The performance of the Shewhart sign control chart for finite horizon processes

In many manufacturing environments the production horizon of the same part code between two consecutive set-ups should be limited to a few hours or shifts. When 100% sampling is not possible, on-line quality control on a quality characteristic should be immediately started by means of a control chart. In this paper, we investigate the statistical performance of a nonparametric (distribution-free) Shewhart Sign (SN) control chart for monitoring the location of a quality characteristic in a production process with a finite horizon and a small number of scheduled inspections. The observations taken from the process are assumed to be continuous random variables. By implementing a Shewhart Sign (SN) control chart, any model assumption about the distribution of observations is needless to guarantee a nominal in-control (IC) performance: after each process set-up, this overcomes the important problem of lack of information about the distribution of the observations collected for the quality characteristic to be monitored. An extensive simulation study is conducted to compare the statistical performance of the distribution-free Shewhart SN control chart to the normal theory based Shewhart Student's t control chart: several types of distributions of observations and different numbers of scheduled inspections are considered to show the advantages related to the implementation of the Shewhart SN control chart. An illustrative example presents the implementation of the Shewhart SN control chart on a real data set collected in a beverage company.