A progressive mean control chart for dispersed count data considering tail behavior

Abstract

ABSTRACT Popular discrete distributions generally neglect tail behavior in the count data despite its significance in many industrial and non-industrial processes. The generalized Conway-Maxwell-Poisson (GCOMP) distribution considered the tail behavior while modelling the dispersed count data. In this study, GCOMP distribution-based progressive mean control chart is developed to monitor ‘over-dispersed and longer tail’ or ‘under-dispersed and shorter tail’ count data and termed as the GPM control chart. Performance evaluation based on the run-length (RL) distribution for the proposed control chart is conducted through the Monte Carlo simulation. The performance comparison shows that the proposed GPM control chart outperforms the progressive mean control chart based on the Conway-Maxwell-Poisson distribution (COMP-PM) for a range of shifts considered in ‘over-dispersed and longer tail’ count data, and for upwards shifts in ‘under-dispersed and shorter tail’ count data. The sensitivity of the Poisson distribution-based progressive mean control chart is also studied and compared with the proposed GPM control chart. It has been found that the proposed GPM control chart is very robust for ‘over-dispersed and longer tail’ or ‘under-dispersed and shorter tail’ count data. Finally, two simulated and numerical examples from finance and telecommunication engineering are used for the demonstration of the proposed control chart.