Dimensional Tolerance Stackups other than Worst Case

[farmer2]

I seem to recall a method that relies on probability or some percent likelihood of tolerancing parts rather that the worst case max and mins which will not occur.

Does anyone know what this is? Is there some published standard or paper?

Thanks,

 

[MintJulep]

Monte Carlo

 

[IRstuff]

Another approach is to RSS the contributory tolerances.

In either case, you need to consider whether certain tolerances are coupled, i.e., they move together.




TTFN

 

[dimjim]

I have seen papers published that were dependent
on how many part per 100 or 1000 that you would
consider an acceptable standard based on normal
probability curves. It may have been Erichello's
book on Precision Gearing. I would guess a
.75 percent of allowable tolerance plus and
minus would be acceptable rather than the full
100 percent of tolerance.

 

[Pud]

I do believe it is called "Statistical Tolerancing".

Here is one of 12,500 - odd Google hits...

http://www.variation.com/techlib/ta-2full.html

Cheers

Harry

 

[tygerdawg]

Juran's Quality Manual discusses statistical tolerancing if I recall. For example, in an assembly of parts, the individual tolerances of each part stacked up will be outrageous...and unrealistic. Statistical tolerancing indicates that IF (that's a big IF, and only IF) all of the component parts have processes that are in statistical control, then the stackup can be reduced through root-mean-square calculation. Isn't valid otherwise.

TygerDawg

 

[farmer2]

IRstuff and MintJulep, could you show the resulting range and equations for the following example using RSS and Monte Carlo:

OD of part = 3.500 +/-.005
ID of bore = 3.513 +.000, -.005

Thanks,

 

[Heckler]

Here are the models that I'm envolved in. But remember garbage in = garbage out when it comes to manipulating data. We are currently having problems implementing these tools through out the company.....it's almost impossible to drive metrics from the shop floor up through management.

TOLERANCE MODEL CHARACTERISTICS

Worst Case - Assures 100% assembly acceptance if all parts are within specification. Costly design model. Requires excessively tight component tolerances

Root Sum Square - Assumes Normal distribution and ±3 tolerances. Some fraction of assemblies will not meet specification. May adjust ZASM to obtain desired acceptance fraction. Less costly. Permits looser component tolerances.

Six Sigma Assembly Drift - The same as the Root Sum Square equation with Zp (equal to the number of process standard deviations in each tolerance) replacing Zi.

Six Sigma Component Drift - Most realistic estimates. Accounts for process mean shifts and their long-term affects on assembly distribution.


Best Regards,

Heckler
Sr. Mechanical Engineer
SW2005 SP 5.0 & Pro/E 2001
Dell Precision 370
P4 3.6 GHz, 1GB RAM
XP Pro SP2.0
NVIDIA Quadro FX 1400
o
_`\(,_
(_)/ (_)

Never argue with an idiot. They'll bring you down to their level and beat you with experience every time.

 

[tlee123]

farmer2,

Worst case with your numbers:

max OD of smaller part = 3.505
min ID of larger part = 3.508

So, as long as the parts to made to spec, the min diametral clearance would be .003. Therefore, with in-spec parts, you have 100% chance of the parts fitting together without interference.

In your case, how are the parts inspected? If you're inspecting a sample of the incoming lots, there's a chance the parts might not all be to spec and therefore could cause an intereference. What's your situation?

 

[farmer2]

tlee123,

Thanks for the reply. I realize the worst case min is .003. All parts are inspected.

What I was looking for was a statistical analysis of the min and max clearance which is not based on worst case. By using a different tolerance range, the max clearance could be reduced.

 

[GregLocock]

The exact answer to that depends on the distribution of your tolerances. Assuming a normal distribution is unsafe in many components.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[vonlueke]

As I understand it, root mean square (RMS) isn't used for tolerance stack-up. It might be used for a single tolerance (?). I assume tygerdawg meant root sum square (RSS).

Apparently "statistical tolerancing" is an ambiguous term for root sum square (RSS), the latter being more descriptive.

farmer2: Assuming your tolerances are normally distributed (which is the best assumption you can make in the absence of further information, because the normal distribution is very common in a majority of physical phenomena), then if you use 0.667 of each tolerance, i.e., x = 0.667(tol1 + tol2 + ... + toln), this gives you 2*sigma standard deviations, which gives you, on the average, a 95.4% certainty for each individual tolerance (not the stack-up).

If you stack two tolerances, what is the probability they'll both be at this 0.667 extreme edge simultaneously? (1-0.9545)^2 = 0.0021. In other words, the certainty is 99.8% that the stack won't exceed 0.667 times the summation of worst-case tolerances. (The certainty is actually even higher, considering that the probability of getting both positive or both negative extreme tolerances simultaneously is actually even lower than 0.0021, but let's not go there since the certainty is already more than high enough for practical purposes.)

So, taking your example, first convert your asymmetric tolerance to a symmetric tolerance; i.e., ID = 3.5105 +/-0.0025, OD = 3.500 +/-0.005. Then, assuming all tolerances are normally distributed, you can say with a 99.8% certainty, gap = (3.5105-3.500) +/-0.667(0.0025+0.005) = 0.0105 +/-0.005. If you stack three or more tolerances, the certainty just increases.

 

[winpop123]

I have a different point of view than a majority of the posts so far but here goes....

First I have never used statistical tolerancing. I have used GD&T per ASME Y14.5 off and on for a number of years.

A couple of key points are that as a design entity you always have to make your designs so they fit at worst case. Unless you have a special case at your company where you make every part, how do you control who Purchasing has make your parts? I have always designed parts to always fit at worst case condition and don't have any "outragoues tolerances".

Statistical tolerancing is probably a valid way to do things in theory but in my "real world" it would never work.

 

[IRstuff]

And that's been the fundamental problem in US manufacturing for at least 30 yrs. Designers allow for the worst case and suppliers are more than happy to take the worst case.

The only problem is that every part becomes the "worst case," and there is almost never a "nominal" case part.

TTFN

 

[MintJulep]

Farmer,

I couldn't do the calcs these days without blowing the dust off a statistics text.

As Greg writes, you need to know the distribution of variations to do either.

 

[MechNorth]

Statistical Tolerancing is the alternative to worst case. To use it, however, your manufacturing group needs to provide you with their production statistics for the appropriate machines / processes / features. It's not a minor undertaking, and as indicated above, it's even harder if you have a non-Normal distribution. For a Normal distribution, determine how many sigmas you want to control within, set the mean as the nominal for your calculations and the acceptable limits as your tolerances, and work from there.

Statistical tolerancing does not have to be put on the drawing for you to use statistics in a "typical case" rather than "worst case" scenario. You can substitute the production stats into the worst-case stack-ups to find a typical case instead. This will quiet those that doubt the "worst case" results as having "never happened, and never will".

A comment was made above about statistical tolerancing being an interesting theory and not being in the "real world". That is true for many companies that do not understand the reason for going this route. Where you don't require that every part-A will fit with every part-B, but that rather eventually every part-A will mate with some part-B, then statistical tolerancing can save you sums of money. Ever had a screw that didn't fit in the first hole that you tried, so you went and tried it in another hole where it did fit, then grabbed another screw from the same batch and fit into the first hole... that's statistical tolerancing at its simplest. Statistical processing is used in making bearings, automobiles, fasteners, electronic components,...




Jim Sykes, P.Eng, GDTP-S
Profile Services
CAD-Documentation-GD&T-Product Development

http://www.profileservices.ca