Process Capability for Discrete Data

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• #33541

Griffiths
Participant

If you have discrete data, can you run process capability?  If so, what is the best tool to use?  Can you provide examples?

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#90888

JENNIFER
Participant

Brett,
Yes, you can perform capability studies for discrete data- Binomial or Poisson in nature.  Minitab 14 will do this for you.  Binomial for discrete data where the number of defective items out of the total number inspected is available- and Poisson for discrete data that is associated with the number of defects observed in/on an item.
-Jennifer

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#90902

Doc
Participant

Also, a common question from newbies is “How do I calculate Cp, Cpk, … for discrete data?”
The answer to that question is . . . you don’t.
Don’t make the same mistake many make and try to somehow treat discrete data as if it were normally distributed. It isn’t. Instead, focus on the appropriate proportions, counts, rates, etc . . .
The most often used metric is PPM defective, regardless of the type of data. You’ll see that in all of the Minitab capability outputs, regardless of the data type. I would assume other similar software (JMP, StatGraphics, Statistica, etc…) does the same thing, but don’t know that.
You can, if desired, convert the PPM into a Sigma Level. This web site has tools for that if you look around for them.

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#90978

Statman
Member

Why would a sigma level be any more valid than a Cp of Cpk?
Aren’t they measuring the same thing?

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#91645

Philip Whateley
Participant

Cp and Cpk attempt to define a PREDICTION of the probability of any one item being conforming or non-conforming. ALL attributes data is related to the history of a PROCESS. Therefore the application of capability to attributes data is invalid. (e.g. does it make sense to talk of the probability of an item being 95% conforming?)
It is clearly also invalid to back calculate a “Z-score” from ppm defective etc. as this is based on the assumption of a normal distribution generating the non-conformities.
Also, even for variables data, conversions between Cp, Cpk and expected defectives should be used with extreme caution. because: (1) the ralationship is for the limiting case of an EXACTLY normal distribution. In reality, a normal distribution never exists in nature, ESPECIALLY out to the tails. ANY relationship between Cp/Cpk and PPM can be seriously in error once you go beyond 1.5 to 2.0 sigma away from the mean. As you will also never have enough data to prove you have a normal distribution out to the tails, the raltionship between capability and ppm will be no better than your assumption as to what distribution you have.

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#91652

Eileen
Participant

Brett,
You can determine an estimate for the % defective. This is the same as defining capability for continuous data (Cp and Cpk).
If you have a p-chart to establish process control, the best estimate for capability is 1-(p-bar) (converted to %). For example, if you have a p-bar of .035 from the control chart, then the process capability is 1-.035=.975 or 97.5% is your process capability.
Another strategy was based on various sampling plans with a certain level of defectives. A good rule of thumb was to run 350 parts. If no defects were found then the capability was assumed to be “acceptable”. If you use this strategy, you need to define what you believe is the appropriate capability, and then develop the appropriate sampling. Of course, this says nothing about the stability of the process and should be viewed as only a preliminary capability assessment.
Eileen

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#91790

Statman
Member

Phillip,

Thank you for your response to my post.  I think you have done a great job of explaining my concern that either Cpk or the sigma metric are valid representations of attribute data capability.  You have made me think about some very good points that others should think about when they are attempting to compare process performance across variable and attribute CTQs.

Since Cpk and Sigma level with variables data attempt to define a prediction of the probability of any one item being conforming or non-conforming, can a non-conformance be weighted on the same magnitude of loss to the customer as an actual defect?  This could only be true if the specification limit clearly delineated between pass/fail which can never be the case since any deviation from the target will represent some loss.  There is a big difference between assessing the ability of a process to meet spec and chance that it will create a defect.
With both attribute and continuous data we use historical data to develop a metric for process performance.  But when we calculate a sigma value from the historical data the process to arrive at the sigma value has a transposition depending on the data type (data-distribution parameter-sigma value-defect for variables and defect-distribution parameter-sigma value for attribute). In other words, we are using a reference distribution to predict a defect level with variables data and a defect level to predict a reference distribution with attribute.  Is it a reversible process in terms of relative meaning of the metric?
Does sigma in terms of a Z-Score have any logical meaning when applied to attribute data?  First, as you stated, we cant assume that a normal distribution is generating the defect, and secondly, the dispersion in distributions for discrete parameters are correlated to the mean value of the distribution.
As you also stated, small deviations from normality will cause an exponentially higher degree of error in estimation the further you go out into the tails.  So when you are comparing the actual count of defects to a normal distribution estimate of defects, you have one parameter with a much higher risk in error in estimation.

All else being equal, Im going to stick with PPM for attribute and Cpk/Ppk for variables.

Regards,

Statman

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#91797

Philip Whateley
Participant

In terms of your comments regarding capability in general, I would suggest you read Don Wheeler’s excellent book “Beyond Capability Confusion” from the SPC Press.
I think that you are right. The best measure of capability for attributes data is a count of the defective items. This may also be true for variables data if there is any evidence of process instability (including the somewhat spurious 1,5 sigma shift) I would recommend that, in addition to Cp and Cpk you always present a histogram of the variables data (I have known processes with Cpk of 0,8 which generated zero defective because of the shape of the distribution)
Phil

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#91799

Participant

Just check the source of the discrete data in terms of whether this count data is independant of each other. Next see the frequency at which these data arrive which would give the indication whether u can use control charts for discrete data in terms of n, np, p and u charts which would indicate the natural boundries and the capability trend in either count or in terms of percentages. By knowing the variance ie standard deviation we will be able to find the Z in terms of the area at which it is residing and the same can be used to find the   Process Capability from the charts or by means of specification wrt Tolerence. If it is a dependant data then one need to essentially understand the R value using the coefficient of regression and then decide on how one can break the data and attribute to the behaviour of the other variable. Hope u all found my comments useful.

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#91803

Mikel
Member

Capability indices and z scores and DPMO are just three ways of saying exactly the same thing. Just more hype trying to convince execs that we have something bigger and better.
Kinda of like an Italian food joint calling grits polenta.

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#91804

Mikel
Member

Jennifer,
Even though I know you are one of the brightest people doing this job – you Minitab folks shouldn’t come on here hyping your products. In the sense of fair play, you might point out that JMP will also do this as well as your not just released, thousands of copies out there, 13.3 version.
Cheers.

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#91883

JENNIFER
Participant

Stan,
Brett requested a tool and Minitab is one solution.  Minitab 14 is the current release that is available for purchase.  The product sells itself, no need for hype.  If Brett already has version 13, he could certainly use it.  By the way, SAS/JMP 5.1 (the latest release) does not perform capability studies for discrete data.
-Jennifer

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#91884

Statman
Member

The software is not doing capability analysis with discrete data? They can do a control chart can’t they?  You can’t count the number of defects? But minitab can count number of defects?
This is the silliest thing I have ever heard.  Why do you need a software package to count number of defects?

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#91886

JENNIFER
Participant

To clarify: calculate process z for binomial data, and summarize poisson.with more than just a control chart.  JMP does not currently do it- certainly you could even use Excel for counting and creating control charts.

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#91892

Statman
Member

And  excel can quite easily calculate process Z.
You should read some of the discussions on the forum about the appropriateness of Z as a metric for discrete data.  You will find that there is not a general acceptance of the practice.
Statman

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#91903

Spiderman
Member

Statman,
Can you elaborate…on the Z score concerning discrete process capability.  What are the issues or disagreements?

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#91905

Statman
Member

Hi Spiderman,Read the posts in this string by myself and Phillip Whateley and read through the posts in the string called “short term sigma long term DPMO”.  Particullarly the posts by Gabriel.  Also, check out Gabriel’s spreadsheet simulation that I eluded to in my last post.Regards,Statman

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#91914

Spiderman
Member

Thanks Statman,
Good stuff…..you just verified that what I am doing is okay….variable-normal-stable-CPK……..variable-non-normal-discrete-PPM
Thanks…..(good stuff you guys wrote!!)

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#91923

Mikel
Member

My mistake on the JMP capabilities. I clearly don’t know JMP as I don’t have a need to use it.
I got confused – I meant to say that we could do this easily in Excel if we wanted to.
Jennifer, don’t get me wrong. I want you on here contributing, you are one of the brightest, most articulate persons I have met in this sport. It is just a no no to promote products or services and if I let it slide with you, I would have to let it slide with RS and MC and Dr. Tony and others.

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#93824

Anand
Participant

i need mini tab process capability guide

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#93838

sathu
Member

Anand,
You cannot use Process capability excercise for Discrete datas.
Plus tell me your data type …& look whether is there any possibility of converting into continous one….Then think about going for Process capability. Use control charts like p,np,u & C charts for discrete data( find out whether it is defect/defective & Same subgroup or Different one)

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