CRPS chart: Simultaneously monitoring location and scale under data-rich environment

The detection performance of a conventional control chart is usually degraded by a large sample size as in Wang and Tsung. This paper proposes a new control chart under data-rich environment. The proposed chart is based on the continuous ranked probability score and aims to simultaneously monitor the location and the scale parameters of any continuous process. We simulate different monitoring schemes with various shift patterns to examine the chart performance. Both in-control and out-of-control performances are studied through simulation studies in terms of the mean, the standard deviation, the median, and some percentiles of the average run length distribution. Simulation results show that the proposed chart keeps a high sensitivity to shifts in location and/or scale without any distributional assumptions, and the outperformance improves, as the sample size becomes larger. Examples are given for illustration.