A Cumulative Sum scheme for monitoring frequency and size of an event

Zhang Yong Wu · Zhen He · Michael B. C. Khoo

28 citations0/0 files storedQuality and Reliability Engineering International

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

Abstract

Abstract This article proposes a Cumulative Sum (CUSUM) scheme, called the TC‐CUSUM scheme, for monitoring a negative or hazardous event. This scheme is developed using a two‐dimensional Markov model. It is able to check both the time interval (T) between occurrences of the event and the size (C) of each occurrence. For example, a traffic accident may be defined as an event, and the number of injured victims in each case is the event size. Our studies show that the TC‐CUSUM scheme is several times more effective than many existing charts for event monitoring, so that cost or loss incurred by an event can be reduced by using this scheme. Moreover, the TC‐CUSUM scheme performs more uniformly than other charts for detecting both T shift and C shift, as well as the joint shift in T and C. The improvement in the performance is achieved because of the use of the CUSUM feature and the simultaneous monitoring of T and C. The TC‐CUSUM scheme can be applied in manufacturing systems, and especially in non‐manufacturing sectors (e.g. supply chain management, health‐care industry, disaster management, and security control). Copyright © 2009 John Wiley & Sons, Ltd.

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References

1999Research Issues and Ideas in Statistical Process Control 2006The Use of Control Charts in Health-Care and Public-Health Surveillance 1985Counted Data CUSUM's 2002Some effective control chart procedures for reliability monitoring 1998Designs of One- and Two-Sided Exponential EWMA Charts 1985Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed 2004Should Observations Be Grouped for Effective Process Monitoring?2000Cumulative quantity control charts for monitoring production processes

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