On the performance of classical control charts applied to process residuals

We study the relative performance of Shewhart, CuSum and EWMA control charts applied to the residuals of an autocorrelated production process measured by their average run lengths (ARLs). We derive integral equations for the ARLs of these charts and solve them using Gaussian quadrature. Numerical results indicate that Shewhart chart performs worst except when the decreasing rate is close to zero and the shift is large and EWMA chart performs better than the CuSum chart except when both the decreasing rate and the shift are small.