The triple generally weighted moving average control chart for monitoring Poisson observations

Quality control charts are widely used to monitor the production process or service process, detect the process mean shifts as soon as possible and improve the quality of the process. In many practical applications, we need to use attribute control charts. The quality characteristics of interest, such as the number of nonconformities or defects in an inspection unit may follow the Poisson distribution. In this paper, we propose a triple generally weighted moving average control chart for monitoring Poisson observations (regarded as PTGWMA control chart). The average run length (ARL) is used to evaluate the performance of the control chart. We use the Monte Carlo Simulation to compute the ARL of the control charts. The average run length (ARL) of the proposed control chart is compared with the existing PEWMA, PGWMA, PDEWMA, PDGWMA and PTEWMA control charts. The results show that the PTGWMA control chart outperforms its competitors in detecting small process mean shifts for Poisson observations. We also provide two illustrative examples to demonstrate the proposed PTGWMA control chart is more effective than the existing Poisson control charts in detecting the small upward process mean shifts and the downward process mean shifts for Poisson observations.