Ongoing Cpk and Global/Historical Data

[gtg168w]

Hi - I have a group of parts that all require cpk>1.33 to be shown for the critical dimensions (on avg there are 3 criticals per part).

From the AIAG manuals, I know that Cpk is process capability relative to the center of the tolerance.

My confusion lies in how to calculate cpk for my in-process production runs to monitor the process by using cpk as an SPC tool. The customer didnt ask for any charting, but wants cpk reports with each lot shipment.

I am getting stuck because part of me assumes there must be a large enough sample size to have confident statistics. For my initial cpk that is going to be done with the upfront part approval (not PPAP for this part, but they still want to see cpk>1.33 for initial approval to run production), I was planning to take subgroups of sample size , n=4, and then do 25 subgroups (m), m=25. So for one of the criticals, there will be 100 data points, and for my initial capability, myself and the customer will be satisfied.

BUT - what do I do for ongoing cpk reporting? I dont want to take 100pc samples and divide them up in to small n=4 subgroups, do I? Can't I just take 5 pcs as inprocess sample pieces, maybe 2x per shift. (we only run 1 shift). That would give me n=5 for sample size and 2 subgroups (m=2) on each day. Would that give me a cpk that means something?

I ask about global/historical data in the thread topic because I'm wondering if if I can, OR SHOULD, use the Xbar data from the initial cpk study during my inprocess cpk calculations? Since cpk shows subgroup variance relative to center of the TOL, I guess including historical data wouldnt tell me the relative location of the current process mean, but would be the "global" mean for life of the data taken?

Thanks! - JB

 

[Surehawk]

This indeed sounds wierd. Your initial idea to make a capability study with 25*4 pieces sounds like a good start.

How many do you produce per hour? Is it timeconsuming to measure these parameters? How many units are measured anyway by the operators?

Customers often have a lot of demands, and wanting you to have a capable process does not sound wierd in itself. But if it means extra cost to you, calculate how much and say you have to put it on the price of the unit.

 

[debyang]

IF the customer do didn't ask for any charting, but wants cpk reports with each lot shipment, maybe they are just ask for every lot's performance index(Ppk) not capability index.

You might just calculate every lot's SD from the inspection data and send them Ppk value lot by lot.

 

[Bill McNeese]

Customers often want Cpk values but they do not understand process capability and all the caveats that go along with it. If your process is in statistical control, the Cpk value does not change. Yes, if you calculate it for a lot, it will be different, but that differnce is simply due to commmon causes of variation.

One approach is to take your intial study (n = 4, k = 25 or n = 5 and k = 20), plot those results on an Xbar-R chart. Then add your in process results (use the same subgroup size, it is easier) to the chart over time. Plot those results over time. As long as the process stays in control, the process capability will stay the same.

If you have lots of out of control points, then you have other issues besides reporting the Cpk value to the customer. The first step is to check how stable the process through the Xbar-R chart. Plot the data over time and see what it tells you.

 

[bobdoering]

People often cite the AIAG requirement to meet capability, which arises from the PPAP 4th edition section 2.2.11.3. Unfortunately, they stop reading after 2.2.11.4. There is a whole section right after it that is equally important : 2.2.11.5 Processes with One-sided Specifications or Non-Normal Distributions - especially the NOTE after it. Had they read it, it would be clear that before you even start to report Cpk, you need to understand your process variation, its distribution, and whether Cpk is even applicable! It is not always 100% applicable, no matter what your customer thinks!

 

[gtg168w]

So it is becoming clear that people ask for SPC indices and reporting and may have no clue what they even want, what it means, or if they are even asking for the right reporting.

But, I still need to keep them happy, without making them feel incompetent about the interpretation of their print note requirements.

If anyone has a clear suggestion on actual formulas to use for the cpk reporting I would appreciate it. I downloaded 2 of the cpk templates but most have chosen the wrong ones, as one kept giving me errors, and the other is locked/looks like a sales pitch when I try to run the macros.

If I need to tell the customer that I can give them cpk up front, but technically the in-process needs to be reported as ppk, I will do that.

When plotting over time to show what my performance/indices looks like at each sampling point (lets say 5 pcs taken every 4 hours), does that change my calculation for cpk? Because my understanding of cpk is that it is just a selection between the minimum of the scaled distance of the process mean to the middle of the tolerance. That means for each new "point" at the next "time" the sampling is done, my cpks calculated at each point don't rely on or share data with previous samples? I feel like the statistics would mean more if each cpk calculated also had a way to include information from all the previous data sets. Maybe this is not a problem because the initial condition to test for process performance = in-control by first testing ppk of the data, because as Bob said, cpk only works for in-control and normally distributed processes.

Thanks again for all your help. I ask a lot of questions. I really like to understand the why behind it, so that I can really use these tools.

Thanks - JB

 

[debyang]

It is no need to worry about the previous data when the report is made on lot by lot basis. If you do follow SPC rules to monitor the process you should know the interval when each lot begins to process and ends.

Just collect all those data you got for that particular lot, calculate the mean and sd by using all data(if n=4 and you have 10 points on SPC chart for that lot, there are 40 inspection data) the smaller value of (USL-mean)/3/sd and (mean-LSL)/3/sd will be the lot's Ppk.

If your process is in control in theory you do not need to recalculate each lot's Cpk, instead, you can report the previous lot's Cpk as the new lot's.
However, you can calculate each lot's Cpk as the method mention above. That is, averaging the lot's 10 R to get the lot's average R, then dividing the average R by d2(n=4) to estimate the lot's sd. Finally, calculate (USL-mean )/3/sd(estimated) and (mean-LSL)/3/sd(estimated), the smaller one is that lot's Cpk.

 

[Bev D]

If anyone has a clear suggestion on actual formulas to use for the cpk reporting I would appreciate it...If I need to tell the customer that I can give them cpk up front, but technically the in-process needs to be reported as ppk, I will do that.

Bill McNeese gave you the right answer. I understand that you do not want to insult your customer even tho they may be asking you to do something silly - however, they probably don't understand that but they will appreciate what you give them if it is correct and useful. Focus on meeting their real need and not the boiler plate requirement...

It is non-sensical to continually recalcualte the Cpk (or Ppk) index. especially with small sample sizes. use your original Cpk data and plot future samples on a control chart. as long as the process remains stabel teh Cpk has NOT changed. You can update the Cpk estimate if you like by using ALL of the data. it is non-sensical to segragate data by arbitrary time periods. You really should only recalculate the Cpk wehn you have made an IMPROVEMENT. When you have an excursion where the quality level degrades (out of control points on the control chart) all you need to do is correct the cause of the excursion to return to the original stabel period.

As for the difference between Cpk and Ppk, you need to use the formula that provides the 'long term' performance. Some customers say Cpk when they mean Ppk. (this is because in the beginning there was only Cpk and it used the total standard deviation and had nothing to do with the within subgroup variation.)