The Effect of Median Based Estimators on CUSUM Chart

Abstract

Cumulative Sum (CUSUM) chart has been used extensively to monitor mean shifts. It is highly sought after by practitioners and researchers in many areas of quality control due to its sensitivity in detecting small to moderate shifts. Normality assumption governs its ability to monitor the process mean. When the assumption is violated, CUSUM chart typically loses its practical use. As normality is hard to achieve in practice, the usual CUSUM chart is often substituted with robust charts. This is to provide more accurate results under slight deviation from normality. Thus, in this paper, we investigate the impact of using robust location estimators, namely, median and Hodges-Lehmann on CUSUM performance. By pairing the location estimators with a robust scale estimator known as median absolute deviation about the median (MADn), a duo median based CUSUM chart is attained. The performances of both charts are studied under normality and contaminated normal distribution and evaluated using the average run length (ARL). While demonstrating an average power to detect the outof-control situations, the in-control performances of both charts remain unaffected in the presence of outliers. This could very well be advantageous when the proposed charts are tested on a real data set in the future. A case in point is when the statistical tool is used to monitor changes in clinical variables for the health care outcomes. By minimising the false positives, a sound judgement can be made for any clinical decision.