Question

A system has 10 essential components. Each component has an exponential time-to-failure distribution with constant failure rate of 0.04 per 4000 hours. The mean-time-to-failure, in hours, of the system is .................

Hint:

For a system with multiple components, the mean-time-to-failure is the inverse of the sum of the failure rates of individual components.

Answer 1

- For a system with $n$ components, the mean-time-to-failure (MTTF) is calculated using the reciprocal of the total failure rate.
- Given that each component has a failure rate of \( 0.04 \) per 4000 hours, the system failure rate is the sum of individual component failure rates.
- Therefore, the total failure rate for the system is \( 0.04 \times 10 = 0.4 \).
- The MTTF of the system is the reciprocal of the failure rate, which is \( \frac{1}{0.4} = 2.5 \times 4000 = 10000 \) hours.