Answer to Question #2356 Submitted to "Ask the Experts"

Q

Why is it that doing multiple measurements and repeated measurements can reduce random errors? Are there any other ways of reducing random and systematic errors?

A

Radiation emission and detection is random and should follow expected statistical fluctuation. One can do a series of experimental counts with a radiation source and the detector/counting system to determine if the counting variance is larger or smaller than would be expected. This is called a "chi squared" counter test. If it shows there is too much or little variance, then there may be some systematic error.

To reduce the random counting error, rather than taking a series of counts on a given sample, "invest" the counting time in a single count duration. For example, with a background measurement, if you had a true background count rate of 1,000 counts per minute (cpm), you can estimate the standard deviation by taking the square root of your count. If you do a series of five one-minute counts, and you get say 1,000 counts for one result, you'd have 31.6/1,000 or a relative error of 0.03 in this case. If you invested that counting time for a single five-minute count and got 5,000 counts, you'd have 70.7/5,000 or a relative error of 0.01 in this case. The series of counts will not improve your relative error, only acquiring more counts will do that.

Look over the references given in this category of ATE. The books and various manuals noted all have good sections on counting statistics.

David J. Allard, CHP