City Guilds Model Questions Vol1 2023 Engineering Question 47

Two machines, A and B, operate continuously (24 h day⁻¹) throughout the year (8760 h). Machine A has a mean time between failures (MTBF) of 500 h, downtime cost of ₦500 per hour, and repair cost of ₦3000 per failure. Machine B has MTBF 800 h, downtime cost ₦400 per hour, and repair cost ₦2500 per failure. Preventive maintenance is performed on both machines together every \(T\) hours. Each preventive maintenance event costs ₦3500 and causes 2 h of downtime for the whole workshop. Assuming failures follow an exponential distribution, the probability that a machine fails before the next maintenance is \(1-e^{-T/\text{MTBF}}\). Calculate the total expected annual cost (in ₦) for \(T = 200\) h and for \(T = 400\) h, and state which interval is more economical.