The Variable Sampling Interval control chart for short production runs

Global market competitiveness imposes to many companies a high level of flexibility to allow for theproduction of a large variety of products. To limit work-in-process, decision makers periodicallyschedule according to a make-to-order management strategy the production of finite batches of thesame product code. Scheduling calls for frequent set-up activities which reconfigure a manufacturingprocess to switch between different codes. This can limit the production horizon of one product codeto a few hours or shifts. In this context, efficient on-line quality control monitoring by means ofcontrol charts is strategic to eliminate scrap or rework and to meet the demand on time according tothe production plan. Design of control charts in processes with limited production horizon is achallenge tackled by Statistical Process Control (SPC) practitioners and scholars.Under this framework, this paper investigates the issues related to the implementation of the VariableSampling Interval (VSI) Shewhart control chart in a process with finite production horizon. When theproduction horizon is finite, the statistical properties of a control chart are known to be a function ofthe number of scheduled inspections. In the case of a VSI control chart, the quality practitioner cannotfix the number of inspections a priori due to the stochastic nature of the sampling interval selection.Therefore, the aim of this paper is to propose a new Markov chain approach for the exact computationof the statistical performance of the VSI control chart in processes with an unknown and finite numberof inspections. The proposed approach is general and does not depend on the monitored samplestatistic. With reference to the process mean monitoring, an extensive numerical analysis comparesthe performance of the VSI X chart to the Variable Sample Size (VSS) and Fixed Sampling Rate(FSR) z charts. Numerical results show that the VSI X chart outperforms other charts for moderate tolarge shift sizes. An illustrative example shows the implementation of the VSI X chart in a short runproducing a finite batch of mechanical parts.