A modified Shewhart control chart for monitoring the BerG-GARMA model

Résumé fourni par la source

With technological evolution and increasing data availability, the need to model and monitor autocorrelated count data has grown. Traditional control charts, designed for independent data, can lead to misleading conclusions when applied to autocorrelated counts, with higher false alarm rates or failure to detect true out-of-control situations. To address this, we propose a modified Shewhart control chart to monitor the conditional mean of the Bernoulli-geometric generalized autoregressive moving average process (BerG-GARMA). The chart is constructed using Monte Carlo methods and a simple parametric bootstrap procedure. We evaluate the impact of using parameter estimates instead of true values across different scenarios, evaluating performance through in-control and out-of-control average run lengths. The practical utility of the proposed chart is illustrated through real examples, monitoring service call volumes and crime data. This approach enhances monitoring accuracy for complex count data with temporal dependencies.

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