From: "Thomas David Nichols" <
[email protected]>
Subject: RE: Q: Calibration Issues for Small Firms
/Scalies/Nichols
Suppose you have a digital thermometer that displays two decimal places, and the last digit is stable. That is, it doesn't flicker unpredictably 3-7-6-2-9-4, etc. Then the precision of the thermometer is 0.01 degree, or plus/minus 0.005 degree.
Now suppose you use this thermometer to measure a calibration standard that is known to be within 0.1 degree of 50 degrees. The thermometer's readings vary between 46 and 52 degrees, with a mean of 49 degrees and a standard deviation of 1.5 degrees. This tells you the accuracy of the thermometer.
To summarize, precision is how well you can read the instrument, while accuracy is how close the reading is to the true value.
Measurement uncertainty is a little harder to pin down. Basically, it is the size of the band around a measured value that is known to contain the actual value with some probability, often 90% or 95%. Expressed a different way, it is the band around the true value that will contain the stated percentage of a large number of measurements of the value. It combines all the sources of uncertainty: instrument accuracy, operator errors, the relationship between what is available to measure and what is desirable to measure, the time required to take the measurement compared to the rate of change of the thing measured, the effect of the measurement on the thing measured, and possibly many other factors.
Measurement uncertainty, in turn, has an uncertainty of its own. Your process can tolerate a large error in some measurements, as when room temperature can range from 40 to 120 degrees F, and it never goes below 60 or above 80. In this case, a very simple test can show that your thermometer is good enough, and you really don't need to know exactly how accurate it is. On the other hand, if you are polishing a mirror to a flatness of .05 wavelength of red light, your whole business may depend on how well you can measure flatness.
Either way, though, if the uncertainty in a measurement doesn't matter, the measurement itself doesn't matter.
Thomas David Nichols