Statistics

[3DDave]

The latest version says:

statistical tolerancing: the assigning of tolerances to related components of an assembly on the basis of sound statistics (e.g., the assembly tolerance is equal to the square root of the sum of the squares of the individual tolerances).

The problem I have with this is that this isn't statistics, which is the study of values to determine what the characteristics of a population are - usually, but not limited to: mean, deviation, skewness, and kurtosis.

What appears to be the suggestion is based on assuming a distribution, et al, to predict the amount of acceptable produce, which is the whole reason probability exists.

Statistics is if one looks at the results of a production run to generate a representative distribution and then one can use probability to decide if the required combined variations will have an acceptable rate (might not be 100%).

Predictions are from probability; statistics are from variation.

So it should be Probability Tolerancing.

 

[3DDave]

Just to add - the later depictions don't help the case much. The "statistical" control of a hole and the mating feature don't represent enough terms to allow Root Sum Square (RSS) simplifications to be valid.

If one wants this sort of control then the appropriate identification is "process limit" tolerancing where the exact factory process and all related equipment and management of same is documented and from which the prior production statics have been analyzed to ensure the mean, the deviation, the kurtosis, and skew are understood. More to the point, it's really just a marking that indicates a clearly defined internal company process control is to be used and that process control should be uniquely identified for that dimension/feature; it may not even need a tolerance value on the drawing as QA and QC and manufacturing all have to agree on the controls that will be put on the process to obtain the system level results. The system level analysis will have the details.

It makes sense on a large production run if one characteristic is running close to or over the process limit to look if there is matching under run in a mating part and change the process limits. As long as the on-drawing tolerances aren't violated it should not require any more than as-built tracking, certainly not any more than manufacturing ever telling engineering what the distribution of variation of finished items is**.

Just tossing it over the wall doesn't create a worthwhile requirement.

The topic would be best moved into a document that covers probability and statistics as well as typical distributions of variation in manufactured items as well as measurement repeatability and reproduciblity. Even mentioning RSS is likely to do damage without the background about why central limit theorem is important as a basis for it.

Aside from the need for a sufficient stack to make use of the RSS simplified formula, there should be a never-exceed tolerance on the dimension/feature. Normally, that would be the typical tolerance that is selected - for example the maximum diameter of a hole should be allowed to get as large as will avoid the matching screw pulling the matching washer into it. That would also unfortunately eliminate the ability to make the process tolerance larger.

**This was critical in the 737 hard-over rudder crashes. It turned out the maker of the hydraulic valve sometimes fit an MMC spool into an MMC valve body - which left too little clearance for the thermal transient response from having hot, recirculated hydraulic fluid get introduced into the cold-soaked valve body. This produced a temporary interference fit that drove the fail-safe internal sleeve to full excursion and forced the rudder to the limit in reverse of the pedal application.

Engineering only got the information because of the crash investigation and only when the specific failure mode was identified as a suspect. Both crash aircraft had parts on the measure-limit edge of the specification. Several other valves were identified and replaced on operating aircraft.

 

[drawoh]

3DDave,

Is there any reason to assume that the applied tolerance has some connection to a Gaussian distribution curve?

Consider an assembly consisting of a set of stacked 1/4" plates. It is very likely that all the parts were cut from the same plate, manufactured by the same process, with the same dimensional error.

What would a distribution curve look like on positional tolerances on a CNC machine? Would they be Gaussian, or would they somehow reflect clearance in the milling machine's gears? If I inspect them and they are within tolerance, is there any reason why I would care?

How about I have two different vendors for my parts, both of whom meet my tolerances. One of them persistently skews towards the high side of the tolerance, and the other skews towards the low side. Should I care?

--
JHG

 

[3DDave]

As I mentioned - sometimes the individual feature/dimension distribution matters a great deal. People died on the 737 hard-over rudder crashes due to that factor. That covers your last question. It's tough to say if you should care , but you should know if you should care - just the same as if the material properties from two suppliers were different.

Not sure about the connection vs. Gaussian curve question. If one has enough elements in a stack and the elements each have some distribution - uniform, skewed, et al - the resulting outcome will have a normal distribution. The trick is calculating the mean for non-symmetrical distributions.

I'm also unsure about the stacked plate question - if that is a single assembly it doesn't have a distribution. If you are calculating all possible stacks made from all possible plates - that will have a distribution from which one can calculate the odds that a stack will end up within a range that is part of that distribution, though I think if it's a smaller sample it's variance which may be close to the distribution (and that difference is why this should not be in the Dimensioning and Tolerancing standard and should have its own separate one.)

I did have occasion to work out a problem with a stack of 3 parts, but the measured area included 3-4 dimensions in each part to complete the path, so it got between 9 and 12 contributors. It was an interference problem that prevented assembly. I measured the assembly gap on 10 sample assemblies (not interfering) and calculated the mean and standard deviation. From this I looked up what the odds are that the clearance would be less than zero. It came to 1 in 20, which was the error rate detected in the factory.

That failure was because the QA people had been futzing with the process and changing the ;art process means for some reason. It was s dysfunctional factory and they jealously guarded every scrap of information. My favorite - when it was discovered that a #10 screw was being installed into a #8 hole in a purchased part. When asked to confirm, one of the crack (smoking) team got a part off the shelf and fit a #10 screw through the holes. Turned out, rather than tell engineering there was an error, they had been taking the purchased parts and just drilling the holes to fit.

When I asked to help adjust the process to work I was told they would handle it. Why use math when one can scrap $10-20k parts at a 5% rate? I expect they moved the mean target back to where it was. They were items that were unlikely to be replaced during the life of the product and they could easily have taken measurements and then made matching selections.

 

[geesaman.d]

Predictions are from probability; statistics are from variation.

So it should be Probability Tolerancing.

You're right, but even sound engineering concepts benefit from good marketing. And there's no way you're getting a "probability" of success past most quality and management people.

 

[BiPolarMoment]

How about I have two different vendors for my parts, both of whom meet my tolerances. One of them persistently skews towards the high side of the tolerance, and the other skews towards the low side. Should I care?

(emphasis mine)

We don't all have the luxury of walking into a situation where all the tolerances were properly vetted or just as likely: even manufactured to those tolerances much less QC checked to them. So, in this case I would care how the present manufacturer(s) are delivering parts to increase the likelihood of a functional assembly since I know our drawings are presently inadequate.

But that's my situation, I walked into it.

 

[geesaman.d]

"...Should I care?"

We don't all have the luxury of walking into a situation where all the tolerances were properly vetted or just as likely: even manufactured to those tolerances much less QC checked to them. So, in this case I would care how the present manufacturer(s) are delivering parts to increase the likelihood of a functional assembly since I know our drawings are presently inadequate.

But that's my situation, I walked into it.

1) If a part is within my tolerances, and the stackup math looks better if they were in a different region of the allowable tolerance zone, that's entirely a problem on my end. Measure them and sort them myself or buy to a tighter tolerance. It's well known that sheet metal is consistently produced on the thin end of the thickness tolerance, stainless contains the bare minimum amount of nickel and chromium, etc. So applied to statistical / probabilistic tolerancing, this is a real thing and needs to be predicted and/or monitored. But it's not the vendor's problem who is executing the part to the drawing, unless you made it a special requirement all along.

1a) As for the 737 valve example, it sounds like the manufacturer needed to adjust tolerances or perform a final diametral clearance check at the assembly step. It also seems like a stupid place to use statistical tolerancing - it's only two features / two tolerances.

2) I agree that there are many engineering environments (very small quantity, even one-off lot sizes) where the tolerances are calculated as sensibly as they can be considering they will be used just once. The prototype is often the only production copy. Lot quantities lack statistical significance. An OOT condition on one piece can be directly evaluated with the mating parts actual condition before it gets rejected. The tolerances are a guideline to assuring success at final assembly and test, and the success at final assembly overrides any tolerances. It's not a problem to be corrected nor a situation to apologize for; it's simply different. I've spent my career in such environments and it would be a luxury to pretend my tolerances are always met, much less that they be a bell-curve centered on the mid-tolerance.

 

[3DDave]

1a) As for the 737 valve example, it sounds like the manufacturer needed to adjust tolerances or perform a final diametral clearance check at the assembly step. It also seems like a stupid place to use statistical tolerancing - it's only two features / two tolerances.

That's a different case than I was describing and was in concern of "does the buyer care if they are at different ends of the tolerance zone." In that case it turned out that they should have. That's not a statistical management problem though statistics was used to determine where other similar problem valves were used. They could have used that information after the first crash, but didn't understand the need to.

They did effectively determine the clearance; it was within specification - they just didn't understand the transient thermal condition that altered that clearance.

"Statistical tolerance" as described in the standard aren't statistics - they are probability. The "worst case" stackup method is a probability calculation where the presumption is that there is a specific distribution which the standard fails to define.

Even on a quantity of one the manufacturing method used will likely have a distribution. What diameter hole results from a certain size drill bit, over the hundreds of holes that are drilled on previous parts. What location error there is from where holes were intended to be over the hundreds of holes that are drilled. One can use those statistics to develop the distributions and then one can select/adapt designs that are tolerant to likely variation and decide what will give an acceptable likelihood the part/assembly being designed will be compliant and that with those variations will still have acceptable performance.

My previously associated factory refused to keep feature-level information. Their assembly line had screwdrivers, wrenches, and die grinders.

What's sad is if the perception of "statistics" is better than "probability" the reason for that difference is ignorance of both.

tl;dr - statistics is what one does in the factory about past efforts; probability is what one does in design and manufacturing engineering about future efforts.

 

[drawoh]

We don't all have the luxury of walking into a situation where all the tolerances were properly vetted or just as likely: even manufactured to those tolerances much less QC checked to them. So, in this case I would care how the present manufacturer(s) are delivering parts to increase the likelihood of a functional assembly since I know our drawings are presently inadequate.

I am assuming that my tolerances are assigned based on my needs. I have a good understanding of how accurate manufacturing is, and I make my designs work. If we all agree that the drafters are f%^&*king idiots, that the fabricators are f%^&*king idiots, and that the inspectors are f%^&*king idiots, then there is no point collecting statistics.

There was a good discussion a few years ago on how manufacturing copes with drawings...

thread1103-322065

--
JHG

 

[BiPolarMoment]

I don't know if you misinterpreted; I was saying that *do* I trust *you* to do those things for *your* own work.

 

[3DDave]

That's a good link.

15 May 12 15:19
The automotive ISO quality standard TS16949 defines critical characteristics and their symbols. These are supposed to be decided on during your APQP multifunctional group meetings although usually design engineering decides on 90% of them. Generally it's going to be the dimensions that have the smallest tolerances, affect fit/function or have safety and regulatory affects.

Having these things specified on the part drawing is better than letting someone with no knowledge of how the part works arbitrarily decide what to measure.

Which is a good basis for why "Statistical Tolerancing" has no place in Y14.5 as it is and would be too complicated to add to be useful. In some other document, just like they did for the specialized Casting detailing requirements, the symbols and so forth can be explained. But it's going to take agreement from an APQP group as a whole as to what is being monitored and what calculations/predictions concerning product performance are appropriate based on that ability to monitor.