Robust memory-type control charts for monitoring location parameter under non-normal data

Control chart is popularly used to monitor and improve the quality of a process. This statistical tool can be categorized into memoryless and memory-type control charts. An example of memoryless control chart is Shewhart chart which uses the most recent information of samples in a process. Conversely, the memory-type control charts such as cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) use both past and recent information in the process. Thus, make the charts more sensitive in detecting small to moderate shifts. Recently, the CUSUM and EWMA charts were combined to form mixed EWMA-CUSUM (MEC) and mixed CUSUMEWMA (MCE) charts to further improve small shift detection. However, these MEC and MCE charts are based on mean, thus they rely on the normality assumption. Under non-normality, parameters estimation based on the mean will be perturbed, leading to increased false signal and delayed detection of shifts. To solve this problem and improve the monitoring process, three median-based location estimators (median, modified one step M-estimator (MOM), winsorized MOM (WMOM)) which possess the highest possible breakdown point (50%) were used in the construction of the MEC and MCE charts, yielding six newly robust charts, namely MEC!" , MECMOM, MECWMOM, MCE!" , MCEMOM, and MCEWMOM. Via extensive simulation studies using SAS programming software, the proposed robust charts were tested under several conditions, focusing on g-and-h distributions, sample sizes, design shifts and shift sizes. Optimal parameters for the charts were derived to achieve the pre-determined average run length (ARL) under normality and subsequently, the robustness of the charts were assessed based on the ARL upon departure from the distribution. Validation of the charts’ performance were conducted using water quality and marker band data. From the simulation, the MEC charts based on the MOM and WMOM estimators are the best since the charts have good in-control robustness and fast detection capability. Moreover, the proposed charts have been validated using real data, demonstrating their practical applicability. Both simulation and real data analyses show that the proposed median-based charts outperform the standard charts across various conditions specified in this study. The findings offer practitioners feasible alternative charts for monitoring processes when the underlying data deviate from normality.