Using statistical tolerance <ST> symbol to indicate design intent

[Wunderbear]

Hi,

I recently learned about this G,D and T symbol <ST> to indicate that a tolerance has been statistically allocated. After a bit of digging, I found an example of a typical note associated with this symbol (REF: dimensioning and tolerancing handbook by Paul Drake): "Tolerances identified statistically <ST> shall be produced by a process with a minimum Cpk of 1.5"

So my questions are:

1. Is this a commonly used symbol? I havent come across this symbol before on any drawings I have looked at before
2. This symbol seems useful. I have used RSS tolerancing in the past to do my stackups and I always end up making assumptions about the process with no good way of communicating this to the fab shop. To that end, this seems like a good way to communicate the "design intent" to both the shop and the inspector. What are the potential downsides of this approach? I can think of one where the inspector now has to perform a cpk study around this dimension on a statistically significant sample from every lot adding to overhead (this might not necessarily be a bad thing)

Thanks
Sid

 

[Belanger]

1. No, not at all common.
2. The downsides are that the official standard does not spell out the parameters that come with <ST> such as a Cpk value. So a note is required, and it would probably have to spell out more than just the Cpk threshold (sample size, etc.).

Another downside: Many people think that <ST> simply means that it's a critical dimension which must be tracked statistically by the QA folks. While it sort of means that, it also means that the tolerance number itself was determined by statistical methods.

John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems

 

[greenimi]

Randomization could be another issue on why this is not used very often.

 

[Wunderbear]

So how is this requirement usually communicated? If I rely on my RSS calculations, how can I communicate to the vendor the design intent that I am really hoping for him be mean centered around the nominal? In the absence of good data for the process capability, is my best bet to inflate my RSS calculations by 'benderizing' or anticipating a 1.5 sigma mean shift?

 

[3DDave]

The US DoD has MIL-STD-1916, available for free from

http://quicksearch.dla.mil/

Also see MIL-HDBK-1916 which describes how to implement the mil standard and is also available for free from

http://quicksearch.dla.mil/qsDocDetails.aspx?ident_number=205665

This is a symbol that should not be in the Dimensioning and Tolerancing standard at all.

The problem is that there is an entire branch of mathematics (Statistics) that is devoted to the subject and a little symbol in an unrelated standard doesn't cover it. Were someone to create a separate documentation standard, such as is done for Castings and Forgings, to elaborate on Standard and Uniform methods that would be cook-book copied, including exactly how data is collected, how data is processed, how the results are transmitted, and how the results affect the final products, that would be useful.

It would also include the methods that designers would use to allocate tolerances and do the tolerance analysis required to understand the requirements. My experience is that almost no designers have such an understanding. For the few who do - they can create their own documentation with little problem and there's no reason to let the ones who don't have a pretend symbol. A flag note is sufficient.

This is more like the 1982 version inclusion of 'quadrants' because they were trying to embrace the CMM makers.


Here's a document that covers some of the subject - faculty.washington.edu/fscholz/Reports/isstech-95-030.pdf

"At this point the above symbol indicates that tolerances set with this symbol are to be monitored by statistical process control methods. How that is done is still left up to the user."

Further:

"In the basic statistical tolerancing scheme it is assumed that detail part dimensions vary randomly according to a normal distribution, centered at the midpoint of the tolerance range and with its ±3σ spread covering the tolerance interval. For given part dimension tolerances this kind of statistical analysis typically leads to much tighter assembly tolerances, or for given assembly tolerance it requires considerably less stringent tolerances for detail part dimensions, resulting in significant savings in cost or even making the difference between feasibility or infeasibility of a proposed design.

Practice has shown that the results are usually not quite as good as advertised.

Assemblies often show more variation in the toleranced dimension than predicted by the statistical tolerancing method. The causes for this lie mainly in the violation of various distributional assumptions, but sometimes also in the misapplication of the method by not understanding the assumptions. Not wanting to give up on the intrinsic gains of the statistical tolerancing method one has tried to relax these distributional assumptions in a variety of ways. As a consequence such assumptions are more likely to be met in practice."

It is not a simple subject and it was a huge mistake to add a symbol for it without a complete explanation of all the known expected effects and contractual obligations.

 

[chez311]

3DDave,

Thats an excellent - well thought out post. I was always a little perturbed by the addition of the <ST> symbol with what seemed like an afterthought - I understand the desire to provide a tool that knowledgeable designers can utilize to their discretion, but I have to imagine that many people see that and think they can apply it to their print with the hope that they are somehow invoking the magic of statistics without doing the proper analysis or without knowing enough about the processes which create those features.

The only thing I would add is that there is the suggestion in the standard that one could put two different set of tolerances on a single feature, one marked with the <ST> symbol to be controlled within specified statistical limits (looser "extremes" with an assumed normal distribution around nominal) and another to be controlled to only the arithmetic limits (tighter "extremes" with no assumption of normal distribution). This is shown in Fig. 2-25. I doubt that this is a common practice, and I have never personally come across it.

Practice has shown that the results are usually not quite as good as advertised.

Assemblies often show more variation in the toleranced dimension than predicted by the statistical tolerancing method. The causes for this lie mainly in the violation of various distributional assumptions, but sometimes also in the misapplication of the method by not understanding the assumptions. Not wanting to give up on the intrinsic gains of the statistical tolerancing method one has tried to relax these distributional assumptions in a variety of ways. As a consequence such assumptions are more likely to be met in practice.

Could you explain this quote? I'm not sure exactly what is being said here - I get the gist, it just seems like the last sentence seems to contradict the first.

 

[3DDave]

I think the two fit together - if the prediction for 3-sigma is X and the actual produced 3-sigma result is 1.5*X, then that is not a good result because there is greater variation than predicted.

 

[dgallup]

This is pretty widely used in automotive applications where there can be a lot of dimensions in a stackup. The automotive quality standard TS16949 uses the notion of critical characteristic symbols and usually one of them is <ST>. It's a bad system in that the symbols are not standardized but vary by the end customer. Each customer will have a quality manual that defines the symbols and what is required for each one.

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

 

[chez311]

3DDave,

Nevermind - I understand what is being said now, took me a little bit for some reason. The last two sentences describe the solution, not the initial problem - he's saying that in order to meet whats found in real world assembly the assumptions need to typically account for greater variation (ie: be relaxed). Sounds like a roundabout way of saying that statistical tolerancing is best applied after verification with measurement of real world parts and assemblies, otherwise you don't know if the methods/factors you're using are even valid. That or if thats not feasible or available, then apply a factor to create arbitrarily loose tolerances, hopefully based on previous measurements of a similar part or processes.