Calculating LLD: Conflicting Equations & Application Specificity

[daveb]

I can't seem to find a definitive equation for calculation of LLD (lower limit of detection). Cember has one equation, and other sources I research have completely different equations. I'm more apt to go with Cember's equation ,especially seeing as many of the govermental guides have conflicting equations. I know sometimes the equation can be application specific, so mostly wipes for contamination (whether routine wipes or decommission wipes) is the equation I'm looking for.

 

[Astronuc]

Is this for homework problem or laboratory measurement problem?

LLD would depend on the type of detector and radiation. Are you using a 2$\pi$ detector?

 

[daveb]

Neither. It's for the job. Apparently, some idiot used the wrong formula for the MDA way back when, and no one in the office can seem to find the correct formula. If we could find another that agrees with Cember, we'd most likely go with that one.

 

[Astronuc]

Neither. It's for the job. Apparently, some idiot used the wrong formula for the MDA way back when, and no one in the office can seem to find the correct formula. If we could find another that agrees with Cember, we'd most likely go with that one.

Yep, I've seen that many times before. Something that someone did 20, 30, 40+ years ago, and that person has long since gone (terminated, retired or died), and no one knows why it was done that way. The stories I could tell.

I'll look around. I have an old Cember. You might try Glenn Knolls book, and IIRC there is a Radiation Protection Handbook or Radiological Health Handbook.

 

[Astronuc]

Try these resources

Secondly, you should also review Section 4 of DOE's EML handbook HASL 300. In the discussion and Figures 1 and 2 you will note radioactive decay is a random event, following certain statistical principles. Additionally, a "background" count rate (for example, from cosmic ray and terrestrial gamma ray interactions) will be observed by your detector in a sample measurement. This too will be random in nature and exhibit a distribution about a mean. I believe what you are asking about in your question relates to what most health physicists refer to as the Minimum Detectable Activity (MDA) and Low Limit of Detection (LLD).

Consider the scenario where one has such a low count distribution that the background and sample count distributions begin to overlap (for example, shown in Figure 2). The LLD accounts for the background distribution and statistical "confidence level," and provides a point where one can say that the sample contains detectable net counts, given an acceptable risk of a false positive. The LLD is calculated by multiplying 4.65 times the standard deviation of the background count rate. The MDA is obtained by dividing the LLD by the detector efficiency (E in counts per disintegration), that is, to obtain activity. Other factors can be applied too, such as detector area or sample size to obtain other minimum detectable quantities.

http://hps.org/publicinformation/ate/q807.html

Q: What is a good reference for an introduction to counting statistics?

A: I have found the section beginning on page 396 of Herman Cember's Introduction to Health Physics, Third Edition, McGraw-Hill, 1996, to be a convenient source of information for counting statistics. Others are:

Knoll, G. Radiation Detection and Measurement, McGraw Hill Book Company, 1989 or latest edition

Tsoulfanidis, N. Measurement and Detection of Radiation, McGraw Hill Book Company, 1995

Bevington, P.; Robinson, D.K. Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill Book Company, 1992

http://www.eml.doe.gov/publications/procman/

http://www.eml.doe.gov/publications/procman/Sect4/4_5-3.pdf

 

[daveb]

Thanks. I meant to look at the HP website but it completely slipped my mind. DOH!

 

[Morbius]

Try these resources

http://hps.org/publicinformation/ate/q807.html

Astronuc,

Yes, the Health Physics Society is a great place for people to get answers to their
questions with regard to health effects and safety of nuclear technology.

I referred several anti-nukes who were trying to stir up support for "The Tooth Fairy Project".
I pointed them to:

http://www.hps.org/publicinformation/ate/q616.html

The Tooth Fairy Project is an attempt to assign blame to nuclear power plants for
trace amounts of Strontium-90 found in the deciduous teeth [ "baby teeth" ] of
children from a given area.

The "study" is terribly flawed as discussed by numerous scientists at:

http://mailman.mcmaster.ca/mailman/private/cdn-nucl-l/9911.gz/msg00011.html

For example, Bob Flood of the Stanford Linear Accelerator Center at Stanford
University concludes the following:

"...Ignoring such things as transport mechanisms and food chain
characteristics and jumping straight to assigning blame to nuclear
power plants seems a fair demonstration to the preconceived notions
the project started with. They had the answer before they started;
they are now simply deriving the question..."

Dr. Gregory Greenman
Physicist

 

[JRtheHP]

Is this for homework problem or laboratory measurement problem?

LLD would depend on the type of detector and radiation. Are you using a 2$\pi$ detector?

Hello Astronuc, Your verbal explanation of LLD clarified so much for me. I was searching for a similar definition for MDA. If it helps, I use a Protean gas-flow proportional counter to quantify gross beta-gamma.