An Extended EWMA Control Chart with Multiple Dependent State Sampling for COM-Poisson Processes and Its Application to Air Quality Index Monitoring Data

Traditional attribute control charts for defect counts are commonly developed under the assumption that count data follow a homogeneous Poisson distribution. However, this assumption is often violated in practical applications. To overcome this limitation, a two-parameter Poisson distribution, the Conway-Maxwell-Poisson (CMP or COM-Poisson) distribution, has been widely used to construct control charts capable of effectively monitoring count data exhibiting over- or under-dispersion. Furthermore, the multiple dependent state (MDS) sampling scheme evaluates the current process status not only based on the present sample but also by incorporating information from previous samples, thereby achieving higher detection efficiency than single sampling schemes. This study integrates the COM-Poisson distribution with the MDS sampling strategy to develop an attribute control chart based on the extended exponentially weighted moving average statistic. The average run length is obtained under various shift magnitudes using probability-based computations. The simulation results demonstrate that the proposed chart substantially outperforms existing approaches in the prompt detection of out-of-control conditions. A real-world air quality index (AQI) monitoring study showed that the proposed chart effectively detected increases in weekly AQI counts and provided earlier warnings of potential air quality deterioration.