# DOE Discrete output

Six Sigma – iSixSigma Forums Old Forums General DOE Discrete output

Viewing 17 posts - 1 through 17 (of 17 total)
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• #33005

Sorour
Participant

We’re improving a component of our product, and we are struggling in Prototype and test. The problem is that the issue have as output a discrete value: Ok-No Ok, Black or White (with no greys between) and there are no way to trasform it in a continuous value, and no useful Measurement System available in the world.
Test and regression are good, but take time and money, and there’s no way to control the interaction of the factors, as in DOE. Do you know a DOE approach or similar for this issue, with Y=discrete? Book reference? (in English or Italian as preference).

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#88725

raf
Participant

I think there’s no problem using a discrete output for DOE except that you will need a lot of samples for each run.  As a rule of thumb, you have to get an average of 5 good and 5 bad parts for each run to invoke Normality of data.
Hope this helps

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#88726

Participant

Paul,
I may be incorrect here, but if I recall, there are proper ways to transform this type of attribute data.  As mentioned, you will need a larger sample size.
What you can do is run a count of defects or a proportion of defects.  As you mentioned, you may need to transform the data.  Be sure to check your residuals.  If the proportion or the count do not work, try a couple of the basic transformations.  If the residuals still look bad, do a Freeman-Tukey transformation.  The formula for proportion data is:
ASIN(SQRT((p/(n+1))))+ASIN(SQRT((p+1)/(n+1)))
(You can copy and paste this into minitab, with p being the column containing the proportion of defects and n being the sample size.)
There is also a Freeman-Tukey transformation for count data.  I have not found it on the web and I am not going to rely on my memory from 3 years ago (when I went through black belt training).
Good luck!

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#88728

Michael Schlueter
Participant

Good hint, Paul.
Another name for this transformation is “omega transformation”, which is closely related to the “logit-transformation”.
Perhaps this is self-evident, but: make sure to use radians, not degrees for ASIN.
Best regards, Michael Schlueter

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#88729

Michael Schlueter
Participant

Hi Paul,
Peculiar situation; can you give us some more details? Sometimes there are ways to replace difficult and costly measurements by more effective ones. But this depends on your specific situation.
Best regards, Michael Schlueter

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#88730

Sorour
Participant

Hi, thanks to all.
Unfortunately it’s not possible to enter in the details, but it’s a defect of the product, of course…, and the problem or there’s in or no. A good idea seems to be use the percentage of scrap, but if you consider the number of prototype needed for each trial to have @ least 5 Ok & 5 Nok or more… it’s a big number! ;-)

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#88731

Michael Schlueter
Participant

Thanks, Paul.
Are you saying you have a process with extraordinary ppm-values (big number required) ?

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#88732

Sorour
Participant

Partially Yes, but not only.
Example: if you have 5% of scrap, and you have more than 5 factors. Because you’ll use the % of scrap, you need for every run 100 prototype for have only 1 output for that considered configuration. Even with a fractional design you need at the end hundreds prototype!

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#88742

faceman
Participant

Paul,
If you can get a copy of D.C. Montgomery’s Design and Analysis of Experiments, 5th Ed. you will find that chapter 14 gives you some good options for this type of experiment.
Good Luck!!!!

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#88748

Participant

Dear paul
I can share with you the application of DOE for dsicrete output, If you can give me your email Id. My email Id is: [email protected]

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#88964

Kim Niles
Participant

Dear Paul:
FYI, I’ve experienced your type of situation many times before and have found that almost all of the time, the best thing to do is to work on the response.  It’s rare to have a situation where only discrete output can be used.  Theres almost always some form of variable that could be used, either by focusing in more on the output itself (i.e. finer measures), thinking outside of the box with regard to tabulating the output (i.e. percentages), or through correlation with some other form of variable output (i.e. end use temperature).  Think about it, if you were all seeing, you could probably find a million differences between OK and NG (no good) parts.  On the molecular level they must be very different to varying degrees.  They likely affect or could be found to affect something else to varying degrees.  There must be different ways to look at the big response measurement picture.
Think why is it good or bad?  Perhaps something else such as end use temperature or color correlates well to the discrete good / bad?  Perhaps percentages of good / bad in a sample can be used?  Perhaps you can focus in on how good or how bad good or bad really is?
Good luck either way.
KN –   https://www.isixsigma.com/library/bio/kniles.asp

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#88970

Manee
Participant

Paul
You can use Taguchi’s orthogonal arrays to reduce number of experiments and use ordered categorical analysis for discrete response.  A good book is by Phadke
Manee

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#88975

Milg
Participant

Good day!
You can easily transform discrete data through Freeman-Tukey Transformation by using Calculator of Minitab. For more details on this topic please refer Answers Database of Minitab. ID # 277. I’ve used this already on one of my DOE study. My response was binomial (proportions). Here are the steps: You must have one column for the number of trials (n) and one for the number of successes (x). For example, your number of trials are in C1, your number of successes in C2, your transformed data stored in C3.
1. Choose Calc > Calculator
2. In Store result in variable, enter C3
3. In expression, enter FTP(C1,C2)
4. Click OK
The FTP command is the Freeman-Tukey Transformation function created by Minitab to transform binomial data (proportions).
If response is in counts, FTC function will be used. You must have one column for the counts which must contain nonnegative integers. For example, your counts are in C4, and your transformed data in C5. Follow these steps:
1. Choose Calc > Calculator
2. In store result in variable, enter C5.
3. In expression, enter FTC(C4)
4. Click OK
I hope this will help.

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#88981

Participant

Milg,
Yes!  Thank you.  That is most helpful.
One question:  How did you find this?
After reading your post, I checked and did not find these functions listed in the Minitab calculator.  Freeman-Tukey was not listed in the help function, but by typing “FTC” & “FTP”, help told me what they did.  Did you simply find them on the website?
I was really surprised, because when I went through BB training, we were taught about F-T transformations.  The MBB told us to save the formulas in word and copy and paste into the calculator for use.  He must have been unaware of these functions as well, or perhaps they are new with 13.32.
Just curious.
Once again, thank you very much for the information.

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#89030

Participant

Dear Mr.Paul
Just see waht Dr.Kniles has suggested. it is right. when an item is not OK, it must be due to some reason or observed dimension or attribute of qulity characteristic which has not conformed.This will give you lot of information and clues as how to get a desired solution. I would like to share with you by sending a case study with all details if you can give me  your Email ID.
yours

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#89182

Milg
Participant

Sorry for taking so long to answer your question. I happened to find the two functions of Minitab when I conducted a DOE study myself where my response was a proportion. I know that if the response is a proportion, then it would violate the DOE assumptions of Homogeneity of Variance. I was not taught about the Freeman-Tukey transformation during my BB training here in Cebu. So I look at the Minitab webpage and I happened to browse the Answers Database of Minitab. I also asked Minitab about this through e-mail and they gave me an article by Soreen Bisgaard regarding this transformation. Also minitab had instructed me to do the same. So all my information comes from Minitab.
Milg,

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#89206

Dr. Scott
Participant

Paul,
Your solution lies in the mix of what raf and kniles said. Run enough opportunities in each treatmentment combination to expect > 5 defects on average.
Or, better still, identify the dimensions of quality that the product might fail on, develop continuous measures for these qualities, then use this as your Ys in the DOE.
Disregard the suggestions for data transformations. This is more often than not a faulty approach. Too many Six Sigma people rely on transformations, but in the end it does not work.

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