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aasikolo
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measurement uncertainty statistics

Good Afternoon,

We've been testing a large steel enclosure in a static airspace to measure the maximum internal temperature and corresponding temperature outside of the enclosure.  We want to know the maximum temperature of the outside airspace so that the maxmum inside temperature limit is not exceeded at a 95% confidence level.  The maximum internal temperature is measured near the top of the inside of the enclosure, and the outside temperature is determined by averaging the vertical temperature measurements from top to bottom of the enclosure.  Using the temperature at the top of the encosure would result in a higher outside temperature rating causing the inside to overheat, using the lowest outside temperature would underate the enclosure.

Using these measurements we want to be able to say that X is the maximum average outside temperature so that the maximum temperature inside of the sealed enclosure, Y does not exceed Z degrees F at a 95% confidence level.  

What method should be used to calculate this result?

Please let me know if you need additional information.

Thank You

aasikolo
Math / Science

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aasikolo

8/22/2022 - Mon
Ess Kay

To be safe use the warmest part of the enclosure,


if you want to market, use the average from several temparture samples.
aasikolo

ASKER
We have taken a number of measurements, 5,000+ over several days from twelve measurement points.

I'm looking for the apppropriate method to calculate the maximum possible outside temperature at a 95% confidence level using those measurement results.  We have the uncertainty of the measurement instrumentation, but were wondering what the appropriate method was for making the 95% confidence level calculation.

Thank you.
aburr

The description of the measurements raised several questions which have a bearing on the statistical analysis of the data.
Why the measurements? for safety reasons?
" We want to know the maximum temperature of the outside airspace so that the maxmum inside temperature limit is not exceeded at a 95% confidence level.  The maximum internal temperature is measured near the top of the inside of the enclosure, and the outside temperature is determined by averaging the vertical temperature measurements from top to bottom of the enclosure"
If you want to use the max temp of the outside you must not average the outside temperature.
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"  We want to know the maximum temperature of the outside airspace so that the maxmum inside temperature limit is not exceeded at a 95% confidence level."
I am confused as to the cause and effect here. Is the outside temperature independent of the inside temp? Can you control either the outside or inside temps?
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William Peck
aburr

"Using these measurements we want to be able to say that X is the maximum average outside temperature so that the maximum temperature inside of the sealed enclosure, Y does not exceed Z degrees F at a 95% confidence level.  "
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My interpretation based on the above is that you need to do an experiment several times.
Set up the sealed enclosure and set it in an outside air space which you can heat as you wish. Take the measurements as you originally described and heat the outside air until it is Z degrees below  the inside temp Y. That will give you the X average outside temp.
Calculate the standard deviation of X and report the 95% confidence limit. The more times you do the experiment the narrower the confidence limit.
aburr

The above may not be what you want.
You could heat the inside (Y) until the outside average (X) is Z degrees below Y. Do this several times and you will have a Y value the 95 % confidence limit of which you can find.
aasikolo

ASKER
Good points.

If the measurement uncertainty for the average temperature measurement instrument outside of the enclosure is +/-0.6 degrees F, as it is the inside maximum measurement;  and

The average delta T is 14.7 degrees F with a standard deviation of +/-0.49 degrees F;

Is the maximum outside temeprature = the average - 1.645*U  to assure that the maximum inside temperature is max inside +1.645*u at a 95% confidence level;  OR

is the maximum outside temperature = the average - 1.645 *u to assure that the inside temperature does not exceed the following:

 average outside  - 1.645 *u + delta T +sqrt((U inside)^2+(U outside)^2)?  OR

is the standard error of the y estimate from linear regression to be combined with the measurement uncertainty of X and then the 1.645 k factor applied?

Please advise,

Thank you
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aburr

"Is the maximum outside temeprature = the average - 1.645*U"
I am not sure where this 1.645*u comes from.
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In my thinking I consider that the uncertainties of the measurements was much less than the uncertainties of the experiment arising form the difficulties of getting reliable outside temp measurements and making sure that all the internal and external conditions were reproducible
aasikolo

ASKER
1.645 is a coverage factor, when multiplied by the uncertainty then added to a reading, gives a result that says your reading is X, but the measurement could actually be as high as the reading +1.645*U at the 95% confidence level (one-sided).

The NIST TN1297 document refers to it as a k factor, but ut us actually a z-score.

U for the instruments were calculated using hte instruemnt specifications, but as you point out, it would be bterr to use the standard deviation of the readings.  Still, by definition, there is variability that has to be accounted for, hence the k factor.
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