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

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jackma246

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

So if quadratic model does not fit, there is no way for me to choose between logarithmic or exponential except by hand? And by hand, how would I have a logarithmic function with four factors?
 
J

jackma246

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

I don't think I totally understand how to calculate the regression for a model like this. Can you walk me through step by step with an example? I attached the data for one of the "easier" cases. Thanks so much!

What I did so far was a 1/2 factorial model, and then I replicated 5 times, with 3 or 4 center points. After that, I put in all the data results. Following that, I don't know how to calculate a model correctly that can accurately predict the data.
 

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  • Results - SRAM_cell_6devices.txt
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B

Barbara B

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

Before calculating the model I would recommend some data preparation:
  1. Coding of numeric input factors (Data > Code > Numeric to Numeric), so the levels will be converted to -1 (low level), 0 (medium level), 1 (high level).
  2. Check the response "Frequency" if really all values are free of measurement errors. There are 5 values above 1.0e-06 (up to 1.77e-04) which are much higher than the rest (below 1.0e-07, see attached Summary for Frequency). (Modelling will only work properly if the response values are reliable.)
  3. Multiply response values (e.g. with 10^8) to get most/all of the entries in a column above 0.1. (This will stabilize the results and provide easier analysis, because Excel and Minitab will only use the first 16 decimal places due to internal restrictions and the number of decimal places within Minitab's session window is limited.)

I don't think I totally understand how to calculate the regression for a model like this. Can you walk me through step by step with an example? I attached the data for one of the "easier" cases. Thanks so much!

What I did so far was a 1/2 factorial model, and then I replicated 5 times, with 3 or 4 center points. After that, I put in all the data results. Following that, I don't know how to calculate a model correctly that can accurately predict the data.

Since you mentioned transformation of the response (which actually helps improving the model for your data) the easiest way to get a model would be the "General Regression" menu in Minitab:
Stat > Regression > General Regression
Response: Frequency
Model: Model 'Volt_c' 'Temp_c' 'CI_c' 'RI_c' Model* 'Volt_c' Model* 'Temp_c' Model* 'CI_c' Model* 'RI_c' 'Volt_c'* 'Temp_c' 'Volt_c'* 'CI_c' 'Volt_c'* 'RI_c' 'Temp_c'* 'CI_c' 'Temp_c'* 'RI_c' 'CI_c'* 'RI_c' 'Volt_c'* 'Volt_c' 'Temp_c'* 'Temp_c' 'CI_c'* 'CI_c' 'RI_c'* 'RI_c'
Categorical predictors (optional): Model

> Box-Cox: Check "Box-Cox power transformation (W=Y**Lambda)"
[Either with default "use optimal lambda" or if you want to use the natural logarithm with "Lambda = 0 (ln)"]
> OK

> Graphs: Choose "Four in One"
> OK
> OK

  • 'Volt_c', 'Temp_c', 'CI_c' and 'RI_c' are the coded input factors (see above).
  • color scheme for the terms in the model:
    • blue: main effects
    • sienna: 2-way interactions
    • dark orchid: quadratic effects (only for the numeric factors)

In case you get stuck in the analysis it would be easier for us to help if you can attach the Minitab-project itself instead of the data. (Put it in a zip-archive first, because *.mpj-files aren't permitted as attachments.)
 

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  • Summary for Frequency.png
    Summary for Frequency.png
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Miner

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

Please verify the correctness of the attached observations. These observations are so extreme that they cannot be modelled.
 

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  • Unusual Observations.jpg
    Unusual Observations.jpg
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J

jackma246

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

You're right, sorry, something's wrong with those factors - I was told to just ignore them and leave them out of the model. However, I am unable at this time to get a value for these rows.
 
J

jackma246

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

Also, the problem with that is there are too many interactions and not enough degrees of freedom, I think. There are too many factors
 
B

Barbara B

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

You're right, sorry, something's wrong with those factors - I was told to just ignore them and leave them out of the model. However, I am unable at this time to get a value for these rows.
It's okay to copy the whole data of the column "Frequency" (this would be named automatically "Frequency_1") and simply type a "*" into a cell if an observation is suspicious. The use of the brushing function could be a tremendous help, e.g. if you pick those points out of a time series plot.

Also, the problem with that is there are too many interactions and not enough degrees of freedom, I think. There are too many factors
I don't know what model you wanted to get out of the data, but if you're using main effects, 2-way interactions and quadratic terms for your 5 factors, you'll have to "pay"
  • 4 df for Model
  • 1 df for each numeric main effect (4 df total)
  • 4 df for each combination of Model with a numeric factor (4*4 = 16 df total)
  • 1 df for each of the 6 numeric 2-way interactions (e.g. Volt*Temp, Volt*CI, etc.) (6 df total)
  • 1 df for each quadratic effect of the numeric factors (4 df total)
All in all you need 4 + 4 + 16 + 6 + 4 = 34 df to estimate all main effects, all 2-way interactions and all quadratic interactions. 1 df is used for the calculation of the overall mean. For this model 35 df are necessary.

You've got 405 values = 405 df. If you exclude the 6 extreme values (see Miners posting) there are 405-6 = 399 df left. This is far more than you need and there are 365 df left for the error term.
 
J

jackma246

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

I have calculated all 405 datapoints in order to verify the model but I am trying to use as little corners as possible in order to do so! I want to know how many corners I have to use to get an accurate model (which I will compare to the points that I have calculated), and then in the future, I will not have to calculate as many points.
 
B

Barbara B

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

I have calculated all 405 datapoints in order to verify the model but I am trying to use as little corners as possible in order to do so! I want to know how many corners I have to use to get an accurate model (which I will compare to the points that I have calculated), and then in the future, I will not have to calculate as many points.

The number of datapoints depends on the aim of the analysis.
  • If you solely want to fit a model, you need 36 datapoints (see above).
  • If you want to fit a good model (orthogonality, minimal prediction variation, etc.) and you want to
    • estimate main effects and 2-way interactions you need a 2-level factorial design for the 4 numeric factors (e.g. 2^(4-1) with resolution IV: 8 runs) with addtitional centerpoints (3-5 CP recommended), so there are 8+4 = 12 runs for each model-type necessary. For 5 model-types this leads to 5*12 = 60 datapoints total.
    • estimate main effects, 2-way interactions and quadratic effects you need a central composite design with 31 runs for each model-type (or 27 for a Box Behnken design). All in all you have to get 31*5 = 155 datapoints for a CCD (or 27*5 = 135 for a BBD).
 
J

jackma246

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

I got an R^2 value of 100%, but R^2(pred) and R^2(adj) both have *%. What does this mean?
 
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