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# In Tolerance or Out of Tolerance?

01/08/2010 2:27 PM

Hello, this has been asked before (or very similar at least) but I cannot find the thread (I have searched but no luck).

We have specified that a temperature sensor shall have an uncertainty of measurement of 0.1oC. However when I reviewed the calibration sheet it stated that the uncertainty of measurement was 0.14oC or 0.16oC (I can't remember which and it does not matter).

The question was then asked if the temperature probe was within specification. I answered "Yes" because we had only specified 0.1 and not 0.10. Had we specified 0.10 then the sensor would be out of specification. Basically we had only specified one decimal place.

My question is: Am I correct in my thought process. If not why not. If I am correct but my thought process is incorrect would you knidly explain why.

Joe

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#1

### Re: In Tolerance or Out of Tolerance?

01/08/2010 4:07 PM

I think you're mixing tolerance and uncertainty. But, anyway, if you're talking uncertainty, I think (and this isn't 100% positive since I recently changed my mind) you round up. So 0.14 rounds up to 0.2. Thus, it's out of your spec.

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#6

### Re: In Tolerance or Out of Tolerance?

01/09/2010 12:30 AM

Since when did 0.14 round UP to 0.2? To me, there is no question up to 0.14999 - anything UNDER 0.15 rounds down to 0.1; anything OVER 0.15 rounds up to 0.2. The only question is 0.150; in that case I favor rounding it to the even result.

Now on logarithmic scales it could be another story, but I think it would be rare that anyone measuring temperature to 0.1° precision would be doing so on a logarithmic scale.

Thus 1.4 or 1.6 does make a difference in my mind. Also, as Redfred has stated, it does depend on whether the 1.6 is a 'window width' (±0.08) or really means ±0.16.

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#10

### Re: In Tolerance or Out of Tolerance?

01/09/2010 7:42 AM

I'm with you on this one, rightly or wrongly!!!

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#11

### Re: In Tolerance or Out of Tolerance?

01/09/2010 8:54 AM

In uncertainty, I believe (I'm only about 80% certain) that you always round up. I'll have to check that, but I would like to see the OP clear up whether this is a tolerance or an uncertainty first.

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#12

### Re: In Tolerance or Out of Tolerance?

01/09/2010 1:45 PM

I am refering to uncertainty and not to tolerance.

Mike

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#13

### Re: In Tolerance or Out of Tolerance?

01/09/2010 2:47 PM

OK, thanks. So, if 0.1° is the uncertainty, that represents (at least sort of) one standard deviation. Your spec is ambiguous, but you should probably look at this way. 0.1° represents an absolute uncertainty. If you start using round-off or significant figures on this, you're in essence adding a relative uncertainty to an absolute uncertainty.

Long ago, when I used to make transformers, I had an electrical inspector who tried to pass everything. One day he called me down and said, "I see where the no load current has to be 0.16 A +/- 0.03 A, so that's a minimum of 0.13 A and a maximum of 0.19 A, but how much tolerance am I allowed on the maximum?"

So, +/- 0.14° exceeds +/- 0.1°.

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#9

### Re: In Tolerance or Out of Tolerance?

01/09/2010 7:03 AM

0.14 is rounded to 0.1 and 0.16 to 0.2, even 0.15 is rounded to 0.1

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#2

### Re: In Tolerance or Out of Tolerance?

01/08/2010 4:56 PM

Your specification is poorly worded. There would be no ambiguity if you had specified the uncertainty "not to exceed" 0.1 degrees. Assuming you have a valid reason for this specification, then the sensor does not meet the specification. If, on the other hand, the specification was randomly selected just so that the buyers would have something to reference, then maybe it can be used for your application.

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#3

### Re: In Tolerance or Out of Tolerance?

01/08/2010 6:32 PM

I believe the "not to exceed" is redundant. The level and tolerance has been set.

Until you get to .2 you are OK.

I agree that the sensors MAY be usable, indeed, are usable according to spec.

My level of uncertainty on just about everything must be in the 70's.

Cheers.

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#4

### Re: In Tolerance or Out of Tolerance?

01/08/2010 11:04 PM

I found this: http://www.measurementuncertainty.org/

which I found useful.

Specifications always appear wonderfully watertight prior to the tender and then somehow manage to leak water when it comes to the claims period of the contract :-)

A key question is "So what and does it matter?". Effectively, does your application really need 0.1000 accuracy anyway? Would it suffice to have 0.2000 (in this case 0.14/0.16)?

It doesn't help oil the contract wheels to insist on these things if it doesn't really matter.

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#5

### Re: In Tolerance or Out of Tolerance?

01/08/2010 11:51 PM

The precise phrasing of your written specification and the sensor manufacturer's specification will be the deciding factor. If you specified a tolerance of of ±0.1°C and the manufacturer states a tolerance window of 0.16°C then they meet your tolerance window of 0.2°C.

The most critical question though is do you really require this precision? Temperature measurements frequently suffer from much larger reading errors from an impatient reading done before thermal equilibrium has happened and from naturally occurring thermal gradients that mislead what should be the "real" temperature.

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#7

### Re: In Tolerance or Out of Tolerance?

01/09/2010 4:25 AM

Ideally tolerance should have been specified in a range like +/- 0.1oC or "0 to 0.1oC" etc. In this case if you have specified just 0.1oC, it means uncertainity will be less than or equal to 0.1 C. So 0.14 is definitely out of spec irrespective rounding method and for that matter anything more than 0.10000000 (n zeroes) is out of spec whether you specified in single decimal or double decimal.

- JP Reddy

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#8

### Re: In Tolerance or Out of Tolerance?

01/09/2010 5:16 AM

Hello All,

I think you should all go back to the original question and see what the op wrote. I think you are all mixing up : Precision, Tolerance, Accuracy and Uncertainty. The op asked about the uncertainty (unforutnately the op used the words Tolerance in the title). The uncertainty of measurement is not the same thing as the tolerance, it is not the same thing as accuracy and it is not the same thing as precision. In addition I would imagine that the uncertainty was ±0.1oC and not 0.1oC as stated by the op (however this is only my guess). Non scientific people prefer to use the word accurate rather than uncertain (because an accurate instrument sounds better that an uncertain instrument) but the problem with using the term accuracy is that it inherently assumes that a true value can be defined, known and realised perfectly.

There is a rule in metrology that states that the measurement uncertainty shall be less that 10% of the tolerance. If this rule is met then there is practically no influence of the measurement uncertainty to the tolerance.

Congratulations to lynlynch as he/she is the only one that has gotten the answer correct. The op has only specified one decimal place for the uncertainty and therefore that is all that is applicable. What should have been requested was to report the measurement uncertainty to one decimal place (or else specify two decimal places) then this issue would not have arisen.

Mike