Q.1) Boeing Aircraft Company is interested in learning about the reliability of its toilets on its long haul 747s having

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Q.1) Boeing Aircraft Company is interested in learning about the
reliability of its toilets on its long haul
747s having been notified of passenger complaints. On average the
flight time of these long-haul
planes is 11 hours. It tested 13 toilet units for a duration of 50
hours each. During the test, one unit
failed after 20 hours. One after 25 hours and one after 45
hours.
After the 50-hour test, calculate
1) The failure rate as a percentage, FR(%)
2) The mean failure rate in hours FR(N)
3) The mean time between failures MTBF
4) Estimate how many long haul 11hr trips for a single unit toilet
failure to occur.
Q.2) A lot of 100 repairable pumps was tested over a 12-month
24hr period. Twenty failures occurred
and the corresponding down times in hours were 5, 6, 3, 4, 2, 5, 7,
2, 5, 3, 4, 2, 5, 4, 4, 5, 3, 6, 8, 7
Using data provided calculate
1) Mean Down Time
2) MTBF
3) Mean Failure Rate, FR(N)
4) Availability
5) Reliability over 1.5 years, assuming constant failure rate.
Q.3) A gas-fired power station has four generation units, each
capable of producing electric power at a
rate 200 MW. In order to maintain adequate power supply to the
network three generation units
must run continuously with the fourth on active standby. Using the
binomial expansion of (𝐹+ 𝑅)𝑛
find the probability that three units will be running four years
after installation if the failure rate λ
for each generation unit is 0.06 / yr.