Statistical Tolerances in GD&T (Geometric Dimensioning & Tolerancing)?

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Dylan545

#1
We 100% inspect a part of ours, due to part liability issues and not an out of control process, using hard gages. The 100% inspection is driven by customer requirements and if not then my company would not need to put all that quality time into the parts. One of the print dimensions has a parallelism that has both a statistical tolerance (ST) and a arithmetic tolerance. When building the gages we used the statistical tolerance for this parallelism. We have just recently remade the gages to go back to the arithmetic tolerance. My customer said that since we are not using SPC in process we cannot use the statistical tolerance. I know ASME Y14.5 clearly states that "Features identified as statistically toleranced shall be produced with statistical process controls". My interpretation of the standard was that you can use the statistical tolerances when control is assured? In this case control is assured by the 100% inspection, again driven by part demands and not process instability. Am I wrong when I assumed we were allowed to use the statistical tolerance? Or is there some reason why SPC must be used? If so then my next question is that the standard does not specify what level of SPC you need to be at to use the statistical tolerance. So even if I was running at a .002 Cpk I can use the statistical tolerances as long as I collect the data?
Just wanted to get some expert opinion on this? And if anyone could point me towards literature to support my original claim? I would greatly appreciate it.
 
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Sturmkind

#2
Re: Statistical Tolerances in GD&T?

Hi, Dylan545!

Was the statistical 'tolerance' and arbitrary percentage of the full arithmetic tolerance (like 75%)?

Process SPC Upper & Lower limits are based on the data set observed itself. What does the data say when analyzed in a run-chart format and then when grouped and compared to the hard tolerance limit? Is the data normally distributed?
 

Miner

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#3
Re: Statistical Tolerances in GD&T?

Statistical tolerances are based on the assumption that the process is centered on the target value and that the process variation follows a Normal distribution. So, even though you are 100% gaging the product, this does not ensure that the process is centered, and that the process is Normally distributed.

If for example, your process is centered halfway between the target and the specification there will be a much higher percentage of product at the specification limit. Even though you are inspecting for out-of-spec, the percentage just within spec is higher than assumed. This means that the probability of an undesirable tolerance stackup is much greater.

Your customer is correct. No SPC, no statistical tolerances.
 

bobdoering

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#4
Re: Statistical Tolerances in GD&T?

Of course, the only time you can use SPC for parallelism is if you really stink. The closer you get to zero (as in perfectly parallel), the more non-normal the process is (as in Weibull or beta distributions) and all (well, OK, most) bets are off then. It is a unilateral tolerance with a physical limitation, not a bilateral tolerance with a centered target. The target is zero. Cpk is not applicable.

If you were precision machining, for example, you would not SPC parallelism. It is the incorrect usage of the SPC tool. You SPC the hi/lo values of the thickness, and the range is the parallelism (X hi/lo-R chart). But...that is if the predominant variation is tool wear for that dimension.
 
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B

Barbara B

#5
Re: Statistical Tolerances in GD&T?

Cpk is not applicable.
Cpk is applicable, Cp isn't, due to the one sided tolerance. A physical limit is mathematically different from a tolerance limit. To calculate Cp you have to have a tolerance width (difference between USL and LSL) and without LSL or rather LSL=-infinity Cp becomes always infinity (not helpful to evaluate the process).

But to get a reliable Cpk, you have to describe the distribution of the data with an appropriate distribution function like the truncated normal distribution for data with a technical limit.

Regards,

Barbara
 

bobdoering

Stop X-bar/R Madness!!
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#6
Re: Statistical Tolerances in GD&T?

Cpk is applicable.
The point of Cpk is to understand whether your distribution is centered. Just because you can calculate it does not really give it any meaning, as in this case.

But to get a reliable Cpk, you have to describe the distribution of the data with an appropriate distribution function like the truncated normal distribution for data with a technical limit.
To understand the relationship of your process variation to your specification, you do need the correct distribution. In this case it would not be a truncated normal, but rather a Weibull or beta - and the only difference between them is how they behave as the data accumulated at '0'.


If you step back from the algebra and just look at the definitions, you will see that capability is determining how much of your tolerance is used up by your process variation. Although you do not have a lower spec, the physical zone you can exist in for parallelism is between 0 and your parallelism spec. So not to confuse the purists, I will not call it Cp, but you can look at your capability as (USL-0)/(width of correct distribution). For the normal distribution, the width is defined as +/- 3 std dev. For other distributions, that may not be appropriate. Cpk is designed specifically to determine if that distribution usage is centered within your tolerance. The notion can be twisted to some degree to determine how far your mean is from a unilateral tolerance, but that is really answering a question that was not intended to be asked. So, even though it can be calculated as an academic exercise, its usefulness is vastly diminished.
 
D

Dylan545

#7
Re: Statistical Tolerances in GD&T?

Thanks all for the responses!
I guess I was not clear in my original post. SPC, Cpk, Cp, etc. was used to establish the statistical tolerances. My guess would be the RSS method, but honestly can't remember because I remember studying the standard dist for everything also. The stack up was analyzed and some dimensions remained where they were. Some (like my parallelism) were allowed to open up, because the probability of the worse case scenario was low. Parts (and as any manufacturer believes, the process also) where approved by many tiers of customers. Flash forward to production, hard in-process gages and hard final gages were engineered and manufactured. 100% inspection methods were established and implemented, again due to part liability and not process fault. The process was proven. We, of course, stopped any data gathering, because we trust our process and could not dump any more money into the quality of this product. My question is, did we then, since stopping data collection, have to revert back to the arithmetic tolerance, according to industry standards?
I can hold my own in the GD&T world but haven't dealt much with statistical tolerances. So could someone answer me this? What is the point in opening up tolerances to 3 or even 6 sigma, when to mathematically justify this your process must hold +- 1.5 sigma? This is an exaggeration of course but it always appears to end up that way to me!

thanks again everyone.

P.S. I do believe Cp and Cpk could be used on a parallelism. I think you believe that since the target is 0 it would always be one sided curve. But in terms of studying your process you would need to got to the negative. Calling a angle one way a positive variance and the angle the other direction a negative variance.
 
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Peter Truitt

#8
Re: Statistical Tolerances in GD&T?

IMHO, you should have a contract or clear agreement with your customer that establishes the intensity of inspection. You might start out with 100% inspection of 100% of the parts, but data should begin to justify 100% (in your case?) of <100% of the parts. The goals should be 'dock-to-stock' regardless of whether or not you ever get there. You might need to get better than your customer in doing mathematical error analysis and supplier auditing and reverse-train them to audit you.

I think that statistical tolerancing establishes design requirements that might be used to ensure that a customer requirement such as MTBF is accounted for in the design. Sampling plans are there to ensure quality during production. These are two distinctly different things.
 
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Peter Truitt

#9
Re: Statistical Tolerances in GD&T?

(I don't think that statistical tolerancing in GD&T is, or ever should be, the same as what sampling plans do. Statistical tolerancing is a design specification to meet a customer requirement such as MTBF. Sampling plans fall under quality assurance.)
 
D

Dylan545

#10
Re: Statistical Tolerances in GD&T?

@Peter
pretty close to what actually happened. I pointed them toward a good GD&T class. When doing my yearly audit, we were going over the gage calibrations and someone pointed the parallelism out.
Were are D2S because of our inspection systems (although this hiccup put me through the ringer). The PO is slim at best. The print doesn't have the customary note that is suppose to follow the ST. So all that was left was our individual interpretation of the standard. Which I obviously lost!
 
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