Hybrid synthetic and group runs charts using alternating the charting statistic to monitor the mean vector of a multivariate process

Abstract

For multivariate processes, while developing the multivariate control charts, the test statistics, which are the function of all quality characteristics, are derived. In ACS chart, by alternating the charting statistic, only one of the two/three quality characteristics is inspected (measured) per sample. As ACS chart is operationally easier and efficient, in this article, we use the runs rules to propose two new hybrid control charts namely ‘Alternated Charting Statistic Synthetic’ (ACS-Syn) chart and ‘Alternated Charting Statistic Group Runs’ (ACS-GR) chart to monitor the mean vector of a multivariate process. In zero state as well in steady state case, for bivariate/trivariate processes, when there is no correlation or small to moderate correlation between the two quality characteristics, it is numerically illustrated that the ACS-Syn chart performs better than ‘Multivariate Synthetic chart to detect shifts in the Mean vector’ (MV-Syn-M) chart. Also, ACS-GR chart performs better as compared to the ACS-Syn chart and ACS chart. Further, for some combinations of δ values, ACS-GR chart performs better than ‘Multivariate Group Runs char to detect shifts in the Mean vector’ (MV-GR-M) chart. Considering all the three correlation coefficients, same, similar results are observed for trivariate case.