PCM-2 Manual.pdf - Voss Associates

merely the number of counts observed within a specific counting time interval. The values
associated with the counts collected are usually manipulated algebraically so as to convert counts to
count rates (counts per unit time), change units of measure, to apply sophisticated averaging
techniques to a sequence of measurements, or to derive a value of interest from a complex
relationship of variables as will be illustrated herein.
Eq. 2 is used to signify that a mean quantity, Y, is expressed as a function of "n" variables, Xi'
Y '" f( Xl ' , -' ... , X ) Eq. 2
X J_ x., n
Statistical theory provides us with a general formula for deriving the standard deviation of N as is
illustrated hy Eg. 3 and Eg. 4.
n 0Y 2
2 Eq. 3
'" '" ~ [-1 ox a .t,
1'-1, f .
Eq.4
EXAMPLE: To convert "N" counts collected in count time interval "T" to a count rate "R", the
counts are divided by the count time.
R
N Eq. 5
T
~] 2
1 Eq. 6
[ oN
Eq. 7
Whereas T is a constant, the partial derivative of R with respect to T is zero.
NOTE: An important assumption is made here: the length of the counting time interval is assumed to
be precisely controllable or measurable so that there is no associated uncertainty and it can be treated
as a constant.
Assembling the components Eg. 5, Eg. 6, and Eg. 7 into Eg. 4 yields Eg. 8.
PSM2.MAN