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The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of .97, and the other has a reliability of .99.

a. What is the reliability of the computer?

b. A backup computer identical to the one being used will be installed to improve overall reli- ability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability.

c. If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .98, what is the overall reliability of the system? (Both the switch and the backup computer must function in order for the backup to take over.)

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Answer:

a) 0.97 b) 0.9991 c) 0.008518

Explanation:

a) for the computer to work all modules must work so the lowest probsabiltiy of any one of the modules will determine the reliability of the computer.

b) Probabiltiy that 1st computer works+ Probability that 1st computer fails × Probability that back-up works

= 0.97+ 0.97×0.03

=0.9991

c) Probabiltiy that 1st computer works+ Probability that 1st computer fails× Probability that switch works× Probability that back-up computer works

=0.97+0.03×0.98×0.97

=0.998518

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