Regression Control Chart - Process Capability

S

Stevenli

Folks,

I have collected some data for tool wearing (ream cutter), and set up a regression control chart based on # of parts produced.

Now I'd like to get some helps from you guys on how to calculate the process capability Cpk in this situation.

Best Regards
Steven

Bev D

Heretical Statistician
Super Moderator
Why do you want Cpk? For a customer requirement, for you to understand defect rate to drawing spec, or to simply understand potential stack ups and wear with the final assembly? Believe it or not it matters...

reynald

Quite Involved in Discussions
My take on this:
Tool wearing may be a normal for your process but as a customer I don't think I would really care is your mean/variance are totally within regression control limits.
Your control limits may have a trend that varies over time and I would understand that, but as for my specification limits it is still static and would not change. Thus as a customer I would be asking for the Ppk, computed as usual.

D

Darius

Agree with Reynald, and if you are calculating Cpk, the long range variation (total variation used by ppk) is not taken in account, just the within sample variation, so the trend effect will be negligible (unless it happens very quickly) to the Cpk estimate.

Miner

Forum Moderator
Capability indices assume a normal distribution. With tool wear, you will have a quasi-uniform distribution (a uniform distribution with normal tails on each end). This would make any calculation of Cp/Cpk/Pp/Ppk meaningless.

Bev D

Heretical Statistician
Super Moderator
I agree that as a Customer the most important thing is that I receive in specification parts. A stable and capable process has value in that it is more predictable and reduced variation - within reason for the intended use - are always a good thing. It gives me as the Customer a more predictable delivery at lower cost (which affects my price)

that said I would challenge everyone - including Reynald and the OP - to express what they expect the Cpk/Ppk value to mean to you. Its one thing to say "I must have a Cpk or Ppk value", its quite another to express what that number actually means to you. too often we simply ask for a number, compare it to some standard and claim that its good enough or needs to be improved without ANY thought as to what the number or the goal REALLY means and how they affect us.

Many people are also woefully unaware of how Cpk has evolved in meaning and use over the last 30 years. It ahs become (like the p value) a 'turn your brain off and check the darn box' hurdle to doing business. it has ceased to drive any real quality improvement...

Bev D

Heretical Statistician
Super Moderator
Capability indices assume a normal distribution. With tool wear, you will have a quasi-uniform distribution (a uniform distribution with normal tails on each end). This would make any calculation of Cp/Cpk/Pp/Ppk meaningless.

whoa. not every company uses this definition. many simply use Cpk as THE long term capability using the total standard deviation and never worry about short term variation. Don't just jump to the conclusion that all references to Cpk mean short capability....

Miner

Forum Moderator
This is a simulation of a tool wear process. Exactly what does the standard deviation mean in this context?

Attachments

• Wear Sim.jpg
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Bev D

Heretical Statistician
Super Moderator
total standard deviation is still total standard deviation. it will be very large compared to the SD of a symmetrical bullish shaped distribution that is as wide as the one you show. (as there are MANY parts near the spec limit. All parts are in specification.)
Control limits will be based on the SD about the best fit line and Cpk will based on the total SD.

the real question remains what does the Cpk actually mean to you or the Customer? and of course the real unanswered question - what is the part used for and how were the spec limits established? should we be worried

S

Stevenli

I agree that as a Customer the most important thing is that I receive in specification parts. A stable and capable process has value in that it is more predictable and reduced variation - within reason for the intended use - are always a good thing. It gives me as the Customer a more predictable delivery at lower cost (which affects my price)

that said I would challenge everyone - including Reynald and the OP - to express what they expect the Cpk/Ppk value to mean to you. Its one thing to say "I must have a Cpk or Ppk value", its quite another to express what that number actually means to you. too often we simply ask for a number, compare it to some standard and claim that its good enough or needs to be improved without ANY thought as to what the number or the goal REALLY means and how they affect us.

Many people are also woefully unaware of how Cpk has evolved in meaning and use over the last 30 years. It ahs become (like the p value) a 'turn your brain off and check the darn box' hurdle to doing business. it has ceased to drive any real quality improvement...

I like this great comments, thanks.