Authors : Ayu Abdul Rahman, Sharipah Soaad Syed Yahaya and Abdu Mohammed Ali Atta
Abstract: Unlike traditional Shewhart Chart, Cumulative Sum (CUSUM) chart is more sensitive to small and moderate shifts. Nonetheless, its reliability in monitoring the mean shifts is usually hampered by the underlying distribution of the data. Although, apparent cause of non-normality is owed to outliers, their presence may simply be a genuine part of the process rather than attributing to the special causes. To set these occasional outliers apart from the real distributional shifts, numerous extensions of the CUSUM charts have been suggested. One possible way is via robust estimation. This paper proposes a simple, yet effective way to make the chart highly effective for detecting small sustained shifts. A very robust scale estimator, namely Median Absolute Deviation about the median (MADn) is used as an estimate for dispersion. The performance evaluation of the proposed chart for monitoring mean shift is compared with the standard CUSUM chart using several aspects of the run length distribution the Average Run Length (ARL), Standard Deviation of the Run Length (SDRL) and percentile run length. The simulation results indicate the robust CUSUM chart efficiency in detecting small magnitude of shifts in both normal and outlier-prone data.
Ayu Abdul Rahman, Sharipah Soaad Syed Yahaya and Abdu Mohammed Ali Atta, 2018. A Robust Cumulative Sum Control Chart for Monitoring the Process Mean based on a High Breakdown Point Scale Estimator. Journal of Engineering and Applied Sciences, 13: 3423-3429.