Monitoring autocorrelated processes using a distribution-free tabular CUSUM chart with automated variance estimation

Abstract

We formulate and evaluate distribution-free statistical process control (SPC) charts for monitoring shifts in the mean of an autocorrelated process when a training data set is used to estimate the marginal variance of the process and the variance parameter (i.e., the sum of covariances at all lags). Two alternative variance estimators are adapted for automated use in DFTC-VE, a distribution-free tabular CUSUM chart, based on the simulation-analysis methods of standardized time series and a simplified combination of autoregressive representation and non-overlapping batch means. Extensive experimentation revealed that these variance estimators did not seriously degrade DFTC-VE's performance compared with its performance using the exact values of the marginal variance and the variance parameter. Moreover, DFTC-VE's performance compared favorably with that of other competing distribution-free SPC charts.

[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplementary resource: Appendix]

Keywords:

• Statistical process control
• Shewhart chart
• tabular CUSUM chart
• autocorrelated data
• average run length
• distribution-free statistical methods
• variance estimation

Acknowledgements

We thank the referees for their substantive and thoughtful comments and suggestions. Partial support for our research was provided by National Science Foundation Grants CMMI-0400260, CMMI-0644837 and EFRI-0735991.