MDA Formula

["Scott O. Schwahn" <schwahn@CEBAF.GOV>]

Yes, the formula is correct, with one clarification.  The square root is
actually:
sqrt (Background Count Rate x count time)

This statistic represents a 90% confidence level for L sub d, or the
detection limit, for a counting system.  It takes into account 5% type a
(false detection) and 5% type b (missed detection) errors in both the
background count and the gross count.  The formula is good for any
instrument and situation that produces counts, but as others have cautioned,
the geometry has to be identical for both background and source
measurements.  It is a good approximation, as it assumes that there is
insignificant difference between sigma(background) and sigma(gross), which
is for the most part true when you are simply determining L sub d.

It is perfectly appropriate to use the formula without the efficiency and
probe area/100 portions to come up with a minimum detectable count.  Those
two features simply make it an MDA (per 100 cm2) calculation.  For your
particular application, you would have to make certain assumptions (how is
the radioactivity distributed in the soil, what radionuclides do you expect,
etc.), and then either computer model or spike a representative geometry of
soil.  So, yes, you are right unless you want to go to great pains - it
(without the E and A portions) is of only a go-no go use.

Scott O. Schwahn, CHP
Operational Health Physicist
Thomas Jefferson National Accelerator Facility
(757)249-7551 (w)
(757)249-7363 (fax)
schwahn@cebaf.gov
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At 12:04 AM 7/10/96 -0500, Dan wrote:
>T all fellow radsafers:
>         I need some help on some technical issues.  In NUREG/CR-5489 there
is a 
>formula for MDA for instruments using an integrated count for a preset time:
> 
> 2.71 + 4.65 x sqrt of Background Count Rate x count time
>___________________________________________________________
>    count time x efficiency x active probe area (cm2)/100
>
>
>I have been told that this formula is incorrect.  Is it??  If so then what is 
>the correct formula??
>
>Also I am going to use a Ludlum Model-3 with an attached 2" x 2" NaI detector 
>for release surveys of outside ground areas for a decommissioning project
(meter 
>reads in CPM).  Main radionuclides Co-60 and Cs-137.  The MDA formula for this 
>type of instrument is a 25% or 50% increase in the audible count.  Regulators 
>have pointed out that this is a MDC calculation because probe area and 
>efficiency are not used in the calculation.  My question is can the MDA be 
>calculated??? If so, how??? Again I am scanning outdoor ground surface area 
>(some gamma logging too) they (the regulators) want to know how many CPM above 
>background relates to pCi/gram.  I think the geometry and type of survey
make it 
>a mute point and really make it a qualitative (go-no go) type of instrument.  
>Any help in these matters would be greatly appreciated.  
>reply to:
>radconpro@aol.com
>Dan 
>   
>