A parameter-free adaptive EWMA mean chart

Abstract

The adaptive EWMA (AEWMA) chart provides better sensitivity than the EWMA chart when detecting mean shifts that lie within a specific interval. In this paper, we propose a novel AEWMA chart for monitoring the mean of a normally distributed process. The proposed AEWMA chart is parameter-free apart from its decision interval, which makes it very easy to implement, and at the same time, it provides balanced protection against mean shifts of various magnitudes. The idea is to estimate the mean shift using a Shewhart statistic, and then adaptively select a suitable smoothing constant for the EWMA chart based on the estimated mean shift size. The Monte Carlo simulation method is used to compute the zero-state and steady-state run length characteristics. Based on detailed run length comparisons, it is found that the proposed AEWMA chart outperforms the existing AEWMA charts when detecting small, moderate and large shifts simultaneously in the process mean. A real data application is provided to support the theory.

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