Investigation of the effect of inertia on the performance of nonparametric signals of cumulative sum and rhythmic moving average
Volume 6, Issue 1, Spring 2016, Pages 45-56
Maysam Madadi, Majid Nojavan
Abstract In CUSUM and EWMA, a change in process may cause the statistic to move away from the center. In this case, if another change occurs in the opposite direction, the chart needs more time to be warned. This is called the inertia effect. In this paper, the effect of inertia on the performance of non-parametric CUSUM and EWMA sign diagrams is investigated and the two diagrams are compared. To do this, a simulation program is developed that calculates the average length of the sequence in the controlled state (ARL0) and out of control (ARL1) in these diagrams for different parameter values using three different distributions. The results of the simulation show that the values of ARL0 in the CUSUM symbol are not affected by inertia, but the values of ARL1 in the graph increase in large changes and the power of the graph in detecting these changes decreases. Also in the EWMA symbol chart, the ARL0 values decrease and the ARL1 values increase for medium and large changes. In other words, due to inertia in this chart, the number of false warnings increases and the power to detect changes decreases. Due to the less negative effect of inertia on the performance of the CUSUM signal diagram than EWMA, the use of this diagram in the control of abnormal processes is recommended.