# Calculating Cpk when sample size equals to 1

M

#### M.Yung

Hi all.

I have been given the task of compiling documentation required for a PPAP submission. One of these documents require me to calculate the Cpk of the process involved. However, only 1 product can be made per every 8 minutes. I could be wrong, but this leads me to believe that my sample size would be 1 (n=1)

From my understanding, I believe I need to take least 2 samples at same time in order to calculate the Cpk (e.g. 5 samples at time 10:30pm).

How would I go about calculating the Cpk for this?

In addition, there are three Specification Limits that need measuring. Does this mean that 3Cpk's are needed?

Cheers

#### Bev D

##### Heretical Statistician
Super Moderator
yes you need a cpk value for each specification (characteristic)

Cpk can be calculated with n=1 as long as you have multiple samples of n=1.

There is also nothing preventing you from take n=3 or n=5 sequential parts (time between parts doesn't matter)

The key is that Cpk is for an extended period of time not a small period of time. So a daily Cpk or a Cpk for every lot is not valuable (nor is it what a PPAP is looking for)

M

#### M.Yung

Cpk can be calculated with n=1 as long as you have multiple samples of n=1.

There is also nothing preventing you from take n=3 or n=5 sequential parts (time between parts doesn't matter)

So I'm just imagining the scenario in my head...I would take 1 part at 10:08, another part at 10:16, and another part at 10:24. Would this make the sample size 3 (n=3) if I was combine them together?

Cheers

#### Bev D

##### Heretical Statistician
Super Moderator
yes that is correct

M

#### M.Yung

Awesome, thanks a lot Bev!

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#### Darius

So I'm just imagining the scenario in my head...I would take 1 part at 10:08, another part at 10:16, and another part at 10:24. Would this make the sample size 3 (n=3) if I was combine them together?

Cheers

You can, but there must be a rational of the sample size election, check for rational sampling on the net, if there is no theoretical reasons to take 3 is just gibberish, just play with numbers.

#### Steve Prevette

##### Deming Disciple
Super Moderator
Another option is to go with X-mR charting, and use the results in the CpK calculation if the control chart is indeed stable.

M

#### M.Yung

Hi all

Can anyone recommend a book that they personally found very helpful on Cpk's? I realise its writing style may not be what I'm use to, but I'd still be willing to have a look.

Cheers

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#### Steve Prevette

##### Deming Disciple
Super Moderator
I'd suggest that cpk is a second-order (secondary) consideration to actually understanding what statistical process control is and why it works. Too many people jump straight to cpk calcuations without understanding the difference between stable, predictable process data, and unstable, special cause, unpredictable data.

#### reynald

##### Quite Involved in Discussions
Steve,
I have been meaning to watch your Red Bead videos since 2 years ago and I'm glad I was able to do so now.
Impressive on how you and the president handled it.

I learned a lot as well.

Thanks again for sharing.