Control Charts for Poisson Count Data with Varying Sample Sizes

Ryan, Anne G.; Woodall, William H.

doi:10.1080/00224065.2010.11917823

Cited by 63 publications

(33 citation statements)

References 19 publications

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“…Mei et al 17 further developed some variations to the CUSUM method discussed by Hawkins and Olwell. In addition to the CUSUM techniques, Dong et al 18 and Ryan and Woodall 19 considered the exponentially weighted moving average (EWMA) methods to address the issue of non‐constant population size. The latter also compared the performance of EWMA methods with some CUSUM methods under random population size scenarios.…”

Section: Introductionmentioning

confidence: 99%

A comparison of weighted CUSUM procedures that account for monotone changes in population size

Shu¹,

Jiang

Tsui

2010

Statistics in Medicine

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The CUSUM procedure has been popularly used for detecting a shift in the incidence rate of a rare health event. Many CUSUM methods are developed based on a Poisson model with a constant mean number of events. In practice, the expected number of events is likely to vary over time as the population size at risk is not constant but often grows over time. An increase in the baseline incidence rate tends to be masked by the population growth. To efficiently detect an increase in the baseline incidence rate, it is appealing to assign more weight to recent observations and less weight to older observations. This paper compares weighted CUSUM (WCUSUM) and conventional CUSUM procedures in the presence of monotone changes in population size. The simulation results show that the WCUSUM method may be more efficient than the conventional CUSUM methods in detecting increases in the incidence rate, especially for small shifts. An example based on mortality data from New Mexico is used to illustrate the implementation of the WCUSUM method.

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Section: Introductionmentioning

confidence: 99%

A comparison of weighted CUSUM procedures that account for monotone changes in population size

Shu¹,

Jiang

Tsui

2010

Statistics in Medicine

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“…Increasing attention has thus been paid to the problem of monitoring the occurrence rate of an adverse event with time-varying sample sizes in prospective analysis (called Phase II). Related studies have been reported by Dong et al (2008), Mei et al (2010), Ryan and Woodall (2010), Shu et al (2011), Zhou et al (2012) and Shen et al (2013). For a review of surveillance of nonhomogeneous Poisson processes, one may refer to Purdy et al (2015).…”

Section: Introductionmentioning

confidence: 75%

“…Here, we use a reflecting barrier, as did Ryan and Woodall (2010), to avoid inertia problems (Woodall and Mahmoud 2005). Clearly, when the process occurs some change at τ, a large value of Z t would be used to trigger an alarm.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…In the following, we further show that the proposed control scheme also has good performance when sample sizes are time-varying. Referring to the previous studies, the time-varying sample sizes are depicted by three different scenarios based on two logistic models suggested by Mei et al (2011) and one uniform distribution model previously used by Ryan and Woodall (2010). Following the work by …”

Section: Accepted Manuscriptmentioning

confidence: 99%

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Self-Starting Monitoring Scheme for Poisson Count Data With Varying Population Sizes

et al. 2016

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In this paper we consider the problem of monitoring Poisson rates when the population sizes are time-varying and the nominal value of the process parameter is unavailable. Almost all previous control schemes for the detection of increases in the Poisson rate in Phase II are constructed based on assumed knowledge of the process parameters, e.g., the expectation of the count of a rare event when the process of interest is in control. In practice, however, this parameter is usually unknown and not able to be estimated with a sufficiently large number of reference samples. A self-starting EWMA control scheme based on a parametric bootstrap method is proposed. The success of the proposed method lies in the use of probability control limits, which are determined based on the observations during rather than before monitoring.Simulation studies show that our proposed scheme has good in-control and out-of-control performance under various situations. In particular, our proposed scheme is useful in rare event studies during the start-up stage of a monitoring process.

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“…proposed an EWMA version of the rate chart, which is analogous to the CUSUM‐R chart. Ryan and Woodall made a comparison among the CUSUM and EWMA methods in terms of the CED criterion. It would be interesting to investigate the performance of these methods under the criterion of PA.…”

Section: Concluding Remarks and Future Researchmentioning

confidence: 99%

CUSUM Procedures for Health Care Surveillance

Jiang

Shu

Zhao

et al. 2012

Quality & Reliability Eng

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Detecting increases of incidence rate of an adverse health event is critical to health surveillance. Motivated by successful applications in industry quality control and productivity improvement, various cumulative sum (CUSUM) procedures have been developed to monitor rate changes of health events when population size changes over time. Average run length, which is commonly used in quality control, may be inappropriate in some situations when comparing control chart performance in health surveillance applications. This paper provides a thorough statistical comparison of CUSUM‐type procedures in the health care context based on different evaluation metrics. We show that different measures may favor different surveillance methods depending on the corresponding design criteria. We thus recommend a probabilistic measure as the criterion for design and evaluation of CUSUM control charts in health care surveillance. Copyright © 2012 John Wiley & Sons, Ltd.

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Control Charts for Poisson Count Data with Varying Sample Sizes

Cited by 63 publications

References 19 publications

A comparison of weighted CUSUM procedures that account for monotone changes in population size

A comparison of weighted CUSUM procedures that account for monotone changes in population size

Self-Starting Monitoring Scheme for Poisson Count Data With Varying Population Sizes

CUSUM Procedures for Health Care Surveillance

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