... a POD curve that goes to zero on the left, or to one on the right.

That means (but perhaps not as obviously as it should) that the standard POD(a) model with asymptotes at zero and one won't fit the data. (Duh! as they say in the funny papers.)

For situations with a data "floor" (a non-zero lower asymptote) or a data "ceiling" (an upper asymptote less than one) we must use a model having the appropriate characteristics, shown in Figure 1.

Notice that there is a handful of very small cracks that are reported as "hits," the consequence of a corrupting background signal (e.g. "noise"). That means that the lower value of POD cannot be zero. And that means that the standard POD(a) model won't work. (Well, you can force it to give you an answer, but it will be wrong, as we shall see.)

OK. So who cares about the lower left? We're interested in the upper right.

Ignoring the non-zero lower asymptote produces an overall poor fit because
the model tries to compensate for the poor fit on the lower left with a
shallow slope. That, in turn, causes a lousy fit at the upper end as
well. This results in a a_{90/95}, the cracksize with 90%
probability of detection and 95% confidence, that is too large, and is incorrectly computed
to be 42.

With the POD floor modeled correctly the overall fit is greatly improved and a_{90/95} is 28, as seen in figure
4.

While the statistical methods in **MIL-HDBK-1823A**
work in the large majority of situations, they do not work in *all*
situations. When the model (*any* mathematical model, not just a
POD model) doesn't have the same characteristics as the data, then it is the
*wrong* model. Yes, you can torture the software to use it
anyway, but your answer will be *wrong*. No verbal legerdemain
can trick Mother Nature, and if you insist on trying (so you can check the
box and move on), ultimately she will have her revenge.

The Standard mh1823 POD Software has rudimentary capabilities for detecting a POD ceiling by computing the observed fraction of misses for targets larger than a perported a90/95 and comparing that empirical POD with POD = 90%. The new 2016 Workshop Addendum can compute a POD Ceiling (or Floor), and confidence bounds for it, plus the Akiake Information Criterion, and Schwarz Criterion for statistical significance.

If your data suggest that their POD minimum value never reaches zero, or their maximum doesn't approach one you will need the 2016 POD Workshop Addendum software to model a POD Floor or Ceiling with a 3-parameter model having a lower asymptote (POD > 0) or an upper asymptote (POD < 1).

The POD Workshop Software is an integral part of the 2-day POD Workshop and Short Course.