Abstract: The shortcoming of applying a traditional control chart to the residuals of ARMA (auto-regressive and moving average) model estimated from process observation is analyzed, and an improved nonparametric control chart based on bootstrap resampling is presented. Average run length(ARL) considering various factors including model parameters, number of samples and distribution of residuals, are compared by Monte Carlo simulation. The results show the new control chart increases sensitivity to process shifts, and reduces false alarm rates. While bootstrap-based control chart can be built when a set of Phase-I in-control data are given and applied to raw data directly, the control effect is less affected by the number of samples, and so the proposed method is powerful yet simple to use in practice.

Key words: autocorrelated processes, model-unknown, phase-I, Bootstrap, Motnte Carlo simulation, average run length(ARL)