The CUSUM Control Chart for the Autocorrelated Data\\with Measurement Error

As we know, the measurement error often exists in practice, and affects the performance of quality control in some cases. The autoregressive process with the measurement error is investigated in this paper. For detecting the step shift of the autoregressive process mean with measurement error, a CUSUM control chart based on the maximum log-likelihood ratio test is obtained. Simulated in-control and out-of-control ARL's are made for various measurement error and autocorrelation coefficients. The simulation results show that this new CUSUM scheme works well when the process is negatively autocorrelated.