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This paper presents economic and economic–statistical designs of the adaptive exponentially weighted moving average (AEWMA) control chart for monitoring the process mean. It also aims to compare the effect of estimated process parameters on the economic performance of three charts, which are Shewhart, exponentially weighted moving average and AEWMA control charts with economic–statistical design.

The optimal parameters of the control charts are obtained by applying the Lorenzen and Vance’s (1986) cost function. Comparisons between the economic–statistical and economic designs of the AEWMA control chart in terms of expected cost and statistical measures are performed. Also, comparisons are made between the economic performance of the three competing charts in terms of the average expected cost and standard deviation of expected cost.

This paper concludes that taking into account the economic factors and statistical properties in designing the AEWMA control chart leads to a slight increase in cost but in return the improvement in the statistical performance is substantial. In addition, under the estimated parameters case, the comparisons reveal that from the economic point of view the AEWMA chart is the most efficient chart when detecting shifts of different sizes.

The importance of the study stems from designing the AEWMA chart from both economic and statistical points of view because it has not been tackled before. In addition, this paper contributes to the literature by studying the effect of the estimated parameters on the performance of control charts with economic–statistical design.

This study aims to assess the effect of updating the Phase I data – to enhance the parameters' estimates – on the control charts' detection power designed to monitor social networks.

A dynamic version of the degree corrected stochastic block model (DCSBM) is used to model the network. Both the Shewhart and exponentially weighted moving average (EWMA) control charts are used to monitor the model parameters. A performance comparison is conducted for each chart when designed using both fixed and moving windows of networks.

Our results show that continuously updating the parameters' estimates during the monitoring phase delays the Shewhart chart's detection of networks' anomalies; as compared to the fixed window approach. While the EWMA chart performance is either indifferent or worse, based on the updating technique, as compared to the fixed window approach. Generally, the EWMA chart performs uniformly better than the Shewhart chart for all shift sizes. We recommend the use of the EWMA chart when monitoring networks modeled with the DCSBM, with sufficiently small to moderate fixed window size to estimate the unknown model parameters.

This study shows that the excessive recommendations in literature regarding the continuous updating of Phase I data during the monitoring phase to enhance the control chart performance cannot generally be extended to social network monitoring; especially when using the DCSBM. That is to say, the effect of continuously updating the parameters' estimates highly depends on the nature of the process being monitored.