A sum of squares double exponentially weighted moving average chart

The sum of squares double exponentially weighted moving average (SS‐DEWMA) chart is proposed to improve the performance of the single SS‐EWMA chart, in the detection of initial out‐of‐control signals. The SS‐DEWMA chart uses the sum of squares statistic and it simultaneously monitors the process mean and variance in a single chart. A simulation study is conducted to show that the optimal SS‐DEWMA chart provides better zero state average run length (ARL) and standard deviation of the run length (SDRL) performances than the optimal SS‐EWMA chart. In addition, as suggested by one of the reviewers, the cyclical steady state ARLs and SDRLs of the SS‐DEWMA and SS‐EWMA charts are compared, where it is found that the former did not perform as well as the latter. Note that to the best of the authors’ knowledge, a study on DEWMA type charts’ steady state ARL and SDRL performances has yet to be made in the literature. A situation in which the SS‐DEWMA chart could be more useful than the SS‐EWMA chart is explained in Sections