Proper Amount of Data Points for Cpk

[jsoar]

Hello all,
I haven't posted much on here, but I do read a ton of the content on the site. I love it, and it has come in handy often in my career. So a brief kudos to those who take the time to answer so many questions and add tons of value to the site. Thank you.

On to my question, I am currently a Quality supervisor at a manufacturing facility and have been in debate with the Engineering Manager about how many samples should be used to form a good Cpk.

Our customer requires a 100 percent inspection on multiple features and wants to see a good Cpk on those dimensions before lifting that requirement. What we are attempting to do is to use data that has been collected throughout 2013 and show a Cpk. My Concern is that the Engineering Manager would like to use a 30piece sample from data collected over 7 manufacturing runs (each run using multiple lots of material). Using his idea, we would collect about 4+ parts per manufacturing run and use this to establish a Cpk. While the Cpk may look ok, I don't feel comfortable that this Cpk would show the true story behind our process. Also, our production has ramped up significantly half way through the year (Manufacturing runs that are approximately 18x greater in quantity). I don't want to come off as accusing, but at times it seems like as long as a Cpk number can be created not much thought is put into its accuracy. (also, the conversation about why the Engineering Manger is so heavily involved in this process or where the Quality Manager is in all this will have to be for another day )

I'm curious if anyone has any input as to what would be the best route to calculate an accurate Cpk? Also, is this where something like confidence intervals would help me make the case that the sample size should be much greater?

Thank you!

 

[TWA - not the airline]

Do you or the engineering Manager know something about the variability of your process/results? I.e. what is the cause of variation (material lots, operators, equipment ...) and how much does the run-to-run variation, the intra-run variation and the trend contribute to the overall variability? That would help to define the right sampling approach and to defend/sell this to your customer. It would also give you a hint where you could improve...Also maybe your customer has his own expectations that you could find out beforehand. And: If you want to use historical data why can't you just use it all?

 

[Sean Kelley]

Can you do a study of all the data and compare to the data he wants to use/ If you can show a difference then this better warrants the discussion and right now it would seem you don't know what that diffence may or may not be. There may not be a relevant difference but almost always more data is better or a longer time. This yields a better picture of the process unless some changes were made that could skew the same data.

 

[Bev D]

If you have the historical data use it. all of it.
plot it in time series (multi-vari) and then a control chart (the multi-vari will help you determine the rational subgrouping.

if you've incapable periods (excursions) and you can explain hwo you detected them and the preventive corrective actions and control you put in place you can report the CPk for the current (improved) process. This is actually what your Customer wants. Since they know you are doing 100% inspection, using some arbitrary sample will look funny to them. and it is helpful to you: you can develop an sample plan that makes sense and doesn't leave you with escapes that you must explain to the Customer with a possibility of getting bounced back to 100% inspection.

 

[Curtis317]

Use 5 samples or more per manufacturing lot. Then do this for more than 7 manufacturing runs. At least 10 manufacturing runs, ideally 30 runs. This way you get "current" data. Using history may be good but it is what you did in the past and may not represent what you are currently doing. However measuring 100% of a part could be very taxing. So it may be best to work it out with your customer.

 

[Steve Prevette]

I'm curious if anyone has any input as to what would be the best route to calculate an accurate Cpk? Also, is this where something like confidence intervals would help me make the case that the sample size should be much greater?

First, I would tie back to Dr Shewhart's writings on SPC that stated do not declare a process stable unless you have 25 sets of 4 data values. Stability needs to be part of the requirement to do a Cpk.

Second, Yes, you can do a form of variance analysis for CpK, even as simple as plotting sequential CpK calculated values, and determining the variability of the CpK. And that could be used to calculate a confidence interval for the average value of the CpK. Keep in mind the standard deviation of an average is the individual's standard deviation divided by the square root of the sample size.

 

[Miner]

In addition to the previous comments about sampling, I have some purely statistical advice. Remember that every time that you take a sample that there is some uncertainty in how well that statistic can estimate the true population parameter. We call these confidence intervals. In a sample where we desire the mean and standard deviation, both statistics will have confidence intervals.

Next, we want to determine a Cp/Cpk. In order to calculate either/both of these metrics, we need to use mean AND standard deviation, BOTH of which have confidence intervals around them. As a result, the Cp/Cpk metric will have even wider confidence intervals. While a sample size of 30-50 may provide reasonable confidence intervals around the mean, it does not for the Cp/Cpk metric. You need a sample size >= 100 before the confidence intervals around Cp/Cpk become reasonable. I have verified this using Monte Carlo simulation.

 

[TWA - not the airline]

I am wondering if a customer who currently requires 100% inspection and does not seem to have specific requirements regarding how to prove process stability will have the expertise necessary to appreciate something like a confidence interval for a cpk.

 

[Darius]

The confidence intervals of the indicators are almost always neglected but as rational sampling is a cornerstone where the validity of such statistics lies

Cpk confidence Intervals

 

[Bill McNeese]

Why does the customer require 100% inspection? Problems in the past? What Cpk value do they want from you? If you have year's worth of data, you should have an excellent view of what your process is doing over time - should include most of the potential sources of variation.