Production and maintenance control for manufacturing systems

This note addresses the production and maintenance control problem of a fai lure prone manufacturing system consisting of one machine and producing one part type. The machine is assumed to have three working states: good, aver age and bad, and a failure state. In the three working states, the machine can produce parts and some of these parts are rejected with a rate dependin g on the machine state. In the failure state, no part is produced. The stat e transition of the machine is governed by a continuous-time Markov process . The jump rates from average and bad states to the good state are the prev entive maintenance rates and the one from failure state to good state is th e corrective maintenance rate. The production rate and the maintenance rate s are optimized.