PM-7 Operating Manua.. - Voss Associates

Algorithms
Statistical Theory
To use the model for radiological measurements, the average number of
counts expected during a single measurement cycle must be known with
reasonable accuracy. Applying this to background, we would call the
expected number of counts N B(avg) since the measured background average
is the best information available for predicting how many counts will
occur. Another statistical parameter of importance is the standard deviation
or, sigma, of N B(avg) which is defined as the square root of NB(avg). Any
background count, N C , can be scaled to the normal distribution function by
determining how many sigmas N C is away from N B(avg) . The calculation is
shown below. The multiplier of “sigma” will be called SIGMA FACTOR or
“SF”.
–
–
SF
N C
N B( avg)
= -------------------------
sigma
N C
N B
= ----------------- Eq. 2.5
N B( avg)
Because the distribution function is well defined for “x”, the identity of Eq.
2.5 defines the predicted distribution function for background counts.
Suppose that we are interested in finding a number of counts, "N c ", that we
would alarm on in a detector channel such that background alone would
cause an alarm no more than 1 time in 10,000 measurements.
That corresponds to a cumulative distribution of “x” of 0.9999 --
background is expected to be less than “x” 9,999 times in 10,000
measurements for a false alarm rate of 0.0001. Tabulated values for F(x) are
listed in Table 4-1, “Probability Distribution Table”. In this example, F(x) =
0.9999 is known. Entering the table we find that the closest value to 0.9999
corresponds to x=3.72. The alarm set point must then be 3.72 times “sigma”
above N B(avg) . The false alarm rate is determined by SF if the number of
counts above background to alarm on, N A , is determined by Eq. 2.6:
N A
R B
= SF ----- Eq. 2.6
T
Note The false alarm rate of a single detector channel is not equal to the overall
false alarm rate of the portal. As implied by the foregoing, the false alarm rate for
a single channel is equal to 1 - F(SF). For a monitor with “N” independent
channels and the same SF for each channel, the overall probability of false alarm
is equal to 1 - [F(SF)] N . The PM-7 has seven independent channels determined
by the six detectors and the sum channel. If different SF's are utilized, the overall
probability of false alarm for “N” channels is equal to
1 - [F(SF) 1 x F(SF) 2 x . . . x F(SF) N ]. ▲
Thermo Fisher Scientific
Personnel Monitor -7 Techical Guide_4-3_