The guidance system of a ship has three modules that must all function properly
ID: 470029 • Letter: T
Question
The guidance system of a ship has three modules that must all function properly for the system to work. Two of the modules have reliability of .99, the other has a reliability of .90. a. Compute the reliability of the system. b. A backup system identical to the first will be added to the ship. The backup will be switched on automatically if the first system fails. Assuming that the switch to the backup works perfectly, what is the reliability of the ship's guidance system now? Show your calculations. This part is not required. Suppose the backup switch is only 94% reliable. What is your new (revised) answer for the question posed in part b. above? Show your calculations.Explanation / Answer
a. The reiability of the system to work depends upon the odds of the modules to work at same time
= (0.99) * (0.99) * (0.90) = 0.88209
b. The backup system to work, having the same reliability means our system will work if either one of them works or when both of them work
= 1- probability that both systems dont work
= 1- (1-0.88209)^2 = 0.9860
c. Now, suppose the backup switch is only 94% reliable.
therefore to figure out the probability of the system to be working, we will use the value of part (b) and find the probability of them both working and the probability of the first working and the second not working adding to the probability of the second system working but the first not working
= (0.9860)^2+( 0.9860*(1- 0.9860))+(1- 0.9860)(0.94)(0.9860)= 0.9989
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