Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

On-line monitoring of process variability is strategic to achieve high standards of quality and maintain at acceptable levels the number of nonconforming items. Shewhart control charts are the simplest Statistical Process Control (SPC) procedure to achieve this goal. An efficient implementation of a control chart requires the optimal selection of its design parameters. They can be selected according to an economic-statistical objective: an expected total cost per unit of time incurred during production is minimized subject to a statistical constraint limiting the number of false alarms issued by the control chart. This paper investigates the economic-statistical design of Shewhart control charts implementing skip sampling strategies for constructing subgroups and monitoring autocorrelated AR(1) processes. Implementing skip sampling strategies within a rational subgroup reduces the negative effects of autocorrelation on the statistical performance of the Shewhart control chart. A wide benchmark of examples has been generated as a screening experimental design to study the process and cost factors influencing the selection of the sampling strategy. Regression models have been fitted to the results to help practitioners in the selection of the most convenient sampling strategy. Finally, a sensitivity analysis has been performed to evaluate how the parameters misspecification biases the evaluation of the optimal cost per unit of time.