Control charts based on parameter depths

Control charts are designed to monitor on-going production processes by tracking subsequent samples of the production using some statistic of a quality characteristic. We propose to track the parameter depths of estimates of a parameter by means of depth (D)-charts, or the associated depth-based ranks by means of r-charts. More precisely, given a general parameter (e.g. mean, standard deviation or pair given by mean and standard deviation) and some historical data of the production, the parameter depth of an estimate of the parameter on new samples of the production with regard to the historical data is computed. The process is considered to be out-of-control when the depth of the estimate of the parameter falls below some given threshold (control limit). Some control limits of specific D-charts are obtained under the assumption of normality of the quality characteristic.