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

976 Chapter 29 Statistics and probability distributions
Therefore the overall reliabilityof the power supply tothe computer is
R = 1 − (1 −0.511)(1 −0.511) = 0.761
Clearly the existence of a standby power supply does improve the reliability of the
power supply to the computer. In practice, the figure would be much higher than
this because once a power supply failed the standby would take over and maintenance
engineers would quickly repair the failed power supply. Therefore the period
of time in which the computer was relying on one power supply would be very
small.
We have only examined the simplest possible reliability models. In practice, reliability
engineering can often be very complicated. Some models can cater for maintenance
strategiesofthesortwetouchedoninthepreviousexample.Theeffectofnon-uniform
failureratescanalsobecateredfor.Also,manysystemsconsistofamixtureofseriesand
parallel subsystems of the type we have discussed as well as more complicated failure
modes than we have examined.
EXERCISES29.15
1 Acomputer contains 20circuit boards each with an
MTBF of3months. Calculate the probability that the
computer willsufferacircuit boardfailure duringa
monthly period.
2 Threepumpsarerequiredtofeedwatertoaboilerina
power station in order foritto be fullyoperational.
TheMTBF ofeach ofthe pumps is 10days.Calculate
the probability that the boiler willnotbe fully
operational during amonthly periodifthere are only
three pumps available.
3 Aprocesscontrol computer has apower supply with
anMTBF of600 hours. If the power supply fails then
ittakes 2 hoursto replace it.Calculate the average
availability ofthe computer power supply.
4 Aradar station has anMTBF of1000hours. The
average repair time is 10hours. Calculate the average
availability ofthe radar station.
5 Aprocessline to manufacture bread consistsoffour
main stages:mixing ofingredients, cooking,
separation andfinishing, packaging. Each ofthe
stageshas anMTBF of
MTBF m = 30 hours
MTBF c = 10 hours
MTBF sf = 20 hours
MTBF p = 15 hours
Calculate the probability that the processline will be
stopped during an 8 hour shift.
6 Aremote water pumpingstation hastwo pumps.Only
one pumpis needed in normal operation; the other
actsasastandby. Access to thisstation isdifficult and
soifapumpfails itis noteasy to repair it
immediately. Given that theMTBF ofthe pumps is
3000hours, calculate the overall reliability ofthe
pumping station duringa28 dayperiod in which the
maintenance engineers are unable to repair apump
which fails.Calculate the improvement in reliability
that would be obtained ifasecond standby pump was
installed in the pumping station.
7 Repeat the calculation carried out in Question6with
the following information.The pumps,which are
different from those in Question 6,can be considered
to consist oftwo components: a motor andthe pump
itself.TheMTBF ofthe motors is 4000hours and that
ofthe pumps is 6000 hours.