Question

Three communications channels in parallel have independent failure modes of 0.1 failure per hour. These components must share a common transceiver. Determine the MTTF of the transceiver in order that the system has a reliability of 0.85 to support a 5-hr mission. Assume constant failure rates.

Answer 1

Answer:

the MTTF of the transceiver is 50.17

Explanation:

Given the data in the question;

failure modes = 0.1 failure per hour

system reliability = 0.85

mission time =  5 hours

Now, we know that the reliability equation for this situation is;

R(t) = [ 1 - ( 1 - $e^{-0.1t$ )³] $e^{-t/MTTF$

so we substitute

R(5) = [ 1 - ( 1 - $e^{-0.1(5)$ )³] $e^{-5/MTTF$ = 0.85

[ 1 - ( 1 - $e^{-0.5$ )³] $e^{-5/MTTF$ = 0.85

[ 1 - ( 0.393469 )³] $e^{-5/MTTF$ = 0.85

[ 1 - 0.06091 ] $e^{-5/MTTF$ = 0.85

0.9391 $e^{-5/MTTF$ = 0.85  

$e^{-5/MTTF$ = 0.85 / 0.9391

$e^{-5/MTTF$ = 0.90512

MTTF = 5 / -ln( 0.90512 )

MTTF = 50.17

Therefore, the MTTF of the transceiver is 50.17