Design variable-sampling control charts using covariate information

Statistical Process Control (SPC) charts are widely used in manufacturing industry for monitoring the performance of sequential production processes over time. A common practice in using a control chart is to first collect samples and take measurements of certain quality variables from them at equally-spaced sampling times, and then make decisions about the process status by the chart based on the observed data. In some applications, however, the quality variables are associated with certain covariates, and it should improve the performance of an SPC chart if the covariate information can be used properly. Intuitively, if the covariate information indicates that the process under monitoring is likely to have a distributional shift soon based on the established relationship between the quality variables and the covariates, then it should benefit the process monitoring by collecting the next process observation sooner than usual. Motivated by this idea, we propose a general framework to design a variable-sampling control chart by using covariate information. Our proposed chart is self-starting and can well accommodate stationary short-range serial data correlation. It should be the first variable-sampling control chart in the literature that the sampling intervals are determined by the covariate information. Numerical studies show that the proposed method performs well in different cases considered.