The variable sampling interval control chart for finite-horizon processes

The requirement to be globally competitive requires companies to have a high level of flexibility to allow for the production of a large variety of products. To limit work-in-process, decision makers periodically schedule according to a make-to-order management strategy i.e. the production of finite batches of the same product code. Scheduling calls for frequent set up activities, which require the reconfiguration of a manufacturing process, and allows manufacturers to switch between different codes. This can limit the production horizon of one product code to a few hours or shifts. In this context, efficient online quality control monitoring using control charts is strategic to eliminate scrap or rework and to meet the demand at the time specified by the production plan. The design of control charts for a process with a limited production horizon is a challenge for statistical process control practitioners. Under this framework, this article investigates the issues related to the implementation of the Variable Sampling Interval (VSI) Shewhart control chart in a process with finite production horizon. When the production horizon is finite, the statistical properties of a control chart are known to be a function of the number of scheduled inspections. In the case of a VSI control chart, the quality practitioner cannot fix the number of inspections a priori due to the stochastic nature of the sampling interval selection. Therefore, the aim of this article is to propose a new Markov chain approach for the exact computation of the statistical performance of the VSI control chart in processes with an unknown and finite number of inspections. The proposed approach is general and does not depend on the monitored sample statistic. With reference to the process mean monitoring, an extensive numerical analysis compares the performance of the VSI X‾$\skew5\bar X $ chart to the Variable Sample Size and Fixed Sampling Rate z charts. Numerical results show that the VSI X‾$\skew5\bar X $ chart outperforms other charts for moderate to large shift sizes. An illustrative example shows the implementation of the VSI X‾$\skew5\bar X $ chart in a short run producing a finite batch of mechanical parts.