Monitoring of location and dispersion parameters of production processes using hybrid control charts

•M-estimators with logistic curves are less sensitive to single contamination.•M-estimators with logistic curves react just as quickly to real signals as the classic one.•Proposed hybrid control charts can replace the classic mean and range control charts.•Hybrid control charts do not respond to an acceptable level of measurement data contamination. In practical terms, the measurement data from production processes are usually contaminated which may translate into failure to meet the assumed normality. In consequence, using classical Shewhart control charts to monitor the stability of production processes leads to the occurrence of numerous false signals. The purpose of this article is to propose hybrid control charts and to investigate their performance in monitoring the parameters of location and variability of production processes for which there occurs contamination of measurement data appearing at the stage of monitoring production cycles. To construct the control charts proposed by the authors, we should use extended control limits of classical Shewhart charts for means and ranges (Phase I) and robust estimators as test statistics to control the production cycle (Phase II). The article demonstrates the conducted simulation testing of classical and robust estimators for location and dispersion in terms of their effectiveness, as well as determining the relationship between them. These analyses have contributed to the design of hybrid control charts. Comparative simulation tests of classic and hybrid control charts performance have confirmed the effectiveness of the suggested measures. It follows that the proposed control charts can replace the classic counterparts, because they do not respond to an acceptable level of measurement data contamination, thanks to which it is possible to avoid taking unnecessary corrective actions in the production process. The theoretical portion is closed by a case study based on actual data which aims to illustrate the proposed approach.