Solved

measurement uncertainty statistics

Posted on 2012-12-26
11
228 Views
Last Modified: 2013-01-15
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
0
Comment
Question by:aasikolo
  • 6
  • 4
11 Comments
 
LVL 15

Expert Comment

by:Ess Kay
ID: 38721879
To be safe use the warmest part of the enclosure,


if you want to market, use the average from several temparture samples.
0
 

Author Comment

by:aasikolo
ID: 38721980
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.
0
 
LVL 27

Expert Comment

by:aburr
ID: 38721988
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.
-
"  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?
0
 
LVL 27

Expert Comment

by:aburr
ID: 38722027
"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.  "
-
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.
0
 
LVL 27

Expert Comment

by:aburr
ID: 38722034
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.
0
IT, Stop Being Called Into Every Meeting

Highfive is so simple that setting up every meeting room takes just minutes and every employee will be able to start or join a call from any room with ease. Never be called into a meeting just to get it started again. This is how video conferencing should work!

 

Author Comment

by:aasikolo
ID: 38722131
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
0
 
LVL 27

Expert Comment

by:aburr
ID: 38722164
"Is the maximum outside temeprature = the average - 1.645*U"
I am not sure where this 1.645*u comes from.
-
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
0
 

Author Comment

by:aasikolo
ID: 38722189
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.
0
 

Accepted Solution

by:
aasikolo earned 0 total points
ID: 38762785
This link from NIST answers the question

http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd132.htm
0
 

Author Comment

by:aasikolo
ID: 38762998
The link answers the question
0
 

Author Closing Comment

by:aasikolo
ID: 38777550
This link answers the question
0

Featured Post

How your wiki can always stay up-to-date

Quip doubles as a “living” wiki and a project management tool that evolves with your organization. As you finish projects in Quip, the work remains, easily accessible to all team members, new and old.
- Increase transparency
- Onboard new hires faster
- Access from mobile/offline

Join & Write a Comment

Suggested Solutions

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
Article by: Nicole
This is a research brief on the potential colonization of humans on Mars.
It is a freely distributed piece of software for such tasks as photo retouching, image composition and image authoring. It works on many operating systems, in many languages.
Illustrator's Shape Builder tool will let you combine shapes visually and interactively. This video shows the Mac version, but the tool works the same way in Windows. To follow along with this video, you can draw your own shapes or download the file…

708 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

13 Experts available now in Live!

Get 1:1 Help Now