PCM-2 Manual.pdf - Voss Associates

Statistical Control Of Radiological Measurements
INTRODUCTION
Measurements that pertain to radioactive decay of isotopes involve uncertainties that are the result of
the random nature of such decay. This randomness and the affect it has on measurements dictate that
some statistical assessment of the results be made. Furthermore, there is involved with most
measurements a "signal" that must be separated from background component (noise), with each
component exhibiting its own statistical fluctuations. Classical statistical models, when properly
applied, can provide a rich understanding of the events observed" By applying some fundamental
rules to even the most sophisticated counting algorithms, use of the statistical models can be a
straightforward exercise. This document attempts to illustrate what those rules are and how to apply
them. The author attempts to speak to the non-statistician and avoids complex derivations pertaining
to pure statistical theory. Derivations are presented where they will help clarify a technique, and only
as they apply to the subject of radiological measurements. Thus, this document is intended to be
primarily a "how to" discussion that the reader will refer to as an application guide.
THE BASIC PARAMETERS OF THE MEASUREMENT
Simple Measurements
As with any statistical population or sample, the two parameters that provide a reference point and a
scale for observations and/or analysis are the mean, or, average, and the standard deviation which is
frequently referred to as "sigma", deriving that name from the lower case Greek letter "a", used
symbolically as a short-hand reference to standard deviation.
These two parameters, when applied to raw counts of radiological events, are quite simply
determined. Generally, one is interested in the mean number of counts observed (post facto), or
expected (implying future counts to be collected) in a specified counting interval. The "mean" can be
determined from the results of a single measurement as well as the average of multiple measurements
provided that the affect of differing counting intervals, if used, is properly accounted for. If a simple
mean number of counts is known, the theoretical standard deviation is merely the square root of the
mean as expressed in Eq. 1 where N represents the mean.
a = VN
Eq. 1
With the mean and standard deviation known, or predictable, for a set of measurements, the variation
(or deviation) of measurements from the mean is likewise known or predictable with application of
the appropriate distribution function.
Complex Measurements
As will be seen in later sections of this document, radiological measurements are rarely reported as
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