Limited Markov chain embedded method and integration method are given to calculate the respective average run
length of modified Shewhart chart and Shewhart residual chart for 2-order autoregressive process. Performance of both charts
with different parameters are discussed and compared by numerical results. Some conclusions show that, modified chart is
more applicable when both parameters are positive, residual chart is more applicable when both parameters are negative,
otherwise both charts need to be compared through the proposed method. The conclusion provides academic basis to choose
and apply control charts.