A distribution-free tabular CUSUM chart for autocorrelated data

Abstract

A distribution-free tabular CUSUM chart called DFTC is designed to detect shifts in the mean of an autocorrelated process. The chart's Average Run Length (ARL) is approximated by generalizing Siegmund's ARL approximation for the conventional tabular CUSUM chart based on independent and identically distributed normal observations. Control limits for DFTC are computed from the generalized ARL approximation. Also discussed are the choice of reference value and the use of batch means to handle highly correlated processes. The performance of DFTC compared favorably with that of other distribution-free procedures in stationary test processes having various types of autocorrelation functions as well as normal or nonnormal marginals.

Keywords:

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

Acknowledgements

The authors thank David Goldsman and the anonymous referees for several suggestions which substantially improved this paper.