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samples and sampling plans, cpk (related to process capability)
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  #1  
Old 28th January 2009, 02:49 PM
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Question What is minimum sample size to calculate Cp?

Greetings...this seems like the right place to ask this question. After I obtain control in my process by utilizing sound SPC techniques what is the minimum sample size I can use to calculate process capability, Cpk? The discussion always starts with 25 pcs and then fluctuates from 20 to 30 pcs. If you know what the minimum is please attach or list the standard it comes from. I could not find it in AS9103.

Thanks,
Dave

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Old 28th January 2009, 03:09 PM
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Re: Intermediary calculations for Cpk - What do CPU and CPL stand for?

It would be good to understand the process that you are trying to calculate the Cpk for - it does make a difference in some applications!
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Old 28th January 2009, 03:15 PM
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Re: Intermediary calculations for Cpk - What do CPU and CPL stand for?

The processes would be from multiple sources mostly strucrual aircraft parts:

1. Aluminum machined parts
2. Aluminum hydraform pats
3. Steel and titanium machined parts
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Old 28th January 2009, 07:02 PM
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Re: Intermediary calculations for Cpk - What do CPU and CPL stand for?

For the parts that are precision machined, if the processes were properly controlled, Cpk would not be an issue. First of all, they should exhibit a continuous uniform distribution with the only significant variation from tool wear - again, if it is precision machining. With that distribution, the capability is (USL-LSL)/(UCL-LCL). For more information, see Statistical process control for precision machining .

That calculation may not apply to the hydraformed part.
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Old 28th January 2009, 08:44 PM
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Re: Intermediary calculations for Cpk - What do CPU and CPL stand for?

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In Reply to Parent Post by roberdm View Post

Greetings...this seems like the right place to ask this question. After I obtain control in my process by utilizing sound SPC techniques what is the minimum sample size I can use to calculate process capability, Cpk? The discussion always starts with 25 pcs and then fluctuates from 20 to 30 pcs. If you know what the minimum is please attach or list the standard it comes from. I could not find it in AS9103.

Thanks,
Dave
The following is independent of whether Cp or Cpk are appropriate to the type of process.

First, you need to realize that both metrics are dependent on a sample mean AND a sample standard deviation.

Second, both mean and standard deviation have a confidence interval associated with them. Using both confidence intervals in the calculation results in a Cp/Cpk with an even larger confidence interval.

I have run Monte Carlo simulations on this and have found that you really need approximately 20 subgroups totaling 100 sample measurements to obtain a Cp/Cpk with reasonably tight confidence limits. This also agrees with the recommendations found in the AIAG SPC manual.

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Old 28th January 2009, 09:27 PM
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Re: What is minimum sample size to calculate Cp?

I'm looking for a standard that explains what the minimum sample size(data points or number of measurements) required prior to calculating process capability. I found a Boeing standard D1-9000 that is helpful. Sorry couldn't post the link. See 1.14 Process Capability Analysis (Cp and Cpk). See page 196.

Do you know of any other sources?




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Old 28th January 2009, 09:43 PM
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Re: What is minimum sample size to calculate Cp?

For precision machining, and its associated non-normal uniform distribution (which has no dependence on the mean whatsoever and the standard deviation has little to offer), you can not predict a minimum number. It depends on the tool wear rate, and how many parts is takes to generate at least one cycle of the sawtooth curve (unless you are willing to extrapolate based on the tool wear rate determined from a sample) For example, if it takes a week and 3000 parts for the tool to wear from the lower control limit to the upper control limit, then 3000 is the minimum - but if it takes 5 parts to wear at that rate, 25 parts will give you 5 cycles - or more than enough data. A little simplistic, but should illustrate the point effectively. It is critical to collect the data in time order to evaluate the tool wear rate. It is not a random sample function, as the tool wear rate is a dependent (not independent) function of time. As a dependent function, CLT does not apply, either.

Again, the previous link gives some direction to this issue.
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Old 29th January 2009, 06:59 AM
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Re: What is minimum sample size to calculate Cp?

Quote:
In Reply to Parent Post by roberdm View Post

I'm looking for a standard that explains what the minimum sample size(data points or number of measurements) required prior to calculating process capability. I found a Boeing standard D1-9000 that is helpful. Sorry couldn't post the link. See 1.14 Process Capability Analysis (Cp and Cpk). See page 196.

Do you know of any other sources?
No standard exists that I am aware of. The AIAG SPC manual recommends the 100 sample minimum that I mentioned above.

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