# Capability - CPk comparison values

#### Quality Newbie

##### Registered
Hi All,

I'm looking for a way to calculate what the comparable CP numbers are for various levels of a sample size.

If my target at 30 samples for example is a CP of 1.33 but I can't obtain the 30 samples and can only obtain 15 or even 20. How would I work out what the equivalent CP figure would be? Obviously I know it would need to be higher given the lower sample size but I don't know how to work it out.

Could any of you help with this please?

#### Jim Wynne

Staff member
Welcome to the Cove. In short, there is no rational way to do what you're trying to do. In your thread title you refer to Cpk, then you refer to Cp in your question. They're two different but related values. I don't know what industry you're in or what requirements you might be trying to satisfy, so if you could give us more information it would help to give a better answer.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
- smaller sample sizes can result in larger estimates of the standard deviation which would make the Cpk number smaller. You can use a random number generator and sample at different sample sizes to see what happens.
- There is no target Cpk or Cp value for a sample size. (If I’ve interpreted your question correctly?). Such a target would have zero value.
- really small sample sizes are simply NOT appropriate for Cpk/Cp calculations. Stop doing that. It’s just playing with math. A Cpk/Cp calcautlion with 30 samples is pretty silly too.
- of course the whole idea of Cpk/Cp is silly. You’ll learn a lot more about your process capability by plotting your data on a multi-varo chart, then a control chart.

#### Quality Newbie

##### Registered
Welcome to the Cove. In short, there is no rational way to do what you're trying to do. In your thread title you refer to Cpk, then you refer to Cp in your question. They're two different but related values. I don't know what industry you're in or what requirements you might be trying to satisfy, so if you could give us more information it would help to give a better answer.

Thanks Jim,
I've browsed for a while and found this to be a really useful site.
Basically I'm looking to buy off a process and we have been given a target of 1.33 for short term capability apologies on my above thread for putting both CP and cpk that is my mistake.
The exam question really is.
If I can't afford to have the min 30 parts which we currently use. And can only have say 20
What would my equivalent capability value be.

Now I do understand this is diminishing returns and that ideally I want 100+ samples to review capability however in a buy off situation this just isn't possible without extension of the programme timelines.

I've racked my brain for a while on how to come up with and solve this and just ran out of ideas really and thought someone else might already do it or have a solution

Thanks

#### Quality Newbie

##### Registered
- smaller sample sizes can result in larger estimates of the standard deviation which would make the Cpk number smaller. You can use a random number generator and sample at different sample sizes to see what happens.
- There is no target Cpk or Cp value for a sample size. (If I’ve interpreted your question correctly?). Such a target would have zero value.
- really small sample sizes are simply NOT appropriate for Cpk/Cp calculations. Stop doing that. It’s just playing with math. A Cpk/Cp calcautlion with 30 samples is pretty silly too.
- of course the whole idea of Cpk/Cp is silly. You’ll learn a lot more about your process capability by plotting your data on a multi-varo chart, then a control chart.
I agree on the small sample sizes and in using the cp/cpk at all as it is but a snapshot in time. In a buy off situation where we need to be in install and then leave for the next programme.
It was worth a punt if anyone did know of an answer.

#### toniriazor

##### Involved In Discussions
What is your customer requirement for the sample size ? With such small sample size you won't be able to demonstrate long term process capability and why you cannot produce more sample sizes to complete the study ? No orders from customer or other limitations?

#### Miner

##### Forum Moderator
Staff member
I think that you are searching for the concept of confidence intervals for the Cp/Cpk indices, which would increase as the sample size decreases. This would require that the estimated Cp be greater to ensure that the lower confidence limit meets or exceeds the requirement. Minitab Help covers the confidence interval formulas for Cp.

#### Bill Levinson

##### Industrial Statistician and Trainer
Cp and Cpk are based on short-term estimates of the process standard deviation, which you could get from the average moving range of 15 or 20 parts, or alternatively, let's say, the ranges of 5 samples of 4 if you have a rational subgroup of 4. The problem is that the confidence interval would be very wide, and probably too wide to be meaningful. This is why people always want 30 or more parts (preferably 100 or more).

You can also get Pp and Ppk from the standard deviation of all the parts, and do a normal probability plot to assess the normality assumption, but you will still have the same problem with the confidence limits.

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
I suggest that Cpk is really not a good tool in the first place, and serves little purpose in terms of random sampling. I would recommend considering:

1. Setting up an acceptance sampling plan using MIL STD 105 follow on methods.
2. If this is basically the same item being made in sequential lots, run SPC monitoring across batches which will build up a larger sample size and you will be able to see variations from lot to lot.

A point being is use the data you are willing to pay for, in the best manner possible.

#### msbettyhunt

##### Starting to get Involved
Thanks Jim,
I've browsed for a while and found this to be a really useful site.
Basically I'm looking to buy off a process and we have been given a target of 1.33 for short term capability apologies on my above thread for putting both CP and cpk that is my mistake.
The exam question really is.
If I can't afford to have the min 30 parts which we currently use. And can only have say 20
What would my equivalent capability value be.

Now I do understand this is diminishing returns and that ideally I want 100+ samples to review capability however in a buy off situation this just isn't possible without extension of the programme timelines.

I've racked my brain for a while on how to come up with and solve this and just ran out of ideas really and thought someone else might already do it or have a solution

Thanks
Exactly, this is the tough one to solve for me.

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