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

Abstract

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 distributionfree 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.

Monitoring Autocorrelated Processes With Wavelets

“…Other approaches to dealing with detecting shifts in autocorrelated processes include distribution free tabular CUSUM control charts developed by Kim et al 34 and Lee et al 35 A discussion on monitoring short-run autocorrelated processes using time series forecasting-based methods can be found in Snoussi et al 36 and Masarotto 37 developed generalized likelihood ratio charts with control limits determined by bootstrapping. For processes that are not highly autocorrelated, the variable parameters chart developed by Lin 3 is effective in detecting small mean shifts compared to other traditional control charts.…”