Effect of %GRR (% Gage R&R) on Cpk

#1
Hi folks,

A small question about a relationship between Cpk and %GRR. Can you explain whether these two terms are related or not?

Also can GRR be performed based on Cpk values?

Thanks in advance.

Abhinav.
 
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Miner

Forum Moderator
Staff member
Admin
#2
Re: Identifying Common Pitfalls in GR&R (Gage R&R) Studies - Measurement System Analy

Cpk (and Cp) is a measure of short term process variation compared to the specification. The observed short term variation is a combination of actual process variation and measurement variation. The observed variance (s^2) is the sum of the actual variance and the measurement variance.

%GRR is a measure of the measurement variation, so there is a relationship in that the observed Cpk is reduced as %GRR increases. The formulae for the relationship between observed CP and actual CP for different levels of %GRR (and P/T Ratio) are listed in the AIAG MSA 3rd Ed. manual.
 
M

Murphys Law

#3
Yes, they are related.

GR&R is layman's language is the error in your measurement. The higher it is (which = uncertainty), the more you have to question it.

If GR&R is high then you have to question the SPC readings when they lie towards the the spec limits of your SPC: Are you really reading what you think they are? They may be in a grey zone and not quite in spec. (Alternatively they may be perfectly in spec but your measurement tolerance is skewed the other way).

Options for you are:-
- get better standard of measurement
- Increase SS/ measurements on a lot (If 2nd study confirms statistically away from spec area, then accept).
- Check out if you have better steps of measuremnt downstream that you can rule out that QC check. (In my world electrical test on finished product would out a SEM inspection on samples that were notorious difficult to interperate., We no longer rely on the SEM inspection)

As for your other question on GR&R on CPK values, please read up on GR&R. It has nothing to do with how in control your process is. It is to do with the quality of the measurement itself.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#4
If GR&R is high then you have to question the SPC readings when they lie towards the the spec limits of your SPC: Are you really reading what you think they are? They may be in a grey zone and not quite in spec. (Alternatively they may be perfectly in spec but your measurement tolerance is skewed the other way).
a quick correction: spec limits have nothing to do with SPC (Control Limits). While large measurement error can provide some uncertainty for teh acceptability of a piece it ahs surprisingly little effect on our ability to apply SPC to the process and detect changes.


As for your other question on GR&R on CPK values, please read up on GR&R. It has nothing to do with how in control your process is. It is to do with the quality of the measurement itself.
Cpk and measurement error are actually related. Cpk (and Ppk) are a ratio of the observed variation vs the spec limits. a large measurement error can result in a smaller Cpk value than a small measurement error, but it' s also not as drastic as you might think.

as to the OP's other question: "Also can GRR be performed based on Cpk values?" if I have interpreted your question correctly - you cannot use Cpk to determine Gage R&R. Measurement error and and actual product variation are confounded together. you must use a designed approach to separate the two to determine the components of measurement error and product variation.

I would strongly recommend reading the works of Donald Wheeler on this topic. He has several very good articles posted on his web site that are free and are a great start. (there are alternatives to the AIAG manual)
 

Stijloor

Staff member
Super Moderator
#5
a quick correction: spec limits have nothing to do with SPC (Control Limits). While large measurement error can provide some uncertainty for teh acceptability of a piece it ahs surprisingly little effect on our ability to apply SPC to the process and detect changes.

Cpk and measurement error are actually related. Cpk (and Ppk) are a ratio of the observed variation vs the spec limits. a large measurement error can result in a smaller Cpk value than a small measurement error, but it' s also not as drastic as you might think.

as to the OP's other question: "Also can GRR be performed based on Cpk values?" if I have interpreted your question correctly - you cannot use Cpk to determine Gage R&R. Measurement error and and actual product variation are confounded together. you must use a designed approach to separate the two to determine the components of measurement error and product variation.

I would strongly recommend reading the works of Donald Wheeler on this topic. He has several very good articles posted on his web site that are free and are a great start. (there are alternatives to the AIAG manual)
Information on Donald Wheeler's website (SPC Press).

Disclaimer: I am not associated with SPC Press.

Stijloor.
 
#6
"Also can GRR be performed based on Cpk values?" if I have interpreted your question correctly - you cannot use Cpk to determine Gage R&R. Measurement error and and actual product variation are confounded together. you must use a designed approach to separate the two to determine the components of measurement error and product variation.
Thanks for your inputs. I agree that Cpk values cannot be used for GRR studies, but what really I wanted to know is can Cpk values give some guidelines about the the measurement systems. Example:

Case 1: Process with Cpk=2
case 2: Process with Cpk=1

Ques.1.
Can I say with some confidence, keeping in mind the inverse relation between Cpk and GRR, that if I have to prioritize GRR, I should do GRR study for case 2 first than case 1.

Ques2.
Also If the %GRR calculation for case 1 is slightly over the line , say 35 %, can we just pass this gage based on good Cpk value. What if, case 2 gives %GRR=35 %, should we fail this gage because of poor Cpk value.


Thanks guys,
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#7
I would still recommend that you read Wheeler's free articles - this will help answer many of your questions.

as a specific answer: if you need to prioritze (and who doesn't; I have a friend who says "we dont' need better time management; we need better work prioritization") your GR&R work, it's far better to start with the gage used for a process with a low Cpk. Large measurement error has the most effect when parts are at the spec limits. When the process is very capable - even a relatively large amount of measurement error won't matter.

As for your second question: I don't calculate measurement as a % of the tolerance as it is mathematically incorrect and misleading. However, your thought process is mostly correct: Gage R&R isn't a math question; there is no absolute correct numerical answer. Gage R&R is intended for you to LEARN about how your measuring system is performing and then you determine what action is best for that process to ensure good quality parts.

The caution to that is that if you have a customer that requires certain numerical values (such as AIAG requirements) - you have an additional irrational burden to meet. I find face to face discussion with teh customer to explain your process, results and actions to be helpful.
 
D

Duke Okes

#8
Case 1: Process with Cpk=2
case 2: Process with Cpk=1
Ques.1.
Can I say with some confidence, keeping in mind the inverse relation between Cpk and GRR, that if I have to prioritize GRR, I should do GRR study for case 2 first than case 1.
Ques2.
Also If the %GRR calculation for case 1 is slightly over the line , say 35 %, can we just pass this gage based on good Cpk value. What if, case 2 gives %GRR=35 %, should we fail this gage because of poor Cpk value.
Answers to both = Yes. Since Case 1 is capable process (even if R&R isn't very good) it deserves less focus. Since Case 2 is not capable, R&R is useful since it may be a major contributor to the poor Cpk. However, you should first look at Cp. If it's good then it's not an R&R problem but a centrality problem.
 
R

roder - 2012

#10
Hi folks,

A small question about a relationship between Cpk and %GRR. Can you explain whether these two terms are related or not?

Also can GRR be performed based on Cpk values?

Thanks in advance.

Abhinav.
Hope this may help...

1. GR&R and Cpk is related...
Cpk is the measure of the process capability in which data were taken from the measurement system.
GR&R is the measure of the measurement system variation as contribution to the total process variation.
The result of the Cpk is somewhat dependent on the measurment system variation ( GR&R).

2. Maybe, not.
 
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