Optimal Design of Pre-control Plans

Pre‐control is a quality tool for quick set‐up approvals, especially used in short‐run processes. It is based on specifications instead of the natural variability of the process and uses cumulative counts in order to yield a conclusion. Its main drawbacks are a high false alarm rate and a low power to detect process deviations, under certain circumstances. These issues can be addressed by making the technique more flexible, as shown in previous works. In this paper, we introduce a Mathematical Programming approach in order to optimally determine the value of the pre‐control parameters, so that it can meet the user's requirements while minimizing the sample size of the technique as much as possible. We propose and develop a mathematical model for optimal pre‐control and perform some numerical experiments in order to show its effectiveness.