Using Formal search theory
In a Land Search Environment
By
Rick Goodman
Director, Search and Rescue
New Mexico State Police
In the last few years, the land search community has been looking at utilizing more
scientific methodology in search strategies. Theoretical work along these lines has been done
by Don Cooper and Jack Frost and has been published in previous NASAR journals. This article
will attempt to adapt their work into a real-world search environment.
Formal search theory was established during WW II as part of a larger scientific discipline
called Operations Research.
The scientific principles of search theory, as documented in
various university-level texts and scientific journals, are the result of more than 50 years of
research. Although this research as been porimarily directed toward military problems, the
principles of search theory apply to all types of searches, including searches for lost or missing
persons.
For the remainder of this article, the term “formal search theory” will refer to
established theory as described in the scientific literature, most notable Koopman (1) and Stone
(2). For the layman’s description of search theory principles, see Frost (3).
Can we adapt formal search theory to the land search environment? That is a question
that causes many debates. The following is my attempt to analyze this theory and see if we can
apply it to inland SAR missions.
Regions
The theory is simple and very understandable. First, a search area is divided into
Regions based upon factors tending to prove where the subject is more or less likely to be.
Factors such as lost person behavior profiles, the effect of terrain on subject travel, attractions,
deterrents, and time elapsed are some of the primary factors to consider. Physical boundaries,
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such as terrain or man-made barriers, may be used in defining Regions, but only when the
likelihood of the subject being in one area is significantly different from the other area. Within a
given Region, the chances of the subject being at any one location should be the same as the
chances of the subject being at any other location within that same Region.
In developing a Region, other factors such as physical limitations of the Subject and
distance from the Initial Planning Point (IPP) are also used. There must be an equal chance that
the missing subject could be anywhere uniformly though out the Region (Figure 1).
Theoretical Distance Missing Subject
could travel - Time X Miles
Region
IPP
Figure 1
The chance that the lost subject could be located at X, Y, or Z, is the same. A Region
can be many miles square depending on how far the subject could walk or move uniformly
though out the Region.
One must not confuse Regions with ICS Divisions. An ICS Division is a management
area. One can have areas within a Division that have a totally different Probability Of Area
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(POA). One must have the same POA though out a Region. A Region can be so large that it
would exceed ICS span of control parameters. However, we can replace the word Region with
ICS Division as long as we adhere to the above requirements of the POA being equal though
out the Division.
Regions are developed for computing POA for the overall search plan. Consensus is
accomplished using Regions to determined POA. A typical search in New Mexico will usually
involved less then 5 or 6 Regions.
The Region method is much easier then the old way of determining POA. Training
courses such as the Managing the Search Function, Managing the Search Operation, and
others have taught us that POA must be computed for each Segment. A Segment is defined as
an area based on terrain or man-made boundaries that can be searched in 4 to 6 hours. The
segment is usually be sized by the kind of resource assigned to it. A dog team could cover a 1/2
square-mile area in 4 to 6 hours while a helicopter could cover a 3 square-mile in a 4 to 6 hour
time frame. In the above case if the search area was divided up for coverage by dog teams a
search helicopter might be assigned 5 or 6 segments to search.
For example, a 3 mile by 3 mile search area equals 28 square miles (3 x 3 x 3.14 =
28.26) If we use the standard of ½ mile by ½ mile search area using dogs, then 28.26 divided by
.5 = 56 segments that POA could be assign to. This is not an easy task when using standard
shifting POA formulas. Computing POA for 3 or 4 Regions would be made much simpler using
this new (to the land search community) technique.
Once the POA has been developed for each Region, the Region can be segmented and
resources assigned. The ratio of Segment area to the Region in which it is located is then used
to calculate the POA of that segment. For example, if the POA of a Region is 50% and the
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Segment within the Region is 1/3 the size of the Region, then the POA for the Segment would
be 17% see (Figure 2)
Search Segment 1/3 size of Region
1/3 of 50% = 16.666 or 17% Max POA
if segment is covered 100% by search
team.
30% POA
20% POA
50 % POA
Figure 2
Probability of Detection (POD)
Once segments are determined, a resource is assigned to sweep each Segment until the
area within the Segment has been totally covered. Sweep distances have not been scientifically
computed for land-based resources. However, Perkins and Roberts’s (4), Caldwell (5), and
others have attempted to assist the land search community in developing more precise searcher
sweep width spacing. Critical Separation (CS) is a good start in this effort. However, 50 to 70
percent of one CS sweep width is considered a result that approximates formal search theory
sweep-width published data.
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In work done by Koopman, it was determined that if the resource covered all the area
once (the width of the sweep times the length equals the total area of the segment) regardless
of the resource, the resource could still miss parts of the area. He calculated that the POD
where the total area was searched one time would be 63%. If less of the Segment is searched,
the lower the POD will be. The more significant the terrain or other factors, the less chance the
resource has in detecting the target.
This way of estimating POD is radically different then the way we have been teaching it
over the last 30 years. Using formal search theory, a chart is used to compute POD. If the
Segment was totally covered, the POD would equal 63%. If the area was searched a second
time then the POD would be 87% (Figure 3).
87% POD
63% POD
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Figure 3
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Probability of Success (POS)
The Probability of Success (POS) is still computed as before: POA x POD = POS. In
formal search theory, one never uses Rest of World (ROW) or areas that cannot be searched. In
reality, using ROW only serves to discourage the planning staff by fostering a belief that the
missing subject is not in the search area. Few believe that ROW has ever been a major factor in
terminating a search. In formal search theory, if the missing subject is not found in the initial
search area, more areas are added or segment are re-searched. Termination of a search is
made in most jurisdictions by a political body (Sheriff, Police Chief, or Park Supervisor) using
factors such as availability of resources, expected survival of the missing subject, or how well
the area where the subject was believe lost was searched.
In the real world of land search, is formal search theory practical? Let us take a look at
some examples of using this theory in a real search environment. If indeed we use the
conventional size of segments being ½ by ½ mile, and CS in average terrain is 150 feet, any
given resource should be able to be in the search area for 3 hours traveling about 1 mile per
hour. Convention states that we should search about one-half the speed of an average subject
walking though the same area. We can compute the POD for the segment by doing the
following:
Size of segment = 1/2/ by ½ or 6,969,600 square feet.
½ of CS 150 feet divided by 2 = 75 feet.
Team coverage = 3 miles x 75 feet or 15,840 x 75 = 1,188,000 feet or 17% of total area.
POD (from Chart) = 15%
If we use an example from the latest Lost Person data compiled by Roberts, Perkins, and
Hill we find that if we are searching for a lost hunter and we draw a circle 5 miles in diameter, we
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would have a 90% chance of finding him. If the terrain was such that he could be any direction
from the IPP, the search area would be 5 x 5 = 25 x 3.14 = 78.5 square miles in size.
If search dogs and ground teams are deployed, we divide the total area of 78 square
miles into ½ by ½ mile segments. We would need 157 teams (one team per segment) to cover
the total area in 6 hours, 78 teams in 12 hours and 39 teams in 24 hours etc.
Using the example above, even after we completed searching the total area we would
only have a POD of 15%. The POS for this example would be computed by multiplying the POA
= 90% x the POD = 15% or a POS of 13.5%.
Few search managers have available resources to search any area to a 15% POD, much
less a POD of 50% or more in a 24-hour period if the search area has a five mile radius.
I feel that if we plan to use formal search theory in a land search environment, we must
find better ways to drastically cut down the total search area, or only use such a system on
incidents that cover a small land mass. Evidence searches, or searches for lost children, under
six years old, are good examples where we can immediacy use formal search theory.
Example using a lost child under 6 years old
Using the lost person data, to search for a lost child under 6 years old, we would have a
search area of 6.33 square miles (1.42 x 1.42 x 3.14 = 6.22). If we use search dogs and ground
teams, we would need 12 teams to search all 12 segments in 6 hours. In 24 hours we could
develop a POD of 50% (Figure 5) and a POS of 45%.
We would have a POD figure of 17% from the first search period, 34% from the second
search period, 51% from the third period, and 68% coverage from the fourth search period etc.
It would be quite acceptable to use this new (to the land search community) method in the
above example.
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Conclusion
I feel that the work that is being done by Frost, Cooper (6) and others to integrate formal
search theory in land search environment is extremely worthwhile. It has already changed the
way others and I look at POD numbers. No longer can we accept high PODs from returning
resources when they were ask to cover large areas over short periods of time. Time and actual
area searched have to become more important factors in computing POD.
What percentage of the assigned search area could the search resource cover in the
amount of time did they spent in the area? What sweep-width did the resource use while
searching? Answers to these questions are needed to give the search manager a better idea of
how well the segment was actually covered.
To become more effective in its mission, the land SAR community needs to do a better
job of reducing the size of the search areas though better investigation techniques and lost
subject behavior studies. I feel we are on the right track using formal search theory calculations.
However, more data is needed to develop good sweep-width distance in any terrain and
environment, as well as better tracking of resource time and coverage.
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