City Guilds Model Questions Vol1 2019 Engineering Question 40

A piece of equipment experiences an age‑dependent failure rate given by \(\lambda(t)=0.0001\,t\) failures per hour, where \(t\) is the operating time (in hours) since the last maintenance. Two maintenance strategies are considered over a planning horizon of \(1000\) hours:\n\n1. **Time‑based preventive maintenance** performed every \(T\) hours. Each preventive visit costs \(\text{₦}500\) and instantly restores the equipment to \(t=0\).\n\n2. **Condition‑based monitoring** that incurs a fixed daily cost of \(\text{₦}100\). The monitoring detects an impending failure with probability \(0.9\); when a failure is detected, a corrective maintenance action costing \(\text{₦}1200\) is carried out immediately. If a failure is not detected, it occurs and the same corrective cost is incurred at the time of failure.\n\nAssuming failures follow a Poisson process with the given rate function, determine the optimal preventive interval \(T\) (in hours) that minimizes the average cost per hour for strategy 1. Then compute the average cost per hour for strategy 2 and state which strategy is more economical.