129

Van Loon
Participant

WOW – more than 6000 experiments……….
Stat>DOE>Factorial>Create>General>No. factors>Designs>No. levels
Are you sure you are not going to make som fractional or screening,this is a big (expensive) experiment.
Jan

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#169131

Robert Butler
Participant

I don’t know Minitab but given its reputation I would assume that it would have capabilities for fractional factorials and composite designs as well as various choices for optimal.
If you were to take a 1/16th of a 2**8 and add the 2*8 star points and two reps on the center you would have a very conservative composite design with a fractional factorial for the center.  This would be a total of 34 experiments and it would buy you information on all of your main effects and all of their curvilinear behavior.  If you were to try building this from scratch using one of the optimal routines you could cut the number of experiments down to something in the neighborhood of 20.
Your approach is asking for a design that will check all mains, all curvilinear, all two,three,four,five,six,seven, and eight way interactions, as well as all possible two,three,four, five, six, and seven way interactions between all linear and all curvilinear terms.  Somewhere in your Minitab instructions there has to be a way to tell the program that you are only interested in linear and curvilinear effects.  Once you have that command I’m sure the program will give you a design similar to what I’ve outlined above.  If you can’t find the command it is easy enough to build the fractionated composite design just by using a pencil and some paper.
The principal block is
(I), bcgh, aegh, abce, dfgh, cbdf, adef, abcdefgh, abdg, acdh, bdeh, cdeg, abfh, acfg, befg, and cefh.
Tack on the 16 stars for each of the 8 variables, add two center points at 0,0,0,0,0,0,0,0 and you are there.

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#169137

DaveS
Participant

Robert,
Minitab allows you to input your own generator. Im have never had to do this in practice. If I have a need for optimal designs or something not in Minitab, I use Design Expert
But, I wonder why in the world 6 and 8 level designs are even being contemplated. Some years ago I worked in a fiber optic fab facility. On some new product designs the designers (mostly PhD level physicists) wanted five and six levels  DOE. They believed that the responses were  theoretically complicated quartic and above curves.
We did quite nicely with highly fractionated 2 level designs with center points, followed by response surface measurements.
In general, even if the physics and engineering says the response are higher order curves, over the range of actual use, they tend to be adequately modeled by at most third order equations. This I believe is the difference between theory and practice.

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#169145

Taylor
Participant

Lee
You should be able to perform some screening DOE’s within the levels which will allow you to decrease the number of levels with the final design, if not

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#169146

HF Chris
Participant

Why not use SAS or SPSS? Both can run this volume of data. HF Chris

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#169147

roy e.
Member

As other have noted in this thread I do not think the real concern is about the number of data point, but about the need for a 6 level experiment. I agree on revisiting the logic behind the 6 levels to attempt simplifying to 2 or 3.

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#169148

HF Vallee
Participant

Many have suggested reducing levels but none of us know what he is measuring.  Are six levels per factor that hard to measure…. depends on the study.  Are six levels needed… depends on the study. Could there be an interaction missing if one level is not understood… yes.  The question was how to analyze this project with software.
Why do we reduce studies in size? Money? Time? Quick payback? How often do we miss the mark if we had just dug a little deeper.  Don’t get me wrong because a believe in the process but also find many limiting factors in it.  I see reports of .88 r2 and alpha of .05 but then see how the data can be biased and misconstrued, reporting findings not capable unless you have controlled many variables. In many cases an r2 of .68 is great when reached.  Just a little perspective often missed.
HF Chris

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#169175

Taylor
Participant

HF Chris
Agree with you totally, but the reason many folks fail in DOE  is because they are simply not willing to do the initial leg work first. I have been involved in some pretty incredible DOE’s, one in particular involving castings and trying to eliminate porosity, as you can imagine the number of levels of control are many. Anytime, and I just find it easier to prove statistically, you have more than 4 levels within your factors you need to perform screening DOE to prove that the significance is worthy of the final DOE, Obviously range of levels will dictate but with closed in levels of factors I find it rarely necessary to include.  Once significance of High, Middle, & Low have been determined then a focus on the most significant range can be given. Understandibly cost dictates these issues, and simply may not be feasible, and this puts even more stress on the planning of such large DOE’s which may run into months of preparation.

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#169176

HF Chris
Participant

The problem with prescreening is also the same problem with cause and effect root cause analysis, you have to truly understand the system. For example, I worked with composites and adhesives where humidity and temperature interaction is critical. If you did an a priori study with the wrong combination this could be a disaster when introduced as the right thing to do in production. I also agree with you that people fail in DOE because they do not due their homework. The key is to identify the critical measurements that effect their process…. but this can turn out to be the chicken or the egg question, what do you need to know first.HF Chris

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