A run sum Hotelling’s χ2 control chart

A run sum Hotelling’s χ2 control chart is proposed and its average run length (ARL) performance is evaluated using the Markov chain approach. A fast initial response (FIR) feature of this chart is also considered. In the optimization of the run sum χ2 chart, computer programs are used to compute the chart’s optimal parameters. It is shown that the run sum χ2 chart is superior to the various χ2 charts with runs rules and the synthetic χ2 chart, for all sizes of shifts in the mean vector, but less sensitive than the multivariate EWMA (MEWMA) chart toward small shifts. The sensitivity of the run sum χ2 chart in detecting small shifts can be further enhanced by adding more regions and scores, so that this chart is as competitive as the MEWMA chart. We reckon that the run sum χ2 chart is a relatively easy and effective tool for practitioners, as the χ2 chart’s statistics can be plotted in its original scale of measurement, in contrast to the MEWMA chart which plots the transformed measurements.

► We propose a run sum Hotelling’s χ2 chart that monitors the run sum of the scores.
► We compare the ARL performances of the run sum χ2, runs rules χ2, synthetic χ2 and MEWMA charts.
► The run sum χ2 chart outperforms the other charts for moderate to large shifts.
► The MEWMA chart surpasses the other charts for small to moderate shifts.
► The run sum χ2 chart plots the χ2 chart’s statistics in its original measurement scale.