We evaluate the design of individuals and moving range charts through extensive simulations. Via
a SAS program using 8000 replications, average run length is assessed for several shifts in
process mean and variation. From these computations recommendations are made concerning
when to use the individuals chart only, when to use a combined individuals and moving range
chart, and the optimal design parameters when the combined approach is used. The paper
includes discussion, recommendations, and examples concerning the monitoring of accounting
data.