Robustness of the time between events CUSUM

Connie M. Borror · J. Bert Keats · Douglas C. Montgomery

90 citations0/0 files storedInternational Journal of Production Research

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Advanced Statistical Process Monitoring Management and Optimization Techniques Fault Detection and Control Systems

Abstract

Many companies have set Parts per Million (PPM) or Parts per Million Opportunities (PPMO) goals in their quest for continuous improvement. The time-between-events (TBE) CUSUM has been suggested for monitoring the number of good units or the number of opportunities that occurred between discoveries of consecutive bad units. We focus on the robustness of the TBE CUSUM. Robustness, in this case, refers to sensitivity of the procedure to make the proper decisions regarding a shift in the mean defect rate when, in fact, the time between events is not exponential. We examine and report average run lengths (ARLs) under both a Weibull and a lognormal time between events distribution. Our results indicate that the TBE CUSUM is extremely robust for a wide variety of parameter values for both the Weibull and lognormal distributions. The implications of these results in practice imply that users of the TBE CUSUM procedure need not be concerned about departures from the exponential TBE distribution. Practical implementation of the TBE CUSUM procedure is also discussed.

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References

1992Introduction to Statistical Quality Control 1972An Approach to the Probability Distribution of Cusum Run Length 2001Introduction to Statistical Quality Control 1999Robustness of the EWMA Control Chart to Non-Normality 1999A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously 1976The Effect of Non-Normality on the Control Limits of X Charts 1985Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed 2000Cumulative quantity control charts for monitoring production processes

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2014Designing of a new monitoring t-chart using repetitive sampling 2006Design of exponential control charts using a sequential sampling scheme 2009Properties of the exponential EWMA chart with parameter estimation 2006A study of EWMA chart with transformed exponential data 2008A control scheme for monitoring the frequency and magnitude of an event 2014Cumulative Sum Control Charts for Monitoring Weibull-distributed Time Between Events

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