Constructing control charts for autocorrelated data using an exhaustive systematic samples pooled variance estimator

Abstract

SPC with positive autocorrelation is well known to result in frequent false alarms if the autocorrelation is ignored. The autocorrelation is a nuisance and not a feature that merits modeling and understanding. This paper proposes exhaustive systematic sampling, which is similar to Bayesian thinning except no observations are dropped, to create a pooled variance estimator that can be used in Shewhart control charts with competitive performance. The expected value and variance are derived using quadratic forms that is nonparametric in the sense no distribution or time series model is assumed. Practical guidance for choosing the systematic sampling interval is offered to choose a value large enough to be approximately unbiased and not too big to inflate variance. The proposed control charts are compared to time series residual control charts in a simulation study that validates using the empirical reference distribution control limits to preserve stated in-control false alarm probability and demonstrates similar performance.

Keywords:

• autocorrelation
• quadratic forms
• Shewhart charts
• systematic sampling
• time series

Acknowledgment

We are grateful for the insightful comments from the Editor and reviewers which significantly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Scott D. Grimshaw

Dr. Grimshaw is a Professor in the Department of Statistics at Brigham Young University. He is a member of ASQ.