Economic and Statistical Design of Vp Control Charts for Finite-Horizon Processes

In manufacturing environments where the production horizon for a specific product can be limited to a few hours or shifts, statistical process monitoring based on control charts is strategic to cut scrap, rework costs, and meet due dates. In this article, a Markov chain model is proposed to design a fully adaptive Shewhart control chart in a process with finite production horizon. The proposed Markov chain model allows the exact computation of several statistical performance metrics, as well as the expected cost of the monitoring and operation process for any adaptive Shewhart control chart with an unknown but finite number of inspections. Illustrative examples show the implementation of the Vp chart in short runs producing a finite batch of products.