Exponentially weighted moving average chart with a likelihood ratio test for monitoring autocorrelated processes

In this article, an exponential weighted moving average chart based on a likelihood ratio test is developed to monitor the mean and variance shifts simultaneously for autocorrelated processes. A simple method is used to transform the positively autocorrelated data to the negatively autocorrelated data. The average run length of the proposed chart is derived from a simulation approach. The performance of our proposed chart is compared with some existing charts. The results show that the proposed chart provides better performance for detecting a wide range of shifts in the process mean and variance simultaneously. Additionally, the economic performance of different charts under the first-order autoregressive model is provided. A real example of a stepper motor in the heating, ventilation, and air conditioning module is used to demonstrate the application of the proposed method.