Bootstrap-based Design of Control Charts for Autocorrelated Data
One approach to monitoring autocorrelated data consists of 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 implement-ing residual-based control schemes is investigated. The designing procedure uses the AR-sieve approximation assuming that the process 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 undesirably 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.
Quality control Time series Uncertainty modeling Control charts Sieve bootstrap
Giovanna CAPIZZI Guido MASAROTTO
Dipartimento di Scienze Statistiche,via Cesare Battisti 241,35121 Padova,Italy
国际会议
北京
英文
2007-05-30（万方平台首次上网日期，不代表论文的发表时间）