* Bridging Probability of Detection Formula * From: Jack Frost To: 'Martin Colwell' Subject: Bridge POD Formula Date: Tue, 28 Apr 1998 19:29:55 -0400 Martin, I think your question was, "Given a cumulative POD goal and the cumulative POD to date, what does the POD of the next search have to be in order to attain the POD goal?" Attached is the derivation of the formula. Please test it thoroughly by putting the results back into the cumulative POD formula to make sure that answer agrees with your POD goal. I would use a random number generator to generate a POD goal (say, between 75% and 99%) and then use it to independently generate an initial POD value of anything between zero and the POD goal, compute the "bridge POD", then feed it back into the cumulative POD formula, subtract the resulting cumulative POD from the original goal POD, accumulate the differences and their squares, compute the mean and standard deviation of the differences. Also collect the largest (in absolute value) difference. Put all this in a loop that runs a 1,000 times or so. The mean, standard deviation and largest absolute difference all ought to be very, very small if not zero. In Pascal, the formula (with POD's expressed as decimal values) would look like: BridgePOD := 1.0 - ((1.0 - GoalCumPOD)/(1.0 - CurrentCumPOD)); Hope this helps! Jack Frost Bridging POD logic: PODc is the POD Goal (ie the PODcumulative). POD1 is the POD of the first sweep, the current POD. POD2 is the POD of the second sweep, (the Bridging POD), required to reach the PODc Goal in one more sweep from the current POD. Given PODc and POD1, find the value of POD2 needed to get from POD1 to PODc with one more search. PODc = 1-(1-POD1) x (1-POD2) (1-PODc) = (1-POD1) x (1-POD2) (1-PODc) -------- = (1-POD2) (1-POD1) (1-PODc) 1 - -------- = POD2 (1-POD1) (1-PODc) POD2 = 1 - ------- (1-POD1) For example, to get to a cumulative POD of 0.8 (80%) from a POD of 0.2 (20%) requires a POD on the next search of 0.75 (75%). To get to a cumulative POD of 0.8 (80%) from a POD of 0.5 (50%) requires a POD on the next search of 0.6 (60%). To get to a cumulative POD of 0.75 (75%) from a POD of 0.5 (50%) requires a POD on the next search of 0.5 (50%). J. R. Frost e-mail: jack_frost@soza.com Technical Program Manager voice: 703-560-9477/6551, x6712 Soza & Company, Ltd. fax: 703-560-6640 8550 Arlington Boulevard Fairfax, VA 22031 USA