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CUSUM Statistical Monitoring of M/M/1 Queues and Extensions

Summary: [This abstract is based on the authors' abstract.] Many production and service systems can be modeled as queueing systems. Their operational efficiency and performance are often measured using queueing performance metrics (QPMs), such as average cycle time, average waiting length, and throughput rate. These metrics need to be quantitatively evaluated and monitored in real time to continuously improve the system performance. However, QPMs are often highly stochastic, and hence are difficult to monitor using existing methods. This article proposes the cumulative sum (CUSUM) schemes to efficiently monitor the performance of typical queueing systems based on different sampling schemes. The authors use M/M/1 queues to illustrate how to design the CUSUM chart and compare their performance with several alternative methods. The article demonstrates that the performance of CUSUM is superior, responding faster to many shift patterns through extensive numerical studies. The authors also briefly discuss the extensions of CUSUM charts to more general queues, such as M/G/1, G/G/1, or M/M/c queues. Case studies are used to demonstrate the applications of the proposed approach. Supplementary materials for this article are available online.

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  • Topics: Statistical Process Control (SPC)
  • Keywords: Monitoring, Cumulative sum control chart (CUSUM), Sampling plans, Statistical process control (SPC), Metrics, Shifts and drifts in tolerances, Case study
  • Author: Chen, Nan; Zhou, Shiyu
  • Journal: Technometrics