Answer:
The system's Mean Time to Failure is 1,041.[tex]\bar 6[/tex] hours
Explanation:
The number of independent identical motors = 4
The failure rate of each motor, λ = 0.002 failures per hour
Given that in order for the system to work, at least one of the motors must operate, therefore, the system are in parallel
The Mean Time to Failure for a parallel system of four identical components is given as follows;
[tex]MTTF = \dfrac{1 }{\lambda} \times \left (1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} \right)[/tex]
Which gives;
[tex]MTTF = \dfrac{1 }{0.002} \times \left (1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} \right) = 1,041.\bar 6[/tex]
The system's Mean Time to Failure = 1,041.[tex]\bar 6[/tex] hours.
