PCM-2 Manual.pdf - Voss Associates

1. Minimum Count time
Since adjusting count time also adjusts a and hence the associated alarm setpoints, it is possible to set
RA(MIN) equal to RB(MAX)' This is done in Eq. 43 by equating the right hand sides of Eq. 35 and Eq.
36 and then solving for T. Since any lesser value of T would violate the requirement that RB(MIN) ~
RB(MAX), the "MIN" subscript is appended to T to indicate that it is, in fact, the minimum count time
that can be used without sacrificing one of the constraining parameters of the measurement.
_rl~F,iR~-----,----="::-_]
V + Z VRDA x Eff + R B 2 Eq.43
T - M1N
Eff
2. Fixed Count Time
Obviously, using RA(MIN) for the alarm setpoint allows the instrument to operate as close to
background as possible given the limitation of the count time selected. Assuming that the count time
is as long as reasonably allowed, the sensitivity is maximized. Referring to Figure 9, it can be shown
that at the lower alarm set point, RDA has a greater probability of detection than would be
determined by the maximum alarm setpoint. Thus, in the FIXED COUNT TIME mode, the userselected
RDA becomes a maximum permissible RDA (no less than the selected confidence level
should apply to the selected RDA), and at the confidence level selected, a lower RDA exists. This
lower RDA is computed by Eq. 44.
RDA
SF
+ z
RDA x Eff + R B
T
Eq. 44
Eff
To solve Eq. 44 as it is presented requires several iterative steps. Virtually any starting value for
RDA can be placed in the right hand side. When the equation is solved, it returns a new value for
RDA which is re-entered in the right hand side. The process repeats until no change in RDA occurs.
A closed form solution is indicated by Eq. 45. The former method is usually preferred.
RDA
SFW + ~ + ~ + z 2 SFW + R B z 2 T Eq.45
Eff
3. Minimum TYPE II False Alarms
PCM2.MAN