# Oddities of Cpk - Chicken parts

V

#### vasilist

First of all i want to give a lot of thanks to : Marc, Rick Goodson and Dave Strouse for their help in my previous thread.

Let's get to work now :

one of our suppliers in chicken propably doesn't cut inside our specification limits. So i made 18 control charts measuring the weight of chicken parts (1 control chart was made in his facilities, the rest 17 in stores during a week).

Finally i saw in control charts what's happening. Not propably but surely now i know he doesn't follow our specifications. 10 control charts out of 18 were in non-conformance ( i hope i use the right words). Playing with the table of results i found the Cpk for every chart and put it in descending order.

The usual was to expect that the control charts (with conformance) with the higher Cpk would appear first. But in the 7th position there was a control chart which had non-conformance and its Cpk was 0.2987. The next two control charts were in conformance and the next 9 were out of specs. How can that be?

This is the table :

Sample Cpk Conformance

agg18 0,5855 ok
agg5 0,4608 ok
agg13 0,4304 ok
agg7 0,3910 ok
agg14 0,3587 ok
agg4 0,3505 ok
agg2 0,2987 NOT OK <--------------------
agg10 0,2697 ok
agg8 0,2453 ok
agg17 0,2067 not ok
agg6 0,0997 not ok
agg12 0,0869 not ok
agg15 0,0583 not ok
agg1 -0,0222 not ok
agg11 -0,0449 not ok
agg3 -0,1188 not ok
agg16 -0,1318 not ok
agg9 -0,1922 not ok

I hope i was clear and that i used the correct words but in any case anybody wants more details i will be more than happy to give.

M

#### M Greenaway

How do you define 'conformance' and 'non-conformance' in your above example ?

When you say the seventh chart had non-conformance what do you mean ?

V

#### vasilist

With the term non-conformance i mean points out of the specification limits.

I understood that the process is not capable of meeting the requirements of specifications let alone that is not under statistical control.

But that thing with Cpk is totally strange to me as my knowledge in statistics are not so high.

R

#### Ravi Khare

Control Charts

I assume you are plotting Shewhart control charts. (Xbar -R...types).

Control Limits of Control Charts are calculated from the data itself, and often have nothing to do with the Specification Limits.

Quality Parameters like Cpk are calculated on the basis of Specification Limits, and not Control Limits. If the process is not centered within the Specification Limits, you will have Control Chart perfectly under Control but a low Cpk.

A Control Chart under Control merely indicates stability of the process centre and process spread, over a period of time; and not whether it is producing within specifications.

The Cpk is Calculated considering the distribution of the data within the Specification Limits. Even if all the sample data points are within specifications, the process may have a potential to produce out of specifications when run longer. This potential is captured by Cpk.

D

#### Darius

Vasilist, I tink you are mixing SPC Control charts with Capability index, of course they are together, but Control Charts show patterns in the data to look for special causes, so take they off and stabilizate the process (quality). Capability index in other hand show how good you are with the specs (non conformances).

I extracted a paragraph from the 1rst post.

>The usual was to expect that the control charts (with conformance) with the higher Cpk would appear first. But in the 7th position there was a control chart which had non-conformance and its Cpk was 0.2987. The next two control charts were in conformance and the next 9 were out of specs. How can that be?

I recommend you to read the article.

https://www.qualitydigest.com/may00/html/lastword.html

I tink is what you need, it's about the confidence limits for the capability index, so it says that a cpk of 0.2 and a cpk =1.33 could be equal (statistically speaking of course). Your cpk could be the same even when they show a gross difference (deppending on the sample size).

:thedeal:

D

#### DonkeyKong

CPk question

I have a question concerning a CPk issue....I have issue with a print/product that has a min/max tolerance; but no mean. The issue follows: Max USL .434 & LSL .432. No mean is stated or target value.....my co-workers state that I need to perform a tolerance capability study?....I have never heard of such a thing, but my stats might be/is rusty....I just computed the data with .433 being the mean......

The reported data I have is all @ .432 so there is no way of reaching a CPk of 1.00 or better....

Please let me know if you have ever heard of such a thing as Tolerance Limit Capability Study (or if there is some computation that you would utilize to figure out the target value to perform the standard capability study; other than mean)

DK

R

#### Ravi Khare

In case of two sided Limits, both USL & LSL being present, it pays to center the process betwen the two. So you will have the target at 0.433.

From the results that you have obtained ( all 0.432s), it looks like your measurement system does not have adequate discrimination to capture the process variation. If you use a measurement system that has a finer resolution than you now have, you will be able to measure the readings into more number of categories. Statistical Analysis will then be possible.

If you are getting all 0.432s it is likely that your process already has a good capability potential. Once you measure with a higher resolution, and then shift the center of the process to 0.433, you should arrive at a good Cpk.

As for a specific answer to your question; Tolerance Limit Capability study is the study that compares the process variation and centering with externally imposed tolerance limits.

S

#### Spaceman Spiff

DonkeyKong, I wouldn't use the center as Ravi suggested... just yet. I would evaluate whether the process will drift with time, such as stamping parts. The part will only get bigger as the die wears. In that case I would target the nominal to be somewhere near the maximum material condition of the die (or the smallest tolerance of the part). However, if you are cutting something to size, then I would do as Ravi suggested by setting the nominal at the center of the specification limits. :thedeal:

Good luck!

A

#### Al Dyer

capability

Numbers and ratings are the base for what we do. CPk is what it is and only viable with a stable process. I've seen processes with a CPk of 5+ but they are not even within the spec limits.

That is why there needs to be more than 1 capability index.

We have CPk
We Have CP
We Have PPM
We have P-Charts

I could go on forever but I think you get the gist of what I am posting.

Al...

B

#### Bill Ryan - 2007

I've seen processes with a CPk of 5+ but they are not even within the spec limits.

Al

Can you give an example of a process with a Cpk of 5+ that is not within the spec. limits. Maybe it's too early in the morning for me, but I don't see how that is possible. I can see a Cp of 5+ with a Cpk of -5 (everything out of spec.) but the Cpk value is based on the spec. limits.

(I know I'll come to, soon!!!)

Bill