Robust design of control charts for autocorrelated processes with model uncertainty

Statistical process control (SPC) procedures suitable for autocorrelated processes have been extensively investigated in recent years. The most popular method is the residual-based control chart. To implement this method, a time series model, which is usually an autoregressive moving average (ARMA) model, of the process is required. However, the model must be estimated from data in practice and the resulting ARMA modeling errors are unavoidable. Residual-based control charts are known to be sensitive to ARMA modeling errors and often suffer from inflated false alarm rates. As an alternative, control charts can be applied directly to the autocorrelated data with widened control limits. The widened amount is determined by the autocorrelation function of the process. The alternative method, however, can not be also free from the effects of modeling errors because it relies on an accurate process model to be effective. To compare robustness to the ARMA modeling errors between the preceding two kinds of methods for control charting autocorrelated data, this dissertation investigates the sensitivity analytically. Then, two robust design procedures for residual-based control charts are developed from the result of the sensitivity analysis. The first approach for robust design uses the worst-case (maximum) variance of a chart statistic to guarantee the initial specification of control charts. The second robust design method uses the expected variance of the chart statistic. The resulting control limits are widened by an amount that depends on the variance of chart statistic - maximum or expected - as a function of (among other things) the parameter estimation error covariances.