Answer to Question #700 Submitted to "Ask the Experts"

Q

I would like to know what the definition of minimum sensitivity of an instrument is. It seems like it should be fairly straightforward, but we have a lot of discussion about it at work. Thanks.

A

MARSSIM (see below) uses the terms critical level, detection limit, and minimum detectable concentration to define detection sensitivity. Below is a discussion of details that are intended to assist in a better understanding of these terms. Many counting situations occur under conditions where the background count rate is approximately a constant in which case the probability distribution for the background count is given by a Poisson distribution. If the sample does not decay appreciably during the sample count time then the fundamental binomial probability distribution for the decay of a radioactive nuclide can be approximated by a Poisson probability distribution. Paired counting occurs when the background and sample count times are the same. If both the instrumentation and the background are stable, then credit may be taken for counting the background longer than the sample; this is advantageous when more than one sample is to be counted. For many situations of interest to health physicists it is acceptable to approximate the exact probability distribution for the net count (the difference between the gross count and the background count in the sample count time) by a Gaussian distribution. The two quantities of interest are the true background count rate and the true sample count rate. Statistics allows us to estimate the true background count rate from the background count. Similarly the true sample count rate can be estimated using the difference between the gross count and the background count in the sample count time. While neither of these quantities can be exactly determined, confidence intervals for both of these estimates, at a given level of confidence, become smaller as the count times increase. Health Physics frequently uses the theory of statistical hypothesis testing to determine if a sample contains radioactivity above background. The null hypothesis is taken to be that there is no activity above background in the sample. The alternative hypothesis is that there is activity above background in the sample. Frequently health physicists are satisfied to be correct 95% of the time concerning the detection of low levels of activity, so they take both the errors of the first and second kinds equal to 0.05. Then a critical level, L_c, is determined so that when there is no activity in the sample there is a probability of 0.05 of getting a net count greater than L_c. Here the probability distribution for the net count when there is no activity in the sample is utilized (if the exact probability distribution is used the above condition should be equal to or less than 0.05). Samples are then said to contain activity above background if the net count is greater than L_c. To specify the a priori ability of this procedure to detect low levels of activity the detection limit, L_d, is specified. The quantity L_d is the contribution to the net count from the sample that will result in the detected decision with a probability of 0.95 and with a probability of 0.05 of falsely concluding there is no activity in the sample (error of the second kind). Quantities such as the minimum detectable concentration and the minimum detectable activity are determined by multiplying L_d by the appropriate factors.

The above information should be used to explore the available literature. Chapter 6 of MARSSIM is available on-line at EPA's website. Section 3 of NUREG-1507 is available on-line at the Nuclear Regulatory Commission website. Further reading and details are available from the references provided in these two references. Many books on statistics have a section on hypothesis testing.

William E. Potter