A mathematical model for the optimal robust design of cause selecting control charts

Cause selecting charts (CSC) are statistical control-charts for monitoring multiple sequential processes; in contrast, Shewhart control-charts are useful for monitoring independent processes. The economic-statistical design of CSC involves the selection of the optimal design parameters that include the width of the chart, sample size, and sampling interval. The application of economic-statistical criteria is a well-established and active research field. However, these design approaches may not be reliable for a dynamic production environment due to the uncertainty associated with the values of the model parameters. The purpose of this paper is to develop a robust economic-statistical model for the design of CSC. The model is intended to minimise the risk associated with the incidence of different scenarios in a real production environment. Through the use of examples and sensitivity analysis, it is demonstrated that the model provides design parameters that are more sensitive to shifts, protect against the occurrence of other scenarios, and results in charts with a higher power. [Received: 21 July 2018; Accepted: 24 March 2021]