topic Cp/Cpk for attributes in Discussions

Cp/Cpk for attributes

LambdaCapybara4 — Wed, 28 Aug 2024 09:11:31 GMT

How do I calculate Cp/Cpk or Pp/Ppk for attribute data using JMP?

Re: Cp/Cpk for attributes

Byron_JMP — Wed, 28 Aug 2024 17:11:13 GMT

So, that's a sticky wicket my JMPy friend.

You'll need to somehow take pass/fail data and convert it into something continuous, or better yet, get the underlying continuous data for making the pass fail decision.

Often we use attribute control charts (U, P, C, P', U') for attribute data to track the proportions of pass/fail over time.

The sticky part is that process capability depends on calculating a "sigma" (overall/long-term or within/short-term) and comparing the number of "sigma's" to the distance between the mean and the nearest spec limit. ... and it kind of assumes things are generally "normal".

Attribute data has a binomial distribution, so we can still get control limits for plotting data in an attributes chart, but process capability, no so much.

In this example I have boxes of 10 units (n trials=10) and a random assortment of pass/fail for each box

Re: Cp/Cpk for attributes

LambdaCapybara4 — Wed, 28 Aug 2024 17:31:08 GMT

Hello,

Thanks a lot!
can we keep on discussing that, pls?

There is a sample data file called "Braces" (under Samples\Data\Quality Control) and there are data of # defects with varying sample sizes. If we have some spec limit, just for example, say up to 25 defects the unit is "pass", then why can't we simply calculate the capability indices using Process Capability option under Distribution platform, where LSL=target=0 and USL=25...?
and say it's a non-parametric distribution....

am I mixing a lot of stuff here?

Re: Cp/Cpk for attributes

LambdaCapybara4 — Wed, 28 Aug 2024 17:33:03 GMT

correction - find a proportion (#of defects/unit size) and then spec limits for the proportion

Re: Cp/Cpk for attributes

Byron_JMP — Wed, 28 Aug 2024 18:02:35 GMT

Restating the question just a little:

Since I don't have your data...

suppose I have a table with 100 rows and this formula in one column:

Abs( Round( Random Normal( 10, 10 ), 1 ) )

This data represents the percent defective things per lot/batch/wafer whatever. And it has an upper specification limit of 25.

My data might look like this.

I could fit an Weibul or Gamma or Exponential distribution to the data.

Then from that fitted distribution I could get a process capability report.

Its important to note that we aren't looking a capability of an attribute anymore, but a variable, which is percent defects.

It might still be a really good idea to run a P, C, or U chart along with this data.

Re: Cp/Cpk for attributes

statman — Wed, 28 Aug 2024 21:23:44 GMT

Pardon my editorial, and please ignore me if it upsets you, but Capability on defects/defectives is non-sensical. Why would you put a spec on the number of defectives/defects? It is OK to have defectives and defects? What is the purpose of such a capability metric? What is an acceptable capability metric? How do you assess consistency before you calculate capability? Do you want to be consistently bad? Don't you want to figure out what is causing the defects rather than report a capability metric?

Byron is spot on. First you need to realize there is a difference between defectives and defects. For defectives, you are limited to the number of samples. They are categorized according to pass/fail (binomially distributed). For defects, there is no limit to the number of defects per sample. This is count data (poissonly distributed). Byron's first idea is to use a continuous measure instead of a categorical/discrete metric. What is the defect? Can it be measured? For example, a visual scratch...can the length, depth, area of the scratch be measured? Or why is it failing (go/no-go)? The dimension doesn't meet the spec. Then measure the actual dimension.

The estimates of "sigma" for defectives (p-charts):

And for defects (c-charts):

would assume those value (p and c) are constant, which is definitely not what you want. You want them to begetting smaller.