The Detection of Shifts in the Ratio of Two Poisson Means with an Exponentially Weighted Moving Average Control Chart
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Abstract
The Exponentially Weighted Moving Average (EWMA) control chart is widely used for detecting and controlling the variations in production processes in order to gain efficient manufacturing process. The control chart can be applied to engineering, medical, financial, psychology fields, and etc. In general, one of the control chart performance metrics is Average Run Length (ARL). Therefore, the objective for this research is to approximate the ARL using Markov Chain Approach (MCA) for EWMA control charts for a binomial distribution underlying the ratio of two Poisson means. The proposed MCA is compared with Monte Carlo Simulation (MC) by using absolute percentage relative error. In addition, this research compared the efficiency of EWMA and Cumulative Sum (CUSUM) control charts and found that in the aspect of process change detection, CUSUM performed better than EWMA for all changing levels.
Keywords: Exponentially weighted moving average, Cumulative Sum, average run length
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