City Guilds Model Questions Vol1 2017 Engineering Question 24

A machine contains two critical components, A and B, whose failures are independent and follow exponential distributions. The failure rates are \(\lambda_A = 2\times10^{-5}\) h⁻¹ and \(\lambda_B = 5\times10^{-5}\) h⁻¹. The plant operates continuously (24 h day⁻¹).\ (a) Compute the system mean time between failures (MTBF) when both components must be functioning.\ (b) A preventive maintenance is performed on component A every 2000 h, after which its failure rate drops to \(0.5\times10^{-5}\) h⁻¹, while component B's rate remains unchanged. Determine the new system MTBF after the first maintenance interval.\ (c) Estimate the expected number of system failures in one year (8760 h) before and after the maintenance schedule.