SEARCH PROBABILITY THEORY

SARBC

Search and Rescue Society of British Columbia

Probability theory is a branch of mathematics with which a person may systematically deal with uncertain events. In a search, uncertain events are prevalent. There needs to be a way to quantify these events and represent them more precisely with numbers.

The chances (probability) that the subject is in a particular area is uncertain before and after the area is searched. These "chances" can be estimated by representing them as a percentage. (I.E., there is a 50% chance that the subject is in the area). An estimate of the probability of the subject being in the area is referred to as POA (probability of area).

The chances (probability) that the subject will be found by searchers is uncertain before and after a search has been made. This probability can be estimated and represented as a percentage (i.e., there is a 50% probability that your search team will spot the subject). The probability of the subject, or clues, being found by searchers is referred to as POD (probability of detection), and assumes that the clues or subject is in the area being searched. POD can be estimated by searchers after searching an area and considering all the variables that might affect it.

Definitions

POA Probability of Area - the chances that the subject, or clues, are in the area being searched.

POD Probability of Detection - the chances of finding the subject or clues given that they are in the area being searched.

POS Probability of Success - the chances of being successful with a particular search, in a given area.

Success is seemingly easy to represent; you either find them, or you don't. However, the chances of being successful can be estimated before an attempt is made, then used as a planning tool. For instance, why would you search an area if there is little chance that the subject is there (i.e., low POA); and, if he or she is there, the chances of you finding them are slim (i.e., low POD)? The chances (probabilities) of being successful are a function of both the chances that the subject is in the area and the chances that you (resources) will find the subject. The probability of being successful is referred to as POS (probability of success).

Once POD and POA are estimated, POS can be derived through this simple equation:

POS = POA X POD

While these calculations may have little value to the field searcher, they are used by search managers to represent intangible possibilities with exact numbers for planning purposes only. Quantifying probabilities allows a manager to estimate how effective they have been, or will be. A manager must know how effective they have been in order to do the following:

1. Distribute resources appropriately.

2. Decide when to search or research an area.

3. Decide when to increase or decrease the search area segment.

4. Decide when to suspend an unsuccessful search.

5. Rationalize actions to family and media.

6. Mitigate or serve as defense in litigation.

The figures themselves (30%, 40%, etc.) are meaningless unless used as relative terms to each other. A 50% POD, by itself, means nothing; but, when compared to 30%, the contrast becomes significant.

Estimating POD

Estimating POA and POS are important planning tools to the search manager, but POD is important to the field searcher because it can be both estimated and affected by what goes on in the field. Because of this, searchers need to have an understanding of POD, its estimation, and its use. A good place to start learning about POD is from some important conclusions regarding POD that were derived from an experimental analysis of grid searching conducted by Jon Wartes in the early 1970s.

POD Experiments

Experiments were conducted by Explorer search and rescue (ESAR) groups in the moderate to dense underbrush of Washington State where trained ESAR grid searching teams were used. Grid searching (line searching) was used exclusively, varying the space between searchers, and three average between-searcher spacings were tested: 20, 60, and 100 feet. The search objects varied in size and represented responsive/immobile subjects, unresponsive/immobile subjects, and small clues. Each method was tested 20 times, including 8 at night.

Some of the conclusions attributed to these experiments are:

- The average trained grid search team takes 3.5 hours to go one mile in the conditions defined (daytime).

- Average POD's:

20 ft spacing = 90%

60 ft spacing = 70%

100 ft spacing = 50%

- Generally, efficiency of the searches increased with wider spacing (especially during the day). Efficiency is a relative comparison where a more efficient search is less searcher-intensive than a less efficient search.

- POD increases when an area is searched multiple times. Multiple searches of an area with efficient search patterns are better than one less efficient, yet more thorough, search. Rarely should an area be searched only once.

- Repeated sweeps of the same area with wide spacing will be more efficient than a single sweep with close spacing.

Field Input for POD

While search managers usually use research, training, and history to determine POD for a resource, their estimation of POD can also be dependent on input from field searchers.

Managers have numerous scientific methods to estimate POA and POD, but they will also require input from searchers regarding factors that affect POD estimation that can only be gained from the field. To offer this input, field workers must have knowledge of the factors that affect POD estimation.

An easy way has been devised for field personnel to convey a POD estimate to management after a search has been conducted. A simple question is asked of field searchers and the answer allows the field personnel to quantify their experiences in a way that can be directly converted into a POD.

"If there were 10 clues of varying size in the area you were assigned to search, how many would you have found?"

There are several key parts to the question that must be considered. First, notice it addresses, " . . . in the area you were assigned to search." Obviously, if a team never reached the area they were assigned to search, the answer to the entire question must be zero (0). Also, note that, " . . . clues of varying size" are referred to. This should cause the searcher(s) to consider, in their own mind, the average density of underbrush and other factors that would make finding smaller clues more difficult. If the search area was an open field, no matter how small the clue (within reason) there is a good chance that a searcher would find something (i.e., high POD). On the other hand, if the greatest portion of the search area was densely timbered, hiding even large clues, the chances of seeing clues of any size must be correspondingly affected (i.e., low POD).

In general, the question forces the searcher to consider all variables that affected their search such as terrain, spacing between searchers, searcher consciousness, fatigue, and visibility. The number given by the searchers can be directly converted into a POD (i.e., 5 equals 50%, 2 equals 20%, 3.5 equals, 35%, etc). Search managers can compare this figure with their original estimates (before the search) and contrasts can be considered. If the manager's original estimation (before the search) is close to the field personnel's, both are probably relatively accurate. However, if a great difference exists between field and management estimates, either field personnel under- or overestimated their abilities, or management under- or overestimated the area. Nevertheless, when such a discrepancy exists, some serious reconsideration should take place.

Estimating POD after searching in the field is an important part of the overall search effort. The problem is that this is a difficult thing to do. How do you estimate, with any precision, the chances that you would have found a clue in the area you were assigned to search? What variables affect this estimation?

Let's face it, you either found something or you didn't. If you found something, you are likely to estimate a high POD. On the other hand, if you found nothing, you may be inclined to make a low estimation of POD.

When a search team goes into the field, they should have a good idea of the POD that is expected from them. This information should be part of the briefing that the team gets before their assignment. This expected POD should indicate to the team how thorough their efforts should be as well as how long they need to be in the area.

POD Influences

When search managers estimate the POD expected from a team, they allow certain criteria to influence their decision, most of which are management considerations. However, some of the information is important to field personnel because it allows them to see what affect POD from the searchers end of things. The POD influences include:

1. Time available to accomplish task. Less time (rushing) usually reduces POD.

2. POD desired or accepted. If a high POD is desired, it can usually be accomplished.

3. Amount of time searchers are available. Again, if searchers hurry because they are late, POD suffers.

4. Size of the segment to be searched. Generally, the bigger the area, the lower the POD.

5. Type and effectiveness of resource to be used. Some resources have intrinsically higher POD's than other. Grid teams vs. Dog teams, for instance.

6. Search method or combination of methods. The way a search is conducted can directly affect POD.

In addition, search managers usually consider factors that might affect searchers and subsequently decrease POD. These considerations also need to be understood by field personnel so that POD can be accurately estimated:

1. Prejudice - searchers that don't believe that clues are in the area.

2. Searcher fatigue.

3. Searcher boredom or other preoccupation.

4. Weather - may influence visibility and searcher comfort.

5. Terrain and vegetation.

When all of these factors are considered, expected POD can be estimated by search managers. But, the best estimates are still to come from the searchers after experiencing the search area.

The importance of the estimation of POD that comes from the searcher cannot be underestimated. When a POD estimate comes from an experienced search team or member, it is taken very seriously by search managers. The figure suggested may serve as the final POD for that team in calculations used by managers and ultimately factor into the determination and estimation of success or failure in that area.

It is possible, then, that the POD estimate derived from the searcher or search team determines important subsequent actions such as whether the particular area is searched again or is considered searched well enough. Such a decision may make the difference between success and failure.

There are four specific factors that enter into POD estimation from the searcher's point of view. They include:

1. Research - knowledge of the area through research or experience can be invaluable in estimating POD. What are the difficult areas to search in the area? Where are the high probability areas within the segment assigned to search? With the resources at my disposal, what are my chances?

2. Training - search training and practising with actual clues is good practice for actual situations. When searchers can train, practice searching, and practice POD estimation while getting feedback regarding actual number of clues found, they can get a good idea of their actual POD.

3. History - if you have experienced POD estimation before, you can bet it will be easier this time. Even if you have estimated POD poorly before, that experience can have a positive effect this time.

4. Quantification - ask yourself the following question:

"If there were 10 clues of varying size in the area you were assigned to search, how many would you have found?"

The answer can be directly converted to a percentage that represents your idea of POD. Individual team members can average their estimates together to come up with a team POD estimate.

Our experience with the above approach to POD estimation (quantification), is that it can be very accurate, especially when used in conjunction with the other listed factors (research, training, and history). More specifically, from teaching POD estimation to novices, our experiences and research indicate that searchers are able to acceptably estimate POD after only 3 or 4 practical experiences with quantification in the field. That is, novice searchers can estimate POD relatively accurately after very few field practice sessions. Keep in mind, however, that these results are based on proper, supervised training experiences that ultimately include all of the factors listed above.

Values That Must Be Assigned

1. A value that gives a priority to the mission urgency

2. A value that gives priorities to search areas....(PA)

3. Values to ability of resources to detect subject....(PD)

4. A value that is the product of PA X PD to measure success....(PS)

Practising POD Estimation

You can set up your own training session to gain experience and knowledge in POD estimation.

First, gather a number of "clues." These items should represent clues that might actually be found during a search and can include everything from candy wrappers to sleeping bags. They should vary in size and color and should not be made known to the searchers involved before the exercise begins.

Second, select an area that is representative of that which could be involved in a search. It should be rather large, one-quarter square mile works well. The area should be easily marked so that its boundaries are easily delineated, and searchers should not be overly familiar with it.

Distribute the clues throughout the area chosen in such a way as to mimic the way in which they may be actually found during a search. Do not, for instance, put a sleeping bag high up in a tree. Place the bag near a camp site or in a vehicle. Map the locations of the clues precisely on a map.

Lastly, search the area with the clues in it with varying types of searches. Also, vary the number of searchers and their approach to the area (i.e., from the north, south, etc.). Have the teams document exactly what they found and where they found it. The clues found should be compared with those placed in the area. The number of clues found should be divided by the number of clues placed to indicate the actual POD. The actual POD can be compared to that estimated by the team which actually searched the area. When this exercise is practised several times, searchers will become more familiar with what it is that actually affects POD in the field.

It is a good idea to use two areas for the exercise. One, used as a control, should contain clues but should not be used for POD calculations. In addition, clues should not be placed so close together or in such a quantity as to clutter the area in an unrealistic manner. Realism is important and a great number of clues is unnecessary.

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