Generalized exponentially weighted moving average (EWMA) and double EWMA (DEWMA) charts based on the Conway–Maxwell–Poisson (CMP or COM-Poisson) distribution, also known as the GEWMA and CMP-DEWMA charts, are effectively used for monitoring the counts of non-conformities in a process. To further enhance their performance, this study utilizes design and adjustment parameters to develop generally weighted moving average (GWMA) and double GWMA charts, also known as the CMP-GWMA and CMP-DGWMA charts, to monitor COM-Poisson attributes. Numerical simulations indicate that the CMP-DGWMA chart outperforms its prototype CMP-DEWMA and CMP-GWMA charts in detecting small location and dispersion shifts, as well as both shifts together, in terms of average run lengths. Finally, an example is provided to demonstrate the efficiency of the proposed CMP-DGWMA chart and its counterparts.
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