# Short Run - Low Volume Cpk Calculation

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#### tohbin

Cpk Calculation

We report Cpk monthly for our process. In order to report the Cpk, we must have at least 25 data points on the chart (say Xbar-R chart). But sometimes volume in certain month is so low that we won't be able to get 25 points on the chart. Is it right to calculate Cpk even though my data point is less than 25 or should I get previous month data with the current month in order to make it 25?

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#### Atul Khandekar

Process Capability calculation is an ongoing thing. If you decide to calculate on the basis of 25 points, at any given point of time, you can take the last 25 points.

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#### tohbin

But if I use the last 25 points which may include points from previous month in the case when I do not have enough points in the present month, would that be reflective of my current month Cpk? Or because it is an ongoing calculation, it doesn't matter as long as I have 25 points?

But then comes the question if I have more than 25 points in the current month, I won't have problem with Cpk calculation. Then, the previous month data will not be included. Isn't this in contrast to the practice above?

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#### Atul Khandekar

I do not know what is the reason for reporting Cpk on a 'monthly' basis. What are the chances that you will have exactly 25 subgroups/points in a month? Sometimes you will have less and sometimes more than 25. In my opinion, Cpk should be calculated over a 'horizon' that is independent of calendar days. In your case, the horizon would be last 25 points. With every new subgroup added, you calculate the Cpk based on the last 25 points. This way you will be able to monitor the improvement ( or deterioration) in your Cpk.

Do you calculate new control limits every month?

-Atul

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#### tohbin

No, I don't calculate control limits every month. The reason for calculating Cpk every month is for the purpose of monitoring the improvement of the process month by month.

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#### David Mullins

tohbin,
you haven't told us your calc method.
I'm always dubious of how people use x&R charts to calculate other things.
Even computer programs use different calc methods, and these often aren't aligned with the calc method endorsed by the auto manufacturers.

CPK calc methods inlcude:

(1-k)xCp
or
Cp = (USL - LSL)/6xStd.Dev
Cpl = (Mean - LSL)/3xStd.dev
Cpu = (USL-Mean)/3xStd.dev
Cpk = Min(Cpl,Cpu)
or
Cpk is calculated using RBar/d2 or SBar/c4 for Sigma in the denominator of you equation. This calculation for Sigma REQUIRES the process to be in a state of statistical control. If not in control, your calculation of Sigma (and hence Cpk) is useless - it is only valid when in-control.

What are you using?

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#### tohbin

I'm using the following method.
Cpl = (Mean - LSL)/3xStd.dev
Cpu = (USL-Mean)/3xStd.dev
Cpk = Min(Cpl,Cpu)

Has this got anything to do with data points less than 25 in a month?

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#### Sam

Tohbin,
I had the same problem at a previous company I worked for. Sometimes it would take 3 months to get a sample size of 25.
The method I used was to:
1- Select ten parts from the run,
2- measure the specified dim.,
3- if the average ,+/- the range of the ten parts was within specification I would accept the parts,
4- if not, 100% inspect the lot back to the last point that the parts were accepted.

This metod was acceptable to our auditors and to our big 3 customers.
You might also find this method in the Juran Handbook.

If what you want is to report Cpk, then report the figures that you have with the way the process is run. If you haven't run for a mth, then report the same figures as the previous month.
Remember Cpk is on-going over time for processes that are in control. For it to be an efective method of reporting, the data should be gathered from a continous running lot.

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#### Al Dyer

Sam,

If it took 3 months to get the 25 piece sample how often do you ship that product?

How could you get the numbers?

Was it a line dedicated to making 100 parts/year?

If not did you set up a capability study every time you set up the line?

Somethings not making sense here??

More help with the details Sam?

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#### Sam

"If it took 3 months to get the 25 piece sample how often do you ship that product?
I was referring to the 25 subgroups of 5 parts each.

How could you get the numbers?
1- When you have reached the 25 sugroups you can report Cpk, from that point on you can report Cpk even if you only add one subgroup at a time, however, if there are three/four weeks between entries then it won't give you that warm fuzzy for the process right now, So;
2- Select the ten parts,measure and accept the lot if the avg. +/- range is within drawing spec.

Was it a line dedicated to making 100 parts/year?

No - 600 different parts, from a few hundred per year to 10000 per year.

If not did you set up a capability study every time you set up the line?
No, just report Cpk. A complete would be done at the completion of each 25 subgroups.