The Poisson CUSUM Chart for Monitoring Small Counts: Addressing the Estimation Uncertainty.

Area of Science:

• Statistical Process Control
• Epidemiological Surveillance
• Quality Improvement

Background:

• Estimating parameters for Poisson cumulative sum (CUSUM) charts can lead to false alarms, especially with small counts.
• Current methods, like large sample sizes or wider limits, are often impractical or ineffective for small Poisson counts.
• Existing approaches struggle to maintain desired in-control performance.

Purpose of the Study:

• To evaluate the impact of parameter estimation on Poisson CUSUM chart performance for small counts.
• To introduce and validate a novel exact method for Poisson CUSUM charts that guarantees in-control performance.
• To compare the proposed exact method against existing approximate methods.

Main Methods:

• Described three approximate Poisson CUSUM methods from the literature.
• Introduced a novel exact approach for Poisson CUSUM charts, avoiding heuristics and approximations.
• Validated the exact method using simulations and a retrospective case study of chikungunya infections.

Main Results:

• Simulations confirmed that existing methods fail to achieve desired in-control performance.
• The novel exact approach demonstrated guaranteed in-control performance.
• The knowledge-based exact method successfully detected nine major outbreaks with only one false alarm in the chikungunya case study, outperforming existing methods.

Conclusions:

• The proposed exact method offers a reliable solution for Poisson CUSUM charts with small counts.
• Domain knowledge integration enhances the exact method's out-of-control performance and outbreak detection.
• The exact approach provides superior performance and practical effectiveness in epidemiological surveillance.