(Sanitized)

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80B01138A000100050062-1
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 3
• Document Creation Date: December 19, 2016
• Document Release Date: May 31, 2001
• Sequence Number: 62
• Publication Date: January 4, 1968
• Content Type: MF

Approved For Relee 2006/01/03 : CIA-RDP80B01138A00IW0050062-1
4 January 1968
Problems when the Targets are
Subject to Death
Certain Probabilities in. Search
Let us assume that. a sensor system surveys the target
rea at the rate of i, looks per day. Let us assume that, because
.1 the combination of sensor and target parameters, the probability
.at +I:hu censor will detect the target or any one pass is P. Let us
Irthermore assume that the average lifetime of the target, expressed
>> days, is T.
For an on-going surveillance program-one that has reached
the ready state condition of knowledge-the expected fraction of the
-,rget.s which are correctly stated to be in existence is a useful
f,nerai measure of the overall capability of the surveillance system.
Clearly, the probability that the existence of a target is
orr. ecla y stated, given that it was most recently seen "i" looks ago
n(la.al s the probability that the target is still alive after the period of
Iline which "i" looks consume, given that it was alive "i" looks ago.
The problem arises in determining the probability on the
+.l;ht hand side of the above equation. This probability depends not
,,r,I y on the average life of the target, T, but also on the actual form
,)I the various mortality functions. Two such more mortality functions
"rill be examined. Case 1: On targets surviving exactly T days, the
probability of death at any age than T is zero; the probability of death
in the T day is 1. Case 2: The probability of death in any day, given
that the target was alive at the beginning of the day, is independent of
the age of the target. This is the so called mark off assumption. If,
furthermore, the probability that a target dies between any two succes-
sive looks of the sensor is small, then we may use a poisson appiroxi-
niation that the probability of death between any two looks is .
LT
Approved For Release 2006/01/03 : CIA-RDP80B01138A000100050062-1
 Approved For Releye 2006/01/03 : CIA-RDP80B01138A00+0050062-1
The expected lifetime of the target in both Case 1 and 2 is T clays.
The expected coverage of the surveillance can, of course,
he obtained by multiplying the probability that the target was seen "i"
looks ago between probability that the target is still alive if it was
known to he alive "i" looks ago and summing over "i" the range of
summation is from "i" to infinity. The results are:
Expected Correctness = 1
Expected Correctness
I + (1_P)T,T
P (LT - 1)
PLT + 1 - P
Numerically it appears that in the usual domain of the
parameter, there is little difference in the two values. For example,
if L = 1, T = 100, and P = 112, the expected correctness according
to Case 1 is . 9800 -1 ; according to Case 2 it is . 9802-. For extreme
cases,where the probability of a death of the target becomes significant,
the two sets diverge. For instance, if Tie take L = 1, T = 100, as
before, but reduce P to the value to --0.0-, we have a case in where
the probability that the target dies before it is seen is significant, In
this case the value given by the Case 1 formula is . 366 and by the
case 2 formula .495.
Let us assume the same target and sensor parameters as
before, and assume that a new target comes into existence. Let us
assume the probability that this new target will have been detected
by the sensor on the "nth" look in the target area or earlier. Let us
.+.sswne the mortality functions of Case 2 above. Then,
Approved For Release 2006/01/03 : CIA-RDP80B01138A000100050062-1
 Approved For Rel a 2006/01/03 : CIA-RDP80B01138A0W00050062-1
probability target will have been detected on or before "nth" look
[Z(1-P)1 - [Z(1_P)N+II
1-P
where,
Z = 1 -
1 -[Z(1-P)]
1
LT
It is interesting to note that there is some finite probability
the target will have died before it has bee detected or this probability
of never detecting the target is
1+(1 - Z)
PZ
Approved For Release 2006/01/03 : CIA-RDP80B01138A000100050062-1