


28th January 2009, 02:49 PM

Inactive Registered Visitor
Registration Date: Jan 2009
Location: New Mexico USA


Posts: 3
Thanks Given to Others: 0
Thanked 0 Times in 0 Posts
Karma Power: 22 Karma: 10


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

28th January 2009, 03:09 PM


Stop Xbar/R Madness
Registration Date: May 2002
Location: LaGrange, OH


Posts: 3,909
Thanks Given to Others: 1,292
Thanked 1,421 Times in 1,084 Posts
Karma Power: 457


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!

28th January 2009, 03:15 PM

Inactive Registered Visitor
Registration Date: Jan 2009
Location: New Mexico USA


Posts: 3
Thanks Given to Others: 0
Thanked 0 Times in 0 Posts
Karma Power: 22 Karma: 10


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

28th January 2009, 07:02 PM


Stop Xbar/R Madness
Registration Date: May 2002
Location: LaGrange, OH


Posts: 3,909
Thanks Given to Others: 1,292
Thanked 1,421 Times in 1,084 Posts
Karma Power: 457


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 (USLLSL)/(UCLLCL). For more information, see Statistical process control for precision machining .
That calculation may not apply to the hydraformed part.

28th January 2009, 08:44 PM


Forum Moderator
Registration Date: Apr 2002
Location: Greater Milwaukee area, Wisconsin


Posts: 3,404
Thanks Given to Others: 591
Thanked 1,977 Times in 1,252 Posts
Karma Power: 425


Re: Intermediary calculations for Cpk  What do CPU and CPL stand for?
Quote:
In Reply to Parent Post by roberdm
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.
__________________
"A fool can learn from his own experiences; the wise learn from the experience of others."  Democritus, 460370 B.C.

28th January 2009, 09:27 PM

Inactive Registered Visitor
Registration Date: Jan 2009
Location: New Mexico USA


Posts: 3
Thanks Given to Others: 0
Thanked 0 Times in 0 Posts
Karma Power: 22 Karma: 10


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 D19000 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?

28th January 2009, 09:43 PM


Stop Xbar/R Madness
Registration Date: May 2002
Location: LaGrange, OH


Posts: 3,909
Thanks Given to Others: 1,292
Thanked 1,421 Times in 1,084 Posts
Karma Power: 457


Re: What is minimum sample size to calculate Cp?
For precision machining, and its associated nonnormal 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.

29th January 2009, 06:59 AM


Forum Moderator
Registration Date: Apr 2002
Location: Greater Milwaukee area, Wisconsin


Posts: 3,404
Thanks Given to Others: 591
Thanked 1,977 Times in 1,252 Posts
Karma Power: 425


Re: What is minimum sample size to calculate Cp?
Quote:
In Reply to Parent Post by roberdm
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 D19000 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.
__________________
"A fool can learn from his own experiences; the wise learn from the experience of others."  Democritus, 460370 B.C.

Lower Navigation Bar


Do you find this discussion thread helpful and informational?
Visitors Currently Viewing this Thread: 1 (0 Registered Visitors (Members) and 1 Unregistered Guest Visitors)


Thread Tools 
Search this Thread 


Display Modes 
Rate Thread Content 
Linear Mode


Forum Posting Settings

You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts
HTML code is Off




