Quick Reference Math

SARBC

Search and Rescue Society of British Columbia

Math and Info Pocket Card templates in Acrobat PDF format

Basic Formulae, Proportional POA, Height of Object (PDF document - 12k)

Team Leader info, Terrain Analysis, Acronyms, BC layout (PDF document - 14k)

Numerical Influence of Clue, O'Connor, Probability Zones, Scenario Analysis (PDF document - 17k)

Speed Tables (PDF document - 9k)

Influence of Clue - full page (PDF document - 10k)

O'Connor Method - full page (PDF document - 5k)

The following formulae are included in the Pocket Card templates above.

Consideration of the maximization of the ROW POA - through the 
utilization of resources and area segment coverage (single/multiple - 
same/different resources) 

ROW POA[updated] = ROW POA[current] / (1-OPOS)
The ROW POA as calculated by shifted POA should be the same as this result.

OVERALL  POS
OPOS = (POD 1)*(POA1) + (POD2)*(POA2) + (PODn)*(POAn)

Relative Increase
For what-if use of resources
RI = 100(ROW POA[updated] - ROW POA[current] / ROW POA[current])

Proportional POA

Some people feel more confident using values which are proportional (or 
relational) to each other. They don't want to worry about whether or not 
they add up to 100%. Also see next page for the O'Connor method 
(letters). 

To use proportional initial POA's, don't worry about whether the values 
add up to 100%. 

Example:                        Converted to %
        Segment 1       - 29            21%
        Segment 1       - 35            25%
        Segment 1       - 40            28%
        Segment 1       - 18            13%
        Segment 1       - 13            9%
              ROW       - 5             4%
TOTAL                   - 140           100%(rounded)


Potential Clue Influence Levels for Search Segments

A - Clue strongly suggests subject is in segment
B - 
C - Clue suggests subject is in segment
D - 
E - Clue suggests nothing about subject in/not in segment
F -
G - Clue suggests subject is not in segment
H -
I - Clue strongly suggests subject is not in segment

Clue Authenticity Ratings

Clue is Very Likely Authentic
Clue is Likely Authentic
Clue is Even: As Likely Authentic as Not
Clue is Likely Not Authentic
Clue is Very Likely Not Authentic


Numerical Influence of Clue

Potential Influence Level
Authenticity Rating
        A       B       C       D       E       F       G       H      I

Very Likely Auth
        100.0   70.7    50.0    35.4    25.0    17.7    12.5    8.8    6.3
Likely Auth
        100.0   77.1    59.5    45.9    35.4    27.3    21.0    16.21  2.5
Even: Auth/Not Auth
        100.0   84.1    70.7    59.5    50.0    42.0    35.4    29.7   25.0
Likely Not Auth
        100.0   91.7    84.1    77.1    70.7    64.8    59.5    54.5   50.0
Very Likely Not Auth
        100.    100.    100.    100.    100.    100.    100.    100.   100.

This allows us to reflect the Influence of a clue to POA's, and change 
them accordingly. 

To apply the values above to the current POA distribution, use the 
following formula. 

D = S1[old]*IOC[1] + S2[old]*IOC[2] + S3[old]*IOC[3] + . . . . Sn[old]*OIC[n]
(S=area segment POA)

S1[new] = (S1[old]*IOC[1]/D*100
S2[new] = (S2[old]*IOC[2]/D*100
S3[new] = (S3[old]*IOC[3]/D*100
        . . . . . . 
Sn[new] = (Sn[old]*IOC[n]/D*100

To reverse the effect of a bad clue, apply the complement of the bad 
clue to the current POA distribution to undo its effects. 


To use the O'Connor method (letters) instead of the Mattson Method 
(percentages): 

A - Very Likely
B -
C - Likely
D -
E - Even Chance
F -
G - Unlikely
H -
I - Very Unlikely


O'Connor Method - Relative value to determine initial POA's 

                VERY LIKELY     -       <-      ->      -       VERY UNLIKELY
                A       B       C       D       E       F       G      H     I
If lowest letter 
used is:
        A       1
        B       2       1
        C       3       2       1
        D       4       3       2       1
        E       5       4       3       2       1
        F       6       5       4       3       2       1
        G       7       6       5       4       3       2       1
        H       8       7       6       5       4       3       2      1
        I       9       8       7       6       5       4       3      2     1


As an example, If you evaluated area segments and they ranged from Very 
Likely to Unlikely (A - G), then, going down the side to "G", use the 
numbers under the top row. 

If there were 4 area segments, and they were evaluated as:

        Segment 1 - G
        Segment 2 - A
        Segment 3 - C
        Segment 4 - D
Then:
        The total will be 17 (1+7+5+4) or (G+A+C+D)
        The person's POA for Segment 1 is 1/17
        The person's POA for Segment 2 is 7/17
        The person's POA for Segment 3 is 5/17
        The person's POA for Segment 4 is 4/17

Which now have to be converted to percentages:
   Seg 1 - 6%   Seg 2 - 41%   Seg 3 - 29%   Seg 4 - 24%    = 100% (rounded)

Area - with variable searcher spacing (meters/feet)
       and searcher speed (Km or Mi per hour)

(Sq Km)
AREA = (# searchers x hours x speed x spacing) / # sweeps x 1000


(Sq Mi)
AREA = (# searchers x hours x speed x spacing) / # sweeps x 5280


                            Scenario Analysis 
                       (Conditional Probabilities)

Segment Initial POA             Weighted POA                 Planning POA
     Area A  Area B    Area A(p=.70)    Area B(p=.30)___________
 1    .30     .10      .70 x .30=.210   .30 x .10=.030     .210+.030=.240
 2    .25     .05      .70 x .25=.175   .30 x .05=.015     .175+.015=.190
 3    .20     .05      .70 x .20=.140   .30 x .05=.015     .140+.015=.155
 4    .10     .30      .70 x .10=.070   .30 x .30=.090     .070+.090=.160
 5    .05     .25      .70 x .05=.035   .30 x .25=.075     .035+.075=.110
 6    .05     .20      .70 x .05=.035   .30 x .20=.060     .035+.060=.095
ROW   .05     .05      .70 x .05=.035   .30 x .05=.015     .035+.015=.050
(p = probability that scenario is valid)    
Area A (Seg 1-3)         Area B (Seg 4-6)

Scenario Analysis is the consideration of alternate search scenarios. It 
is common for an overhead team to consider all the segments in a search 
area and assign POA's. Each planner is assuming his/her scenario and 
assigning POA's accordingly - accounting for a divergence between 
planners for each segment. Indeed, five people may allocate their POA 
according to five different scenarios, that is, making entirely 
different assumptions about the lost person's behaviour. As a result, 
the averaged, or Mattson POA's may be less than optimal for planning 
purposes. 

Scenario analysis involves having the Plans Chief present a number of 
explicit scenarios to those assigning POA's to the segments. They are 
asked to estimate the probability of each scenario (as decimal). 
Planners then assign POA's to all of the segments for each of the 
scenarios. 

For example: 
If there are two scenarios, planners would estimate POA for each segment 
twice. 

Once a planner has assigned POA to every segment for every scenario, 
each POA is weighted by multiplying it by the probability of the 
scenario to which it applies. 

The weighted POA for each segment are then summed across scenarios, 
yielding one set of POA for a given planner. 

These planning POA can then be averaged with the POA from other planners 
in the usual manner, yielding a set of consensus or Mattson POA with 
which to plan the search. 

The table above represents hypothetical POA for one planner.

The planner has assigned a probability of .70 for Area A and .30 for 
Area B. His un-weighted POA assignments appear in the 2nd and 3rd 
columns. In the 2nd column, for example, these POA estimates are made 
under the assumption that the Area A scenario is valid, while POA 
appearing in the 3rd column pertain to the Area B scenario.