Nonparametric predictive inference in statistical process control

Statistical process control (SPC) is used to decide when to stop a process as confidence in the quality of the next item(s) is low. Information to specify a parametric model is not always available, and as SPC is of a predictive nature, we present a control chart developed using nonparametric predictive inference. The proposed ’extrema chart’, based on the extrema of a sample of observations from the process, is a generalisation of an existing nonparametric method, which controls a process using single observations. We examine the average run length (ARL) of both the one-sided and two-sided extrema chart, and a simulation study is presented to compare the extrema chart with the well known X chart and CUSUM chart. The disadvantage of these charts is that when the process mean and variation of the in-control process have to be estimated, the ARL is biased. This is not an issue for the extrema chart, as no knowledge about the underlying distribution is required.