082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

974 Chapter 29 Statistics and probability distributions
Engineeringapplication29.10
Reliabilityofaradiosystem
A radio system consists of a power supply, a transmitter/amplifier and an antenna.
During a 1000 hour period the reliabilityofthe various components is asfollows:
R ps
= 0.95
R ta
= 0.93
R a
= 0.99
Calculate the overall reliabilityof the radio system.
Solution
R =R ps
R ta
R a
= 0.95 ×0.93 ×0.99 = 0.87
thatis,thereisan87%chancethattheradiowillnotfailduringa1000hourperiod.
Using Equations (29.4) and (29.5) it is possible to generate a formula for the reliability
of a systemconsisting ofnseries components:
R = e −k 1 t e −k 2 t ...e −k n t = e −(k 1 +k 2 +···+k n )t
wherek 1
,k 2
,...,k n
arethe mean failure ratesof thencomponents.
Engineeringapplication29.11
Reliabilityofasatellitelink
AsatellitelinkisbeingusedtotransmittelevisionpicturesfromAmericatoEngland.
ThecomponentsofthissystemarethetelevisionstudioinNewYork,thetransmitter
groundstation,thesatelliteandthereceivergroundstationinLondon.TheMTBF of
each ofthe components isasfollows:
MTBF ts
= 1000 hours
MTBF tgs
= 2000 hours
MTBF s
= 500000 hours
MTBF rgs
= 5000 hours
Calculate the overall reliability of the system during a 28 day period and a yearly
period of 365 days.
Solution
Firstwecalculate the mean failure rate of each of the components:
k ts
= 1
1000 = 1 ×10−3 failuresper hour
k tgs
= 1
2000 = 5 ×10−4 failures per hour