CASIE
DESERT SEARCHES: THE EFFECTIVENESS OF HELICOPTERS

Appendix 1: Explanation of Terminology

The term "Probability of Detection", or POD, refers to the probability that a search team (such as a helicopter and crew) finds a victim in a given area given that the victim is in that area. Thus, the term POD, used in search terminology is a conditional probability with the conditioning event that of the victim being assumed to be in the area. This conditional probability, POD, is thus a true measure of a team's ability to detect independent of the possibility that the victim may not be in the area.

The term "Cumulative probability of detection" refers to the increased measure of detection produced by the given (or another) search team conducting multiple searches of the same given area. If p is the "single pass", or single search, probability of detection for a team such as a helicopter with scanning crew, then the cumulative probability of detection produced by two passes of that team over the same area is given by
POD = 1 – (l – p)2.
If the team searches the area three times, then the cumulative probability of detection increases to
POD = 1 – (l – p)3,
and so on. The benefit of searching an area multiple times is qualitatively demonstrated by figure 9 where the single pass probability, p, is assumed to be 0.3. It is typical and instructive to note that the major gain in the cumulative probability of detection occurs with the first several "passes" of the search team. The gain in cumulative POD is not as high with later passes. This fact is borne out in the numerical tables in this document.

Figure 9
Cumulative Probability of Detection as a function of the number of passes.
A larger Figure 9 (21 K) can be seen here.
CPOD

The term "Probability of Area", or POA, refers to the probability that a victim is actually in the area being searched. Exactly how this quantity is to be determined is not the subject of this particular document. In practice, POA can be determined by using past statistical information on previous victims behavior (e.g. "50% of previous lost persons starting at this point wandered into a certain region and were found there"); however, in the absence of such organized data, the consensus estimate of a small group of experienced, knowledgeable individuals can produce a distribution of POAs for principal search areas.

The term "Probability of Success", or POS, refers to the quantity that a search manager must strive to maximize. Mathematically, POS = POA x POD. That is, the probability of finding the victim equals the probability that the victim is in the area being searched multiplied by the probability that the victim can be found in that area if he/she were in the area. Again, this latter probability, the POD, is strictly a measure of effectiveness for a given team; obviously the team could be perfect, with a POD = 1.00, and yet the POS could be quite small due to the fact that the POA is small.

The term "Confidence Level" is a technical term in mathematical probability theory which essentially refers to the level of "sureness" or "confidence" that the search manager is willing to use. Unfortunately, there are only very few things in life that are certain; everything else has uncertainty associated with it. For the search manager, it would, of course, be optimum for him/her to be certain of all decisions. In particular, it would be simpler if when a helicopter crew searches a given area, the POD for that search is known to be exactly, say 0.7. Because of unavoidable uncertainties in data collection for any experiment, it is not possible to present data in this exact form.

More realistically, the search manager must use the experimental data presented in this report in the following way.

As an example, consider the experimental data supplied by Table 4. The "Confidence Level" chosen may be used to assign the "confidence" one may have in using these data. Hence, one may say (see Table 4) that "with one helicopter pass over the area, the probability is 0.8 that the POD for that pass lies between .496 and .839". In other words, the search manager may be 80% sure that the one helicopter pass has "covered the area" with a coverage (POD) of at least 49.6% but at most 83.9%. If the search manager uses two helicopter passes over the same area, he/she can be 80% sure that the cumulative POD (or total coverage) is at least 74.6% but not more than 97.4%. Notice that the search manager can also say that he/she is 40% sure that the cumulative POD is at least 83.2% and not more than 97.4%.

The search manager, in referring to the detailed tables found in this document, will find that it is possible to obtain a very high level of coverage (POD of less than 99.8% but more than 99.7%) with a very high confidence level (99%) if he/she has the helicopter-hours to spend on a particular area. This, of course, is rarely the case, and the proper, optimal use of helicopter time is subject to many other considerations which are not addressed here.

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