A homogeneously weighted moving average control chart for Conway-Maxwell Poisson distribution.

The homogeneously weighted moving average (HWMA) control chart is a new memory-type chart that allocates a specific weight to the current sample and the remaining weight is distributed equally to the previous samples. In this paper, the HWMA control chart is proposed for monitoring count data. This chart is based on the Conway-Maxwell (COM) distribution, which can be used to model under-spread and over-spread count data. The performance of the proposed chart is evaluated in terms of the average run-length (ARL), standard deviation of the run-length (SDRL), median run-length (MRL) as well as the expected ARL, SDRL and MRL values for both location and dispersion shifts in the process. The sensitivity of the new control chart is compared with those of some existing well-known COM-Poisson memory-type control charts in terms of the out-of-control ARL. The results of this study reveal that the proposed control chart performs competitively well with the existing charts in detecting shifts in the location and dispersion parameters in many situations. Numerical examples are given to demonstrate the application of the proposed chart.