Need to be done 100% accurate

Q 1

The propulsion system of a twin-screw cruise ship consists of four high-speed diesel

engines. Each propeller shaft is driven by a pair of engines through a gearbox.

During the course of designing the ship, two different proposals are considered for the

operation of the pairs of diesels in the propulsion system. The first configuration

involves making each pair of diesel engines standby parallel systems. The active

engine of each pair has a failure rate of 7000 per million hours. The standby engine is

assumed not to fail while idle. Switching between engines is imperfect, with a

probability of switching failure of 2%. A gearbox in this configuration has a failure

rate of 280 per million hours. There are no common cause failure modes.

The second configuration is to operate a pair of diesels in an active parallel

configuration. The failure rate of each engine is 5000 per million hours, and is

unaffected by how many engines are working. Common cause failures are modelled

with a beta-factor of 10%. A gearbox in this configuration has a failure rate of 200 per

million hours.

Irrespective of the configuration, the ship will sail safely with just one operational

diesel engine. A cruise lasts five days. Ignoring the possibility of repairing a failed

engine before another engine fails, determine the probability of complete propulsion

system failure before the end of the cruise for each configuration. Hence decide which

of the two design proposals is the most reliable

Question 2

Q 3

Q 4

Q 7 next 2 pages