Re: [Phys-l] Below Detection Limit (was Another uncertainties question...)

[John Denker <jsd@av8n.com>]

On 01/25/2008 03:15 PM, Edmiston, Mike wrote in part:

> In the legal situations the answer is clear... the "below detection
> limits" must count as zero.

Not necessarily.  Even if we restrict attention to legal situations,
the answer depends on who has the burden of proof.  Not all "legal 
situations" are the same.

> You can't cite a violation and issue a fine when there is no evidence
> that the company was actually in violation.  The "not detected" readings
> have to be averaged as zeroes.

That applies in situations where *you* have the burden of
proving a violation.

The situation is very different in situations where the company
has the burden of proving compliance.  The company has to treat 
an undetectable quantity as being equal to D (the detection 
threshold) because it can't prove otherwise.

> I don't know what happens outside of environmental permit compliance,
> but I have worked on a liaison committee between the refinery, the
> health department, and the Ohio EPA for the past 20 years, and it is
> clear that for average values calculated for legal permit compliance
> purposes, the "not detected" values are averaged as zeroes.  I don't see
> how it could be any other way.

There's more to physics than legal technicalities.

The physics works like this:

a)  One hypothesis is that a "no detect" report corresponds to a raw 
reading of zero.

b)  Another hypothesis is that a "no detect" report corresponds to a 
raw reading uniformly distributed on the interval (0, D) leading to 
an average of D/2.

c)  Another hypothesis is that a "no detect" report corresponds to a 
raw reading always infinitesimally less than D.

It would be rash to /assume/ hypothesis (a) describes reality.  Ditto
for hypotheses (b) and (c).

I'm not suggesting that we replace one ill-founded assumption with
another.  I'm suggesting that a prudent person should consider /all/ 
the plausible hypotheses, including (a), (b), (c), and perhaps others.

This is sometimes called a what-if analysis.  It is also sometimes
called scenario planning.  The objective is to make decisions that
produce acceptable results no matter which of the plausible
scenarios comes to pass.
  http://en.wikipedia.org/wiki/Scenario_planning

  1) It may be that D is small enough (mercaptan) that all three 
   scenarios are equivalent.  But maybe not.  
  2) When D is large (carbon monoxide) it might be fatal -- literally -- 
   to assume an undetected quantity should be treated as zero.

This is why scenario planning is important.  It gives you a systematic
method for making good decisions in the face of uncertainty.