For example consider network c since there are four

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Unformatted text preview: he lower path fails. So the network outage probability is the product of the failure probabilities for the upper and lower paths. That is, for network C, P (F ) = (p1 + p2 − p1 p2 )(p3 + p4 − p3 p4 ). If pi = 0.001 for all i, P (F ) = (0.001999)2 ≈ .000004. Network D is similar to network B . Like network B, network D has two stages in series, but each stage of network D consists of two links in parallel instead of only a single link per stage. Outage occurs in network D if and only if either the first stage fails or the second stage fails. The first stage has links 1 and 3, and the event the first stage fails can be written as F1 F3 , which has probability p1 p3 . Similarly, the second stage has links 2 and 4, and the event that the 2.12. RELIABILITY 63 second stage fails can be written as F2 F4 , which has probability p2 p4 . Since the two stages involve separate sets of links, the first stage fails independently of the second stage. So the network outage probability is P {first stage fails} + P {second stage fails}− P {both stages fail}. Th...
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