Posts Tagged ‘POD’

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Calculating Probability of Detection in Search and Rescue

February 9th, 2010

I wrote a couple of weeks ago about how to calculate a probability density distribution for a missing person search. This was the first element of the optimal search problem. The second element is to be able to calculate the probability of detection.

There have been numerous articles and methodologies proposed in the past. Most of these, unfortunately, have been wrong.

In order to calculate the probability of detection of a search resource you need several pieces of data.

Firstly the search resource’s track length must be calculated. In most cases this is simply a case of using a GPS track. However, with a foot search team, this must be multiplied by the number of searchers.

This figure is multiplied by the search resource’s “sweep width”. [I will explain more on sweep widths another time.]

This gives a Area Effectively Swept. This figure is divided by the Size of the Search Area to give the Search Coverage.

Once you know the Coverage you can use Koopman’s Exponential Detection Function to calculate POD.

Simple, eh?

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The POD of a Search Dog

January 28th, 2010

I wrote a short piece last week entitled “The POD of a Search Dog is 100%” and promised to give my thoughts on the subject at a later date. It is interesting to note that the two commenters – Daryl Toogood and Johnnie Walker – highlighted the two main issues I wanted to cover with regard to calculating PODs for search dogs.

Essentially I see two issues here.

The first is whether searching to 100% is a useful tactic, or whether as Johnnie noted “that it has slowed people down”. If you, as a dog handler, are trying to ensure you do not possibly miss the misper – do you spend too much time in any one area? Remember that search, like many other things, complies with that pesky law of diminishing returns. For each unit of search you put in, you get less out each time in added POD.

You would often do better (find more mispers!) by travelling further at a quicker rate.

The second issue here is calculating the POD of a search dog. As Daryl Toogood stated;

I would challenge any dog handler that gives a POD for their dog no matter whether it be 1% or 100% as I am not confident of the system for calculating the POD of a Dog. [Read more here...]

But this leaves search management and the search planning team a very large problem!

In order to best utilise their search resources search planners are required to decide whether to re-search a search sector, or put it aside for now and search somewhere else. Get it wrong and they potentially leave the misper to die in an area that could have been searched. How can we expect them to make such an important decision with so little clue!

I think that I will be revisiting this – both of these issues need discussing in further detail – but feel free to add your thoughts.

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Searching in the Dark

January 27th, 2010

You may remember a long while back me writing a short news article introducing a Specialist Night / Low Light Search Technician Certification Course from Gary Foo. Several comments were made at the time, with Jennie Webster making the valid point that;

Maybe explicit courses such as this would make it more obvious that ALSAR teams can and do search at night?

It’s a good idea in principle, although other courses e.g. UKLSI search techician and team leader have their main exercise at night anyway, and stress the importance of night search too.

The purpose of this piece then is to reiterate that ALSAR and other SAR organisations not only routinely search at night – but actually expect search to continue through the night. As I noted in my piece on do the police suspend vulnerable missing person search too quickly some advice from the ACPO guidance, which I think is worth repeating here…

As a general principle, searching should take place throughout the day and night. This will be determined by the circumstances but in all cases where a full managed search is undertaken, there must be valid reasons why it is not continued throughout the full 24 hours.
ACPO Guidance on the Managment, Recording and Investigation of Missing Persons, 2005

Here is also a quote from the book of the week – Greg Fuller, Ed Johnson and Robert J Koester’s book Man-Trackers and Dog Handlers in Search & Rescue – Basic Guidelines and Information.

…night itself should not be a concern to trained searchers. The possibility of walking off a drop-off and branches snapping back into searchers’ eyes are the chief concerns. All of these concerns exist during the daylight hours…

It is true that searchers will have a greatly reduced POD during night-time searches. However, it is important to remember that POD is NOT the aim of the search. The aim of search is to drive up POS as quickly as possible (FIND THE MISPER!). Waiting 6 -8 hours in order to get a higher POD means that the misper will not be found during those hours. The misper’s only chance of being found is if searchers are actually out searching!

ALSAR teams train at night, they search at night and they find mispers at NIGHT!

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Coverage

January 22nd, 2010

Coverage as a word is often used to describe how much of a search area or sector has been searched. This is wrong.

Coverage has a specific mathematical definition in search theory. It refers to the Area Effectively Swept divided by the Area of the Search Sector.  This figure is then used in Koopman’s Exponential Detection Function to calculate POD.

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Elements of the Optimal Search Problem

January 19th, 2010

Lawrence Stone defined the elements of the optimal search problem in his 1986 book, Theory of Optimal Search.

This was paraphrased extremely well by Cooper, Frost and Robe in their 2003 report – Compatibility of Land SAR Procedures with Search Theory as quoted below;

A probability density distribution on search object location and state (so the probability of containment, POC (a.k.a. POA for “probability of area”), for any subset of the possible locations and states can be estimated),

A detection function relating the probability of detecting (POD) the object if it is in a searched area to the density of the searching effort expended there,

A known finite amount of available searching effort, and

An optimization criterion of maximizing probability of finding the object in a desirable state (probability of success or POS) subject to the constraint on effort availability.

I will endeavour to simplify further. In order to need and/or use the mathematics of search theory you require four essential elements.

  1. The ability to predict the likelihood that an object is in any particular search area or region. This might be done using sophisticated computer software working with the latest missing person behaviour statistics, or could be as simple as a coming up with a consensus within the search planning team.
  2. The ability to calculate the likelihood a given search resource will have of finding the object if it in the area being searched – unfortunately we can’t ask how many clues would you have found! [See my definition of POD for a brief explanation of why]
  3. A limited but known amount of search resource – when do you ever get too much search resource?
  4. A method of calculating the best way to use the search resource to maximise the chances of finding the search object as quickly as possible.

I’ll look in detail at each of these in further posts.

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