Designing a cumulative sum control chart using generalised Conway-Maxwell-Poisson distribution for monitoring the count data

This study proposes a multipurpose cumulative-sum control chart based on the generalised Conway-Maxwell Poisson (GCOMP) distribution and names it the GCUSUM control chart. The proposed control chart monitors dispersed count data considering tail behaviour. Further, the proposed chart can also monitor zero-inflated count data. The proposed chart's in-control and out-of-control performance analyses have been conducted using different run-length (RL) criteria. A comparative study has been presented to show the effectiveness of the proposed GCUSUM chart over established charts for monitoring distinctive features of the count data. It has been observed that the proposed control chart is efficient in monitoring the under- and over- dispersion in the count data while considering the tail behaviour. The GCUSUM chart also monitors the zero-inflated count data without utilising the zero-inflation property. Numerical and real-life examples also validate the effectiveness of the proposed control chart. [Received: 24 July 2022; Accepted: 25 April 2023]