  The monitoring of serially independent or autocorrelated count processes is
considered, having a Poisson or (negative) binomial marginal distribution under
in-control conditions. Utilizing the corresponding Stein identities,
exponentially weighted moving-average (EWMA) control charts are constructed,
which can be flexibly adapted to uncover zero inflation, over- or
underdispersion. The proposed Stein EWMA charts' performance is investigated by
simulations, and their usefulness is demonstrated by a real-world data example
from health surveillance.
