The guidance system of a ship is controlled by a computer that has 3 major modules. In order for the computer to function properly, all 3 mo

Question

The guidance system of a ship is controlled by a computer that has 3 major modules. In order for the computer to function properly, all 3 modules must function. Two of the modules have reliabilities of 0.97 and the other has a reliability of 0.99.

a) What is the reliability of the computer?

b) A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one falls, 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 0.98, 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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Adalyn 1 month 2021-10-18T14:50:44+00:00 1 Answer 0 views 0

Answers ( )

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    2021-10-18T14:52:17+00:00

    Answer:

    a) 0.931491

    b) 0.995307

    c) 0.994030

    Step-by-step explanation:

    a) Since all components must be working, the reliability of the computer is the product of the reliability of the three components:

    R_1 = 0.97*0.97*0.99\\R_1=0.931491

    b) The resulting reliability is now the reliability of the first computer, added to the possibility of failure of the first computer multiplied by the reliability of the second computer:

    R= R_1 +(1-R_1)*R_2\\R= 0.931491+(1-0.931491)*0.97*0.97*0.99\\R=0.995307

    c) If a switch with reliability of 0.98 must be activated to turn on the second computer, the switch’s reliability must be taken into account as follows:

    R= R_1 +(1-R_1)*R_2*R_S\\R= 0.931491+(1-0.931491)*0.97*0.97*0.99*0.98\\R=0.994030

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