Bootstrap Design of Control Charts for Autocorrelated Data

One approach to monitor autocorrelated data consists on applying a control chart to the residuals of a time series model estimated from process observations. Recent research shows that the impact of estimation error on the run length properties of the resulting charts is not negligible. In this paper a general strategy for implementing residual-based control schemes is investigated. The designing procedure uses the AR-sieve approximation for a generating unknown process that allows an autoregressive representation of order infinity. The run length distribution is estimated using bootstrap resampling in order to account for uncertainty in the estimated parameters. Control limits, that satisfy a given constraint on the false alarm rate, are computed via stochastic approximation. The proposed procedure is investigated for three residual-based control charts: Generalized Likelihood Ratio (GLR), Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA). Results show that the bootstrap approach safeguards against an undesiderally high rate of false alarms. In addition, the out-of-control bootstrap-charts sensitivity does not seem to be lower than that of charts designed under the assumption that the estimated model is equal to the true generating process.