The exponentially weighted moving average (EWMA) chart X for monitoring a pro-cess mean was introduced by Roberts (1959)[1]. Various authors have studied thischart. Shamma and Shamma (1992)[19] introduced an EWMA of an EWMA chart,referred to as the double EWMA chart. Since then the EWMA of the EWMA ofthe EWMA (triple EWMA) chart and the EWMA of the EWMA of the EWMAof the EWMA (quadruple EWMA) charts have been introduced into the literature.Their claims are that the double EWMA X chart outperformed the EWMA chartfor the monitoring the process mean. Further it was claimed that the triple EWMAX chart outperformed the double EWMA X chart and the quadruple EWMA chartoutperformed the triple EWMA X chart. We demonstrate that an EWMA X chartcan be designed that outperforms the double EWMA X chart. We show this usingsimulation. The EWMA X has been used to predict the change point. We providea method using the likelihood function to predict the change point. A comparison ismade with the Shewhart X chart
