Gan (1990) and Borror et al. (1998) studied the Poisson EWMA
(PEWMA) control chart, showing that the PEWMA chart has a better
average run length (ARL) performance than the Shewhart c chart. This
article, motivated by the work of Shamma and Shamma (1992), and Zhang
and Chen (2002), extends the idea of the PEWMA chart to create a new
chart we call a Poisson DEWMA (PDEWMA) chart. This requires a
second exponentially weighted moving average, hence the D which
stands for double. We obtain the ARLs and standard deviations of run
lengths (SDRLs) of the PDEWMA chart using a simulation method and
compare them with those of the PEWMA chart. Our results show that the
PDEWMA chart is more sensitive to small downward process mean
changes than the PEWMA chart, and that the PDEWMA chart performs
similarly to, or slightly better than, the PEWMA chart in detecting large
downward process mean changes and upward process mean changes.