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View Full Version : The Logic behind Tolerance vs. Least Count 1/10 Ratio


sarasheed
23rd February 2008, 07:03 AM
This is a good old doubt. What is the logic behind useing a measuring Instrument whose least count is 1/10 of the tolerance of item to be measured? Why not 1/3 or 1/4 as many people recommend?
Is there any standard to justify either of the above cases ?

sarasheed.

Bev D
23rd February 2008, 09:12 AM
basically it comes down to what you want to do with the data and how many false rejections you are willing to tolerate.

when you use a gage that is only 1/4 to 1/3 of the tolerance then you essentially have only 3 to 4 possible results. This is essentially ordinal data. Standard deviation calcualtions will be overinflated so you woudl need to treat the results as 'attributes' data (pass / fail or categorical data)

depending on the criticality of the characteristic either choice may be viable.

BradM
23rd February 2008, 12:10 PM
A[art from Bev's good explanation, here is a paper that Transcat offers from their website on the subject. The graphs may help visual understanding.

Duke Okes
23rd February 2008, 04:18 PM
I believe an old standard such as 45208 or 45662 required a minimum of 1/4, but that obviously gives a higher level of measurement uncertainty.

Stijloor
23rd February 2008, 06:30 PM
This is a good old doubt. What is the logic behind useing a measuring Instrument whose least count is 1/10 of the tolerance of item to be measured? Why not 1/3 or 1/4 as many people recommend?
Is there any standard to justify either of the above cases ?

sarasheed.

Hello sarasheed,

Here is a very simple, non statistical example that I use when teaching metrology.

Using the metric system (based on the factor "10") as an example:

When you're measuring whole millimeters (mm), you want the variations to visible in in 1/10th (0.1) of the values.
When you're measuring in 0.1 of a mm, you want the variations to be visible in 0.01.
When you're measuring in 0.01 of a mm, you want the variations to be visible in 0.001.

Hope this helps.

Stijloor.

Bev D
24th February 2008, 09:53 AM
This is a good old doubt. What is the logic behind useing a measuring Instrument whose least count is 1/10 of the tolerance of item to be measured? Why not 1/3 or 1/4 as many people recommend?
Is there any standard to justify either of the above cases ?

sarasheed.

One more point: I wouldn't use a "standard" as justification for anything. Good statistical and engineering knowledge shodul be combined with practical knowledge of the characterstic and it's design/use intent to determine how much resolution is necessarry for the measurement system.

As I've said before, there is no substitute for good old fashioned thinking. A standard or a rule of thumb or someone's random suggestion is no substitute for knowing what one is doing. The world is not comprised of 'cookbook' solutions.

Jim Wynne
24th February 2008, 10:58 AM
One more point: I wouldn't use a "standard" as justification for anything. Good statistical and engineering knowledge shodul be combined with practical knowledge of the characterstic and it's design/use intent to determine how much resolution is necessarry for the measurement system.

As I've said before, there is no substitute for good old fashioned thinking. A standard or a rule of thumb or someone's random suggestion is no substitute for knowing what one is doing. The world is not comprised of 'cookbook' solutions.

Exactly.:agree1: With each instance of a need for measurement, a decision has to be made with regard to resolution of the results. Sometimes 10:1 might be overkill, and sometimes it might not be enough. It's a matter of understanding variation, and what you need to know about it.

Duke Okes
24th February 2008, 11:56 AM
Standards for what color the lights should be for stop, caution and go are quite useful, as are how to design electrical outlets. So while standards do not always apply to every situation, they greatly reduce the amount of variation we have to deal with. After all, specifications are standards, just not necessarily developed by a standards body (although in the case of types of steel, aluminum, etc. they are).

Jim Wynne
24th February 2008, 12:14 PM
Standards for what color the lights should be for stop, caution and go are quite useful, as are how to design electrical outlets. So while standards do not always apply to every situation, they greatly reduce the amount of variation we have to deal with. After all, specifications are standards, just not necessarily developed by a standards body (although in the case of types of steel, aluminum, etc. they are).

I don't think anyone is saying that standards aren't useful and needed in some instances, but we need to differentiate between vague rules of thumb with uncertain provenance and actual standards.

Bev D
25th February 2008, 06:13 AM
Standards for what color the lights should be for stop, caution and go are quite useful, as are how to design electrical outlets. So while standards do not always apply to every situation, they greatly reduce the amount of variation we have to deal with. After all, specifications are standards, just not necessarily developed by a standards body (although in the case of types of steel, aluminum, etc. they are).
Of course the types of standards you reference are useful and in many cases very desired.
However, your examples are not the same as the type of 'standard' that was meant. I thought I was fairly clear that my reference to a standard was limited to the OP's use in his question: wanting to know if their was a standard to justify the use of a 1/4 or 1/3 resolution of a measurement system.

The two standards you mentioned that might justify a 1/4 resolution are decades old and come from a time when computers rare or at least not commonly used and analyses were done by hand...they have both been primarily superceded, one by ISO9000.

:caution:WARNING: WHAT FOLLOWS IS A RANT. IT IS NOT FIRED DIRECTLY AT THE POSTER QUOTED ABOVE BUT TO BE A GENERAL STATEMENT THAT WILL NO DOUBT TAKE THIS POST OFF TOPIC.:mad:

However, my concern is not the age of these standards but my original statement regarding using logic and reason to determine the resolution that will be useful given the application. Just because a standard says so, doesn't mean it's true.

In general I am more concerned that the quality profession has moved further from thinking and closer to a simple "if a standard or my Customer says I have to do this to comply, or if I can get a standard to justify my lack of thoughtful input or learning that's what I'll do and no more."

Have we all lost our collective minds?

Many on this forum provide - or attempt mightily to provide - thoughful input to questions posted here. the input is meant to teach, learn, explore, reason and hopfully in the end raise the collective usefullness of all who come here.

Now I know that I am most likely merely annoyed by some of the recent posts that seem to have been looking for "agreement" statements to "prove" their point as if we can vote to change the laws of physics; or even the less benign but far more troubling "I've just appointed to implement SPC, or Capability studies or FMEA or whatever and I have no idea how to do this or what it means". I feel for these posters. Their managment has essentially said "this is a requirement; someone has to ensure that we comply to it and I picked you". There is no concern about doing the right thing; only about doing what is necessarry to comply. These situations simply tarnish our profession. Blind compliance to a requirement does not provide quality. But it seems more and more that this is all we have time to do. The proliferation of 'standards' that dictate exactly how to apply quality are obviating our need to think and reason and improve. (my sincere apologies to those who just blew their morning coffee thru their noses; that must have hurt! and for those who are firing up to tell me how useful ISO or AS or whatever is, let me say now that I agree that standards have usefullness; just not when all logic and reason are suspended in their application and execution)

I would refer to Bert Gunter's "Final Fusillade" in his Statistics Corner column for the April 1998 issue of Quality Progress. He states it much more eloquently than I ever could:

"What is the state of the quality profession today? In a word, deplorable. I am frankly dismayed by what I believe has been a retreat from the activism and professionalism of 10 years ago to what seems to me to be a return to the bad old days of passive checking of conformance to rules...This
is all form and no substance, much like the old (and superseded, I hope) military procedures that required 30 pages of documentation to assure that off-theshelf commercial underwear met requirements."

Well, I guess that about does it. I'm going to hit "submit reply" before I lose my nerve

Jerry Eldred
25th February 2008, 11:32 AM
I don't believe the issue is T.U.R. (ratio between the cumulative uncertainties of a measurement standard and unit being calibrated). The issue here, I believe is resolution versus tolerance (which is a completely different issue). I will address it then from that perspective.

Resolution must by logic be better than a tolerance. To resolve a given tolerance, you need adequate resolution to adequately discern it. As digital displays function in decade format, the only plausible method to accomplish satisfactory resolution for a given tolerance is for the resolution to be better than the tolerance. Most all digital displays also have a built in "slop"; that is, plus or minus one count. Therefore this being considered, it is not possible to legitimately arrive at a tolerance without at least a 10X increase in resolution.

I believe some of the QS9000 subdocuments used to require this in MSA. I don't know, but do assume that TS16949 adopted such principles; which I understand to be based on the above logic implicit in measuring circuits.

They used to call it a "Precision to Tolerance Ratio."

I know this topic has been beat to death; but as I haven't been able to post in a few days, please pardon me for "my two cents.":D

BradM
25th February 2008, 12:25 PM
Standards for what color the lights should be for stop, caution and go are quite useful, as are how to design electrical outlets. So while standards do not always apply to every situation, they greatly reduce the amount of variation we have to deal with. After all, specifications are standards, just not necessarily developed by a standards body (although in the case of types of steel, aluminum, etc. they are).

I agree with Duke on this one. You have to start somewhere, otherwise you will have such a stratification in results that diminishes from the advancement of the discipline.


....but as I haven't been able to post in a few days, please pardon me for "my two cents.":D

Jerry, I will take your two cents any day of the week! Thank you.