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

Bev D

Heretical Statistician
Staff member
Super Moderator
#11
As Roder stated the amount of measurement error is included in the observed variation used to determine process capability.

However, you must understand that a GR&R "percentage of tolerance" is of no value in determining how much measurement error effects your process capability. you must knowthe measurement error in terms of it's standard deviation.

(total observed variation)^2 = (measurement error)^2 + (true part variation)^2

You cannot determine measurement error simply by knowing a Cpk value...
 
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bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#12
Another quick correction
spec limits have nothing to do with SPC (Control Limits).
They do in some special cases for non-normal distributions. Although this is true for the normal distributions, I try to temper its use as a blanket statement.

While large measurement error can provide some uncertainty for the acceptability of a piece it has surprisingly little effect on our ability to apply SPC to the process and detect changes.
Remember, it can be measurement system error - including what we chose to measure to control a process as well as how well we measure it. Significant measurement system error can mask the signals that should be evident and may be important in an SPC chart, diluting its effectiveness.

In most cases the statements hold true, but they are not laws of SPC. It would not be such a problem if I did not have to clear that up every time I try to explain that point when dealing with special cases. :cool:
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#13
Another quick correction

They do in some special cases for non-normal distributions. Although this is true for the normal distributions, I try to temper its use as a blanket statement.
Sorry I have to disagree with you. by definition and by the laws of physics the two are unrelated. You choose to use spec limits as tha anchor from which you set the value at which you address tool wear. Allowing the systemic drift to continue until it comes "too close" to the spec limits. You set these "action limits" using the statistical knowledge of the varation about any location of the process. We can set statistical control limits about any local average in a situation where there is a systemic drift. in essence we are subtracting the drift from the simultaneous variation about the drift line... Some call these sloping limits as the are above and below the 'sloping' drift line. It is these limits that are the statistical process control limits. You have chosen - not incorrectly - to focus on the end points where the tool is adjusted: your logo says it all.
we can use the sloping statistical control limits for controlling other aspects of the process. when does variation about the systemic drift line represent a change in the process that is not due to tool wear or the remaining inherent variation in the process...


Remember, it can be measurement system error - including what we chose to measure to control a process as well as how well we measure it. Significant measurement system error can mask the signals that should be evident and may be important in an SPC chart, diluting its effectiveness.

In most cases the statements hold true, but they are not laws of SPC. It would not be such a problem if I did not have to clear that up every time I try to explain that point when dealing with special cases.
a couple points of clarity: I think you are talking about two types of 'errors'; one is what I would term a mistake or an incorrect human choice - choosing to measure the wrong thing. the other is the classical thing we think of when using the phrase "measurement error": this is the variation of the measuremetn system itself as quantified by the standard deviation. It is not a human choice but inherent in the physical system. My comment regarding measurement error deals only with the second error. Clarifying my point further, I never meant to say that this error is never big enough to interfere wiht our ability to see true process variation, I meant that it often isn't as impactful as commonly believed. This misperception is primarily driven by the popular approach to gage R&R whihc expresses error as a % of the tolernace. This approach has been shown to be statistically and mathematically incorrect and often dramatically overstates the effect of measurement error. Intstead of employing a critical assessment of their measurement error, too many people take the path of least resistance and succumb to the popular myths of measurement error. I rail against this in the same way you rail against the "normal centrists" as you call them...
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#14
Sorry I have to disagree with you.
We have that opportunity here! :tg:

By definition and by the laws of physics the two are unrelated. You choose to use spec limits as the anchor from which you set the value at which you address tool wear. Allowing the systemic drift to continue until it comes "too close" to the spec limits. You set these "action limits" using the statistical knowledge of the variation about any location of the process.
Yes, this is utilizing the distribution of the most significant variation for that process - tool wear. We set the control limits to address that variation and decision on the process based on them.

We can set statistical control limits about any local average in a situation where there is a systemic drift. in essence we are subtracting the drift from the simultaneous variation about the drift line... Some call these sloping limits as the are above and below the 'sloping' drift line. It is these limits that are the statistical process control limits.
They are another opportunity for control. This approach removes the most significant variation and seeks to observe the remaining variations. Unfortunately, the remaining variations are insignificant for the control of that process, by the definition of the process. That chart would yield, at best, rare special causes. At lot of work for little return. And, it is not the only process control based on statistics, for sure. The uniform distribution is a statistical tool as effective as the normal curve. The data shows it to be true.

I think you are talking about two types of 'errors'; one is what I would term a mistake or an incorrect human choice - choosing to measure the wrong thing. The other is the classical thing we think of when using the phrase "measurement error": this is the variation of the measurement system itself as quantified by the standard deviation. It is not a human choice but inherent in the physical system.
The point you made was understood, but I have found that the "human error" does enter into the standard deviation, as does all error in the process add up to the total deviation. Addressing that error has provided much clearer data, leading to better decisions. That is why I added that comment.

Clarifying my point further, I never meant to say that this error is never big enough to interfere with our ability to see true process variation, I meant that it often isn't as impactful as commonly believed. This misperception is primarily driven by the popular approach to gage R&R which expresses error as a % of the tolerance. This approach has been shown to be statistically and mathematically incorrect and often dramatically overstates the effect of measurement error. Instead of employing a critical assessment of their measurement error, too many people take the path of least resistance and succumb to the popular myths of measurement error. I rail against this in the same way you rail against the "normal centrists" as you call them...
I am aware of this contention. I have read Dr. Wheeler's writings on that topic. The worst case is the people that take an even lesser path of resistance and ignore resolution entirely, and its effect of measurement in SPC. I sure is handy to have statistically significant categories of resolution that will ensure the plotted points are of some validity and that the range is not from the measurement error (of either type), but rather the other participants of the total variation. Total ignorance of the problem is why we see control charts with 10 categories between the control limits, but dots on every other one. They miss the point of the most basic need for resolution - forget statistically significant resolution. I would be satisfied to rid the world of that problem. Again, even with the mathematical problems of ndc, its need to be calculated to the control limits rather than the specification, et.al., just thinking about the need for statistically significant categories is far and above ignoring it.

....not that I ever said you would have anyone ignore that...
:cool:

I rail against this in the same way you rail against the "normal centrists" as you call them...
Clearly, we both have a ways to go....:cool:
 
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