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Then the system availability can be expressed asP SA ¼ MUTMTBF¼ MTBF MDTMTBFSimilarly, the system unavailability can be written asð2:28ÞP SA ¼ 1 P SA¼ MDTMTBFð2:29ÞThe system reliability block diagram can be drawn, as in Fig. 2.10, for satellitecommunication between two earth stations (A <strong>and</strong> B) to be established.The system availability can be expressed as a product <strong>of</strong> each subsystem’savailability:P SA ¼MUT ESA MUTSAT MUTESBð2:30ÞMTBF ESA MTBF SAT MTBF ESBSubscripts ESA, SAT, <strong>and</strong> ESB respectively denote earth station A, satellite,<strong>and</strong> earth station B. If r <strong>of</strong> n units X 1 , X 2 , X 3 ; ...; X n are required for eachsubsystem to be working, <strong>and</strong> each unit X i has the same availability P ai ; thenthe subsystem availability can be written asP Asub ¼n Pai r Pr ain þnr þ jr nþr þ 1P rþjaiP rþ1aiwhere ðn=mÞ are the binomial coefficients.P n r 1aiþP n r jai þþP n ai ð2:31ÞExample 2.2: The mean times per year <strong>of</strong> the earth stations A <strong>and</strong> B <strong>and</strong> thesatellite are collated as tabulated below. Calculate the system availability.FIGURE 2.10System reliability block diagram.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

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