Question

A system has 4 independent and identical motors, in order for the system to work, at least one of the motors must operate. Each motor's failure rate is 0.002 failures per hour. What is the system's Mean Time to Failure (MTTF)?

Answer 1

Answer:

The system's Mean Time to Failure is 1,041.$\bar 6$ 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;

$MTTF = \dfrac{1 }{\lambda} \times \left (1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} \right)$

Which gives;

$MTTF = \dfrac{1 }{0.002} \times \left (1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} \right) = 1,041.\bar 6$

The system's Mean Time to Failure = 1,041.$\bar 6$ hours.