The Rate of False Signals in Ū Control Charts with Estimated Limits

Diane P. Bischak · Dan Trietsch

51 citations0/0 files storedJournal of Quality Technology

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

The in-control statistical properties of Ū charts have usually been studied from the perspective of the average run length (ARL) until the first (false) signal, known as the in-control ARL. We argue that the ARL is a confusing concept when used with charts with estimated limits and that the rate of false signals (RFS), which focuses on the behavior of charts during extended use, is more intuitive. We use the RFS to illustrate graphically the dangers of using too few subgroups to estimate control limits. We also discuss diffidence charts, which make the inherent uncertainty concerning RFS observable to the practitioner and thus help the practitioner determine what is an acceptable number of subgroups for a given charting application.

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References

1992Introduction to Statistical Quality Control 2001Introduction to Statistical Quality Control 2003The Changepoint Model for Statistical Process Control 1993The Effect of Sample Size on Estimated Limits forXandXControl Charts 1991SPCQCharts for Start-Up Processes and Short or Long Runs 1987Self-Starting Cusum Charts for Location and Scale 2004The Run Length Distribution of the CUSUM with Estimated Parameters 1969X- and R-Chart Control Limits Based on a Small Number of Subgroups

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