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Accuracy

Truth is the first casualty of war
Sen. Hiram Johnson 1918

I have two GPS based speedometers in my car and because my job depends on my having a drivers license, I seldom speed, but I long for the day when I’m pulled over by a cop and they ask me their standard question…

“Do you know how fast you were going sir?”

To which I will reply

“Yes, somewhere between 102 and 103 kilometres per hour.  I would estimate 102.5, but since my GPS speedo has only 1 digit of resolution, I would be assuming a display accuracy I don’t have!”

You see, like most cars, my speedometer reads about 5 km/h faster than the speed measured by my GPS. 

How do I know my GPS is accurate? Well GPS is based on the timing of a signal to a satellite and back, and its atomic clocks are accurate to 97 nanoseconds i.e. +/- 0.00000097 seconds; we know it’s right.  

So, I set my cruise control such that my GPS speedometer flicks between 102 and 103 at which speed, my cruise control displays 107 kph.
IMG 1536

In a similar fashion, we had a frost this morning and my in-car thermometer sometimes read 0 ℃ and sometimes 1 ℃, so in theory the actual temperature was some random number between 0 and 1.  But as Hannibal Lecter says, “life’s too slippery for books, Clarice”.  Things are seldom actually random.

One of the most interesting probability experiments I’ve seen is the Galton Board.  If marbles are allowed to fall randomly through a pyramid of nails/dividers, they fall into the familiar population or normal distribution curve.  Actually, most physical events follow the ‘Normal’ distribution.
 

galton board normal gaussian distribution Graph 200

🔼CLICK the photo to watch a video of a Galton Board in action

So how does this relate to instrumentation?

Well, different instruments have different levels of accuracy, and often the specifications need to be parsed to understand them properly.

Center 300

Let’s look at one of our most popular thermometers; the Center 300.  This is well priced and covers a huge range of temperatures (-200 ℃ to 1370 ℃).  Let’s take a look at the specifications.
Accuracy +/- 0.7% of reading + 0.7 ℃
Resolution 0.1 ℃

So, on the face of it, by way of example, if the actual temperature is 27.0 ℃, the instrument could display anything from 26.1 ℃ to 27.9 ℃.
Now most likely the instrument will follow the Normal distribution, and will be closer to the middle reading of 27 ℃.  BUT, there’s a caveat. 

This refers only to the instrument itself and not the attached probe. A thermocouple probe could easily have a +/- 2.5 ℃ error in itself, so now we’re talking about a final possible span of readings from
 
23.6 ℃ to 30.4 ℃

Now again, it’s probably going to follow a Normal Distribution, and will be closer to the actual temperature of 27, but it’s important to be aware that such a thermometer and probe with a 2.5 ℃ error, is still within specification.
So there are a couple of ways to deal with this

  1. Have the instrument calibrated so that the Actual errors are identified
  2. Get a more accurate thermometer
Center 300 200 pix


The Center 370 – RTD thermometer

Let’s look at another popular thermometers; the Center 370.  This one is IP67 rated and is very accurate.  It covers a more narrow range (-100 ℃ to 300 ℃).  Let’s take a look at the specifications:
Accuracy  +/- 0.1% reading +/- 0.4 ℃
Resolution 0.1 ℃

So, on the face of it, by way of example, if the actual temperature is 27.0 ℃, the instrument could display anything from 26.6 ℃ to 27.4 ℃, so a far closer tolerance than the Center 300 above

Now most likely the instrument will follow the Normal distribution, and will be closer to the middle reading of 27 ℃.  The probe still has an influence on the accuracy, but now it’s a Class-A RTD (Platinum wire) Pt100 

This refers only to the instrument itself and not the attached probe. A class-A Pt100 probe will have a +/- 0.1 to 0.2 ℃ error in itself, so now we’re talking about a final possible span of readings from

26.5 ℃ to 27.5 ℃
 
Center 370 200pix

Now we often calibrate the Center 370, and typically get results of no worse than 0.1 °C to 0.2 ℃ over a wide range of temperatures.  Here's an example of a typical calibration certificate on a Center 370. 

Sample cert 1

If you have questions relating to choosing and using thermometers, we're here and ready to help.  Or if you just have questions, we're happy to talk.  
 

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