Construction and application of AEWMA control chart for autocorrelation process

In conventional exponentially weighted moving average (EWMA) control charts, a basic premise is that the data are independent of each other. However, in the era of big data, with the popularization and application of automatic data collection technology, there are often correlations between data, making conventional EWMA control chart monitoring ineffective. To solve this problem, an AEWMA control chart for autocorrelation processes (adaptive EWMA control chart) is proposed in this study, that is, the AEWMA control chart is constructed by fitting the residual of the time series model, and the optimal parameters of the control chart under autocorrelation conditions are found by combining the three principles with the search algorithm, so that the control limits can be set more accurately for monitoring. Then, by comparing the performance of conventional control chart and AEWMA control chart in terms of average running length, it is concluded that AEWMA control chart is better than conventional EWMA control chart in the case of non-strong correlation regardless of the size of the mean offset. Finally, the application effect of AEWMA control chart in the process of monitoring autocorrelation is demonstrated by an example, which fully proves its superiority in solving the quality control problem under the condition of autocorrelation.