A distribution-free tabular CUSUM chart for correlated data with automated variance estimation

We formulate and evaluate distribution-free statistical process control (SPC) charts for monitoring an autocorrelated process when a training data set is used to estimate the marginal mean and variance of the process as well as its variance parameter (i.e., the sum of covariances at all lags). We adapt variance-estimation techniques from the simulation literature for automated use in DFTC-VE, a distribution-free tabular CUSUM chart for rapidly detecting shifts in the mean of an autocorrelated process. Extensive experimentation shows that our variance-estimation techniques do not seriously degrade the performance of DFTC-VE compared with its performance using exact knowledge of the variance parameter; moreover, the performance of DFTC-VE compares favorably with that of other competing distribution-free SPC charts.