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Reliability Probability

wtrow

New member
Joined
Jan 24, 2011
Messages
17
Suppose a RADAR for aircraft detection works properly with probability 0.9. It is observed
that RADARs fail independently of each other. The aircraft is present in the air-space
with probability 0.2. You want to improve the reliability of such a RADAR. You build
a super-RADAR system having 5 RADARs in parallel, and a logic circuit that uses the
maximum posterior probability detection. What is the probability that your super-RADAR
works properly?

Since they are all in parallel, only one has to work. So I thought I should use the formula: 1-(1-0.9)^5 to solve the whole problem. This seems too easy though. Then I thought of combining the reliability of the detection with the chance of an aircraft being present, giving 0.9*0.2=0.18. Then I solve for that: 1-(1-0.18)^5 = 0.63. Next, solve for the chance of an aircraft actually being present: 1-(1-0.2)^5=0.67. Then divide the first by the second: 0.63/0.67=0.936, giving the total reliability of the array. I still think this is incorrect, however. Any tips?
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,708
I think the aircraft has nothing to do with proper operation of the array. The question, as stated, is "works properly". You don't want it to sound an alarm when nothing is there, do you? Let's not complicate it. Go with your first impression.
 
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