DOE with Attribute Response Data

I would read chapter 14 of DC Montgomery's Design and Analysis of Experiments 5th ed.

you can look at the supplemental text here;

http://www.wiley.com/college/engin/montgomery316490/wave_s.html

choose chapter 14 the take the'Supplemental Text" link.

You can use GLM with a logoistic link.  That works pretty well.

You can transform your data.  Mintitab has a function available in its calculator called Transform proportion.  Here is what it does in case you don't have minitab.

(arcsin(sqrt(np/(n+1))) + arcsin(sqrt((np+1)/(n+1)))/2

I have used it and it didn't normalize as well as I would have liked, but the reidual error was much more homogenous and 'fairly' normal.

You could also use binomial logistic regression to explore any happenstance data that you might have lying around.  It works pretty well even when you can't fix factor levels (like in happenstance data).

Good luck - binomial y's can be a real pain in the neck, but they are fun.

I completed a similar weld schedule optimization project in 1997.  Is your team sure they can not use a variable response?  Are you performing an xray or helium leak test the weld? The only way I can think of that would dictate using attribute data in your case is if the inspection is purely visual inspection.

Belinda,

I don't know anything about laser welding or hermetically sealed stuff.  But, if you do like Tom says and find a continuous response you will be able to have smaller samples sizes and much useable info after your experiment.  If you can change your response to continuous, ignore what I said and do what Tom says.  Don't do the transformations or use GLM unless you really have to.

All,

As suggested the best way is to see if the response can be converted to continuous. However if it cannot be you can still use a technique called Discriminant analysis where the response is discrete and the variables are continuous. I have done a project on seam less steel tube lot rejection very much like the weld issue. I am not sure if there are books available but I used a computer software to feed in all the input variables and the out put response.

The input Xs were - temparature of preheat, walk in temparatue, dwell time (all continuous) and response as Good or Bad lot for scale formation. I got a model where the significant X's were validated and set for a optimum value. We achieved ZERO lot rejection.

If you are lucky you might want to try for a write up or a book on Discriminant analysis.

regards

jagdish

Belinda,

I would recommend the strategy of using some sort of a test to get continuous data for your results. For example, you could use some sort of a pull test value (tensile stress). This would then enable you to use the regression equation to give you the best results for your settings.

I have found that using continuous data instead of attribute data gives the best results in a DOE, that is sustainable also.

KP

Belinda,

You can carry out a DOE when the response is only attribute. You need not to convert/transform the data to continuous. I have used this technique to analyse an experiment with good/bad data. This will help you to find optimum settings on hermetically sealed laser weld.

DS

Dear Belinda

Yes it is possible to use the DOE technique with attribute response data. The data gathered can be converted to % accepatance.First based on DOE plan one needs to conduct experiments and collect the data as pass or fail in each experimental paln. After completeing the experiemnts, the pass data can be converted to % pass out of total tested in each experiemental paln.Record the % pass against plan and calculte the coefficients for each variable. if relation ship between variables and response is a linear  simulation the model with steepest acent/descent method to find the parameters that maximizes the pass percentage. I am sure you will be able to get solution quickly.If you can give me your mail Id I can post you a similar case study which has used this DOE techinque with attributed data. If any further information required may be addressed to bhadra40yahoo.com  

yours

K.Bhadrayya

Belinda,

You need not to convert the data into %, and you con use the figures you get as number of pass and fail. I had used this technique without any problem.

DS

What if you just coded your response variables? For example, code a good part = 1 and a bad part = 2. Would this work as good as converting the responses into a %? I am curious to hear everyone's feedback on this.

Try this approach to analyzing your DOE with attributes data:

• Analyze the experiment calculating the Effects using the Sum+, Sum - technique.    (The effect is the difference the average of the + recipes minus the average of the minus recipes for each column in the design)
• Once you get the effects, you can make a pareto chart of the effects.
• Now you need to calculate the UCL to see what was significant.
• Use this formula:   +/- t * square root of pbar ( 1-pbar)* 4/N where t = 1.96, pbar is the grand average of the experiment and N is teh total number of experimental units in your DOE
• If that doesn't work for you, other options might include redeclaring insignificant bars on the pareto chart as dummies and using those columns to assist with the UCL or collapsing on the design.

Hope that helps.

Belinda;

I don't see a problem with using attribute data to a conduct a designed experiment.  For a class that I took in Experimental Design, one of my projects was to determine the best microwave popcorn, and combination of factors that resulted in fewest unpopped kernels.  I counted the number of unpopped kernels in microwave popcorn as the efffect.  Factors were brand type, cooking time and cooking level - all at two levels.  Obviously, number of unpopped corn kernels is attribute data.  The kernels either popped or did not - pass/fail.  If you are interested in learning more - contact me at user364313aol.com.

TC Trible

Normally, hermetic-weld can be measured by leak teat (pressure drop / helium leak test) as Tom comment. Anyway if you aren't available of those equipments (High invesment if you're looking for helium leak test). Some method can be apply;

1. Try to make cross section of the weld jointed, comepare between good and rejected part. Some porosity or not completed can be define as ratio by all wled area. The attribute will become to variable. If weld joint too small, may be nedd some magnifier / chemical etching.

2. Same as number 1. but use destructive as pull test.

3. Just  a few experienced, for hermetic-weld and the leak level is too small ( 10^-3 - 10^-6 atm.bar/sec ). The welding parameter may be effect at the big leak (>10^-1 atm.bar/sec ). The most effects at small leak are contamination, atmosheric control (Oxigen protection) and material cleanliness.

If you would like to share please feel free to contact; tpheunghhotmail.com

We have done DOE for Laser welding process too. Welding is done wtih shielding gas, Argon. Helium is used in leak test, pass or fail. In some case re-welding works but not always, so single joint is better. Helium tester gives numeric data, but we have also visually inspected joints and traslated attribute data to numeric. Questions about our parameters and observations, can be addressed to: aapi_67yahoo.com

Belinda,

It is desirable to have a measurable output whenever we r performing a DOE. I had faced the same preblem when i was doing one of my DOE. But then i got success when i transformed the results into variable numbers.

If u cannot measure u cant improve that is it.

In ur case y dont u have a dye penetrant test (NDT) after the welding & then count the number of cracks observed (DPMO).

Let me know about the future developments.

cheers,

Imran Baig

Belinda- I liked faceman888's response, using "transform proportion."  In our blackbelt wave, we learned that you can use the "rate" of failure as a continuous normal response, provided that p is not close to 0 or 1, because the normal distrubution becomes bounded. This leaves you unprepared to conduct analysis on low rate defects. (Because p is very close to 0.)

 I have created 2 different hypotheical models in Minitab using the "transform proportion."  ( p (fail) = .00012, p(fail = .006) , and I can see the imediate benefits of using the function which is an increased normality of the residuals, despite a very low defect rate.

I will be conducting an attribute response DOE in the next few weeks. I'm curious to learn about any obstacles that you or other users have experienced using the "transform proportion' function.

Thanks- Mainebear

Belinda,

Hi,

I believe that quality of your welds can be evaluated not only to get "Pass/Fail" or "Sealed/ Not sealed". In the future you require or design quantitative measurements.

For now I would select a DOE plan ( a DOE matrix )and perform experiments with several replications. It looks the morereplications, the better . Then my response ( output ) variable data would be the number of Passed.  It is expected Failed are close to 0. This is just a suggestion, it is not based on a theory.

Jane Raevska

DS:

  But how should we determine the sample size for each experiment?

tks!

Yes there is a way.  You set up the design matrix just as you would with variable data.  At each trial in the design matrix, collect enough specimens to give you some failures (if you're baseline is 2/10, then gather at least 20 specimens at each trial so that you actually have some data) Then transform each trial's data using the Freeman - Tukey transformation .  Analyze the transformed data as you would variable data.

Hi Nic!

    Do we have some fomular to calculate the specimens  for each trail? I think 20 specimens  for the experment which baseline is 2/10 is too small, it may not distingish te difference.

Tks!

Much belated, but if you are still interested, then the answer is:

1. Yes, you do need a special design for this case. Many of the suggestions written here may result in a highly inefficient experiment.

2. You can find all the answers you are looking for at: http://www.math.tau.ac.il/~dms/GLM_Design

Dear Melinda,

I've read your question about DOE for attribute data. You mentioned hermetically sealed laser weld. Now I have simmilar problem - soldering chips on flexible cables (soldered good/wrong). We also want to find the optimum settings for soldering machine. If you read this, could you please give me some informations how were you solving this problem? Thanks a lot.

Miroslav

Dear Miroslav,

Did you solve your problem with soldering chips ? We have a problem with the new soldering oven. DOE can help to find the best adjustment but we have an attribute response and we are not sure how to continue.

I'd like to know if some of you got a good answer for this problem.
I have to compare several leak detection methods (vacuum, pressure, hydrogen and heluim) and establish the most influencial factors, the response variable is pass/fail type. I would appreciate your suggestions (we are using a DOE).
Thanks 

Mutiple Sujective Evaluation can help convert Attribute responses into continuous so that you can do a DOE. The downside is can take a slightly longer time to perform, but will certainly allow you to use the result in a DOE to help you tweak the dials you want to improve your process.