Auxiliary Information Based Mixed EWMA–CUSUM Mean Control Chart with Measurement Error

Measurement error is a usually met distortion factor in real-world applications that influences the outcome of a process. The performance of the control charts can be affected in the presence of measurement error which also leads to erroneous conclusions regarding the average run length. In this paper, we proposed regression estimator-based mixed exponentially weighted moving average-cumulative sum (MxEMCUS) control chart to monitor the process mean and investigate the effect of measurement error on shift detection ability of the proposed control chart. The performance of MxEMCUS control chart is evaluated in the cases of mean shift with and without measurement error. The linear covariate model is used to evaluate the control chart in the presence of measurement error. The case of multiple measurements and linear increasing variance is also investigated in the presence of measurement error. The average run length and standard deviation of run length are used as the performance measuring tool. Based on simulation results, it is concluded that in the presence of measurement error, proposed chart has better performance as compared to other existing charts. An example with real data set is given to demonstrate the implementation of MxEMCUS control chart.