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 4 and 6.

► The single SS-DEWMA chart merges two DEWMA charts, each for the mean and variance.
► The optimal zero state SS-DEWMA chart outperforms the corresponding SS-EWMA chart.
► The steady state SS-EWMA chart outperforms the corresponding SS-DEWMA chart.
► A good zero state ARL performance gives a quick initial out-of-control detection.