Improved control chart for statistical process control using combined X and delayed EWMA statistics

In this paper, we propose a new combination of X and EWMA charts in which we intentionally delay the EWMA statistic one lag to make it independent of X. The intentional delay of EWMA induces a power loss in detecting abnormality. However, owing to the independence of two control statistics, the new chart is much easier to set the in-control average run length at the aimed level than the existing combinations. We numerically show how simple to design the new chart and also show that the new chart performs as well as the existing charts in out-control average run length. Finally, we apply it to the cyber-attack detection problem from the NSL-KDD dataset.