Process control with learning

We study the control of a production process which moves at a random time from an in-control state to an out-of-control state where an increased number of defective units is produced. After each unit is produced, a decision maker has three choices: continue production, invest in routine maintenance that restores the process to control, and invest in a more expensive learn maintenance that, in addition, may decrease the tendency of the process to go out of control. The optimal policy structure is shown to be of the control-limit type with the property that learning is not optimal if the tendency of the process to go out of control is small enough. If there is no opportunity to inspect the process's output, an optimal policy can be interpreted as a fixed production run. For this case an exact algorithm is developed. When the process's output is inspected, an optimal policy can be interpreted as a random production run. Approximation techniques are presented for this case. The fixed production run model is an alternative technique for determining production lot sizes. The random production run model is an alternative to traditional Shewhart process control.