A Synthetic Control Chart Based on Cornish-Fisher\\Expansion

According to Cornish-Fisher expansion, the control limits of Shewhart $\ol X$ control chart were constructed with up to the fourth moment (The moments are estimated from the in-control historical samples when the process distribution is unknown, and no further assumptions are made on the distribution). Then we made a synthetic control chart based on the Cornish-Fisher expansion. The in-control ARL's (average run length) and out-of-control ARL's of the new chart builded here were evaluated to compare with synthetic control chart (see \cite{1}) when the process distribution is Student-t, Weibull, Lognormal and Burr. Simulation results show that the new control chart is more robust than the other methods.