City Guilds Model Questions Vol1 2024 Engineering Question 29

Three machines A, B and C operate in series in a workshop. Their monthly failure rates without preventive maintenance are λ_A = 0.02, λ_B = 0.03 and λ_C = 0.015. A preventive maintenance (PM) performed on a machine for a month reduces that machine's failure rate for that month by 80 % (i.e. the rate becomes 0.2 λ). Each PM requires 2 technician‑hours and costs $100. The workshop has 40 technician‑hours available each month. If any machine fails, the whole system is down for the month and incurs a downtime cost of $10 000. Determine, for a single month, which machines should receive preventive maintenance to minimise the expected total monthly cost (downtime cost plus PM cost). State the optimal PM schedule and the corresponding minimum expected cost.