The Exponentially Weighted Moving Average (EWMA) schemes are a potent tool for monitoring small to moderate variations in the quality characteristics in production lines of manufacturing industries. Practitioners in various sectors widely use the EWMA schemes for scrutinising both the variables and attributes. In the present article, we investigate a modified EWMA scheme based on the power of the difference between the actual number of nonconforming items and its technical specification in an in-control (IC) situation. We abbreviate it as a wEWMA scheme and show that the traditional EWMA scheme is a particular case of the proposed scheme when the power is unity. We establish that the powers lower than unity are more effective for detecting smaller shifts, while for detecting substantial variations in process parameter, one should prefer higher powers greater than unity. Noting that possible magnitude of a shift is often unknown, we propose the optimal design procedure of the scheme, including the determination of its charting parameters to ensure the best overall performance. The results reveal that the optimal wEWMA schemes can be beneficial in detecting a shift very quickly when the sample size is small, particularly for high-precision production processes.
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