Univariate fast initial response statistical process control with taut strings

Abstract

We present a novel real-time univariate monitoring scheme for detecting a sustained departure of a process mean from some given standard assuming a constant variance. Our proposed stopping rule is based on the total variation of a nonparametric taut string estimator of the process mean and is designed to provide a desired average run length for an in-control situation. Compared to the more prominent CUSUM fast initial response (FIR) methodology and allowing for a restart following a false alarm, the proposed two-sided taut string (TS) scheme produces a significant reduction in average run length for a wide range of changes in the mean that occur at or immediately after process monitoring begins. A decision rule for when to choose our proposed TS chart compared to the CUSUM FIR chart that takes into account both false alarm rate and average run length to detect a shift in the mean is proposed and implemented. Supplementary materials are available online.

Keywords:

• Fast initial response CUSUM chart
• individuals chart
• nonparametric statistics
• taut string
• total variation

Acknowledgements

The authors thank Dr Jens Mueller for his assistance with an extensive simulation on the HPC cluster at Miami University, Oxford, OH. Helpful comments from Professor Lutz Dümbgen (University of Bern, Switzerland) on the ‘no-break condition’ for taut strings are appreciated. Correction and improvement suggestions from the Associate Editor and two anonymous reviewers are greatly appreciated.

Data availability statement

All data presented in the article are available in the Supplement.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been funded by a research grant from Zukunftskolleg (University of Konstanz, Germany). The second author has also been partially supported by the Farmer School of Business (Miami University) and thanks Professor Roland Schnaubelt (Karlsruhe Institute of Technology, Germany) for the financial support and hospitality during his stay in Karlsruhe.