Capability Analysis in the Real World

[Tavoludo]

Hi fellows.
I have been preforming CPk analaisys from time ago and I thought I really understand this concept but after read some posts here I'm totally confuse as I was at the beginning .
My questions are:
1. Based on what I read, what really care is the PPk since is this one is the value that tell us how good (or bad) our process is currently doing and what determine if process should keep going or stopped. Am I right?
2. To perform a PPk analysis do we should ensure our process is statistically on control?
3. Let’s suppose I have new crimping equipment and before release it to regular production I want to be sure if this is capable. Do I should first to prepare Xbar-Rbar graphs? (Let's suppose crimp height is the characteristic and is normally distributed) if so,
4. How many samples with N=5 do I should take to initiate the SPC analysis?
5. Once the SPC graph shows a "Normal" trend, from the data that I use to prepare it, how many values do I should take to prepare the PPk analysis? Do those values should be the Xbar from subgroups or just the Xi values?
Maybe those are a dumb questions but I want to feel comfortable again next time I prepare a capability analysis. By the way I'll really appreciate any input from you guys.

 

[Sturmkind]

Re: Capability Analysis on The Real World

Hi, Tavoludo and welcome to the Cove!

"1. Based on what I read, what really care is the PPk since is this one is the value that tell us how good (or bad) our process is currently doing and what determine if process should keep going or stopped."

Some processes will rarely have 'good' Cpk or Ppk because they cannot be perfectly centered like parallelism or flatness. Stamping diameters are usually run at the high limit to maximize punch life and to take advantage of Maximum Material Condition modifiers to the GD&T.

"2. To perform a PPk analysis do we should ensure our process is statistically on control?"

Ppk is short term Process Potential and has been defined as any sample size less than 125 sub-groups.

"4. How many samples with N=5 do I should take to initiate the SPC analysis?"

The only reason for a sub-group size of 5 was it allowed easy shop floor calculation since the values are summed, doubled, and the decimal moved one place to the left to find the average. I generally use sub-groups of 3.

"5. Once the SPC graph shows a "Normal" trend, from the data that I use to prepare it, how many values do I should take to prepare the PPk analysis? Do those values should be the Xbar from subgroups or just the Xi values?"

The sub-grouping of values may approximate normality following the Central Limit Theorum and is the reason for n>=30 (or my favored case = 33).

See this link: http://business.clayton.edu/arjomand/business/l7.html

I hope this helps out!

 

[bobdoering]

Re: Capability Analysis on The Real World

See this link: http://business.clayton.edu/arjomand/business/l7.html

The lecturer is incorrect with this statement:

If a random sample of n observation is selected from any population, then, when the sample size is sufficiently large (n>=30) the sampling distribution of the mean tends to approximate the normal distribution.

The population must be of an independent variable - which tool wear (for example) is not the case, and therefore does not follow the CLT. That is a very important assumption missed by some folks jumping to the one size fits all approach. It doesn't. This is what supports the example for stamping (or precision machining) to allow for tool wear and still be stable and in control even with a trend. Tool wear is a dependent variable, and is handled differently (as in NOT using X-bar R charts!)

 

[Sturmkind]

Re: Capability Analysis on The Real World

As always, good catch, Bob!

 

[Tavoludo]

Thank you both of you guys for your answer. I have a final question:

• In order to prepare a accurate CPk/PPk analysis, what do you recommend for sampling?
  • N=33 with subgroups of 3? or
  • N=33 with subgroups of 1?

Thank You very much.

 

[Sturmkind]

Sub-groups of 3 will provide 11 total subgroups, certainly adequate for potential trend or stratification detection.

 

[bobdoering]

The best answer - of course - is "it depends." AIAG likes to call for 25 subgroups of at least 4 parts for at least 100 points. But, their requirements are written by normalcentrics with little understanding beyond the X-bar-R chart. If your distribution is applicable for traditional SPC charting (centralized, random variation with independent variables) then X-bar R may be fine. If there is too little variation in the sampling (within the 4 parts of the subgroup) then you may want to use X-MR with 1 part subgroup over 100 parts.

You may have heard "you have to be in control before you can be capable" or "you have to be capable before you can be in control" - and that comes from the fact that in traditional SPC there is no relation between control and capability. Just look at the equations! Control is based on variation within the samples, and capability is based on specifications. So, fact is you need to be both simultaneously before you can consider your process viable. Which one comes first may not matter...

 

[Sturmkind]

I agree with Bob -I always check the individuals against their control limits for any obvious information that can be seen (groups, possible trends, etc.) and then sub-group them rationally. That has become so automatic I don't even think about it anymore....

And the AIAG PPAP manual does require 100 variable data-points from a 300 piece consecutive run.

One of the best discussions on rational subgrouping (as well as standard deviation derivations) can be found in the text Statistical Quality Control by Grant & Leavenworth.