A B7XX plane has two similar computers onboard for flight control functions: One that is operational and the second as an active-standby. The time to failure for each computer follows an exponential...

A B7XX plane has two similar computers onboard for flight control functions: One that is operational and the second as an active-standby. The time to failure for each computer follows an exponential distribution with an MTBF of 4000 hours.

(a)
Find the reliability of the computer system (consisting of both computers) for 800 hours when the switching is perfect and the second computer is instantaneously switched on when the first computer fails. Also, find the MTBF of the computer system.

(b)
Find the MTBF of the computer system when the switching and sensing unit is not perfect and the switching mechanism has a reliability of 0.98 when it is required to function.

Supposedly the constant failure rate for both the main and the standby units are constant and are given by λ= 0.02 per hour, and the constant failure rate of the switching and sensing unit is λSW =0.01 per hour.

(c)
Find the reliability of this system for an operating time of 50 hours.