Detecting selected non-random patterns with individuals control charts

Abstract

Western Electric (1956) and Nelson (1984) proposed rule sets to detect visually obvious process upsets on a control chart. Performance evaluation of these rules require simulating situations that correspond to their intended detection purposes such as linear drift, cycling, seesaw and sustained process mean shifts. These non-random process patterns become visually obvious in the presence of reduced variation. Contrary to previous assessments where variance is assumed constant, Western Electric and Nelson rule sets are shown to be preferred over Shewhart X and CUSUM charts for detecting non-random patterns of process mean in the presence of variance reduction over wide ranges of slopes, cycle period/amplitude combinations, alternating shift and sustained shift sizes. One real-data example from Deming's book Out of the Crisis is provided that affirms implications of extensive simulation analyses.

Keywords:

• Shewhart X chart
• CUSUM chart
• western electric alarm rule
• Nelson's alarm rules
• reduced process variation

Acknowledgments

Valuable insights from the Editor, Associate Editor and anonymous referee are appreciated. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources extensively used for simulations reported in this manuscript (http://www.tacc.utexas.edu).

Disclosure statement

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

Data availability statement

The Deming's dataset used in this study is available with the supplemental materials.

Additional information

Funding

This work was supported by Zukunftskolleg, University of Konstanz, Germany [Zukunftskolleg mentorship grant].