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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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.
 Spring '08
 Zahrn
 The Land

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