Poisson and negative binomial dynamics for counted data under CUSUM-type charts

Abstract

Control charts for counted data are commonly designed assuming that counts follow Poisson dynamics. However, in various real situations, the true underlying dynamics of the events are more properly modelled by a negative binomial process. This paper examines the consequences of the Poisson approximation to negative binomial dynamics for counts under CUSUM-type schemes. It is essentially found that, on setting up Poisson dyamics for an underlying negative binomial data structure, the real in-control average run length decreases, whereas the sensitivity of the chart is affected less. These results warn against the routine use of the Poisson assumption in planning control charts for counts.