On the Equivalence of the Bernoulli and Geometric CUSUM Charts

John L. Szarka · William H. Woodall

29 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 Bernoulli cumulative sum (CUSUM) chart has been shown to have good properties in detecting an increase in the nonconforming rate, p, based on the average number of observations to signal (ANOS). The geometric CUSUM chart has also been proposed, in particular for high-quality processes where p is very small. The geometric CUSUM chart has very good properties in a zero-state analysis because of a built-in headstart feature. In steady-state performance analyses, often a shift in the process has been assumed to occur immediately after a nonconforming item has been found. In this case, the performance of the geometric CUSUM chart is said to be better than that of the Bernoulli CUSUM chart. We explore the case where a process shift may occur at any time. We show that the steady-state properties of the Bernoulli CUSUM and geometric CUSUM charts are the same because the charts can be designed to be mathematically equivalent.

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References

2000Statistical Methods for Quality Improvement 1991Detecting a Shift in Fraction Nonconforming Using Run-Length Control Charts with 100% Inspection 1999A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously 2011A Review and perspective on surveillance of Bernoulli processes 2008EWMA control charts for monitoring high-yield processes based on non-transformed observations 2007A comparison of surveillance methods for small incidence rates 1999A quality monitoring and decision‐making scheme for automated production processes 2003Statistical Control of a Six Sigma Process

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