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DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor having 5

J

jackma246

#1
Hi all,

I have an experiment set up for a DOE analysis with 5 factors, with 4 factors having 3 levels, and 1 factor having 5 levels.

The 1 factor having 5 levels cannot be made smaller, each of the 5 levels is a different model of a card we are testing and it is not numerical.

The other 4 can be made into 2 levels, as they are numerical and evenly spaced.

Also, the experiment is not hard to run, it is simulated on a computer - I can run about 400 cases within an hour. However, the point of this is to try to find a way to run as little tests as possible and to achieve a model that can accurately predict the result.

What sort of analysis should I use? Factorial? Taguchi?

Thanks! I am very inexperienced in DOE and Minitab.
 
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Miner

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#2
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

I recommend against the Taguchi approach. I have a LOT of DOE experience, and actually started my DOE career using Taguchi. I like the intent of using it to reduce variability, but have found better ways using classical methods.

Since you must use five levels of the one factor, you should use the General Factorial model in Minitab. Normally, I would recommend a 2^k fractional factorial with center points to begin with, but you appear to need to run different levels not to assess curvature, but to evaluate different models.
 
J

jackma246

#3
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

I'm really new to the Minitab software - How would I begin to use the General Factorial Model for the factor with 5 levels?
 

Miner

Forum Moderator
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#4
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

In the menu go to: Stat > DOE > Factorial > Create Factorial Design, then select
General Full Factorial, Number of factor = 5. Select Designs, enter the number of levels for each factor and the specific levels.
 
J

jackma246

#5
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

Doesn't General Full Factorial require all of the cases to be done? What I mean is, every single possible combination is fulfilled?
 

Miner

Forum Moderator
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#6
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

Yes, it does. What about creating a 2^4 fractional factorial with center points and replicating that across the 5 models?

If you can provide more information about the factors, levels and response(s), we could probably provide more relevant advice.
 
J

jackma246

#7
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

That was my first approach, but my boss wants one model with different intercepts for each model, instead of a different model for each different model.

The experiment in detail:

There are 5 different model cards, TT, FF, SS, FS, SF. We are measuring Voltage, Temperature, Resistance, and Conductance. The response variable is the frequency that the model will output.
 

Miner

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#8
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

Okay, well we can do that. Just have to fool Minitab.

  1. Create a 2^4 fractional factorial with 5 replicates. Do not randomize, or the next step will be very difficult.
  2. Create a new column in the worksheet called model, and enter the designation of the first model for the first replicate, the designation of the second model for the second replicate and so on.
  3. Then use the Define Custom Design feature to force Minitab to recognize this design. Include the new column in the custom design.
 
J

jackma246

#9
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

Thanks! Can this help me find the linear regression then? :)
 
B

Barbara B

#10
Re: DOE Analysis Experiment, 5 factors, 4 factors having 3 levels, and 1 factor havin

Okay, well we can do that. Just have to fool Minitab.
That would be my suggestion, too.
  • Create a 2^4 fractional factorial with 5 replicates. Do not randomize, or the next step will be very difficult.
After the design alteration the runs for each model should be randomized. This could be done using "Modify Design"
Stat > DoE > [NOT Factorial, Modify Design is available for all kind of plans!] Modify Design
Choose "Randomize Design"
> Specify [to randomize only within the models] > Columns not to reorder
Enter the name of the column which contains the models.
> OK > OK

In addition I would recommend 3-5 center points for each replicate to be able to test for curvature later on.
  • Create a new column in the worksheet called model, and enter the designation of the first model for the first replicate, the designation of the second model for the second replicate and so on.
You could also choose 5 blocks. Then each of the 5 replicates will be done within a block. The blocks could be renamed using the model names in the worksheet (TT, FF, SS, FS, SF) after the plan is created. (This would avoid manual randomisation.)

  • Then use the Define Custom Design feature to force Minitab to recognize this design. Include the new column in the custom design.
At this point it gets a little bit tough. There are several options how a factor with 5 levels could be used in the doe:
  • If you use the model column as a block variable (with an arbitrary number of models), you could compare the models (test for differences between blocks). But this design won't be able to test for interactions between blocks and input factors (Voltage, Temperature, Resistance, and Conductance).
  • If you try to define the model column as another input factor in the 2-level factorial design you'll get an error message "Text factors must have exactly two levels." 2-level-factorial design do have 2 levels for each input factor (and sometimes a third middle one for center points of numeric factors).
    But the corner points do only have two levels low and high. Therefore you can't use a model factor with 5 levels as an input factor in a 2-level factorial design.
  • You could define this 2^4-design plus model column as a general factorial design with 5 input factors. But this will handle all factors as text variables. In the end you could test whether different levels lead to different responses (e.g. different temperature levels cause a significant shift in the response), but you won't get a regression model with numeric factors (e.g. if temperature increases about 1°C, response decreases about 0.3). And you won't be able to test for curvature.
    This is no Minitab specialty but the approach described by Montgomery (Design and Analysis of Experiments) which is also used in DesignExpert. The reason for this slightly unexpected handling of input variables is the aim of a general factorial experiment: These are used for screening purposes only so the only goal of a general factorial is to answer the question "Are there differences in the response due to different factor level?" and not "How could the differences in the response be quantified?"

The regression equation isn't written directly in the session window but could be put together if the coefficients of the model are stored:
Stat > DoE > Factorial > Storage > Check "Coefficients"

Barbara
 
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