Statistical process control for queue length trajectories using Fourier analysis

This paper presents a new statistical process control method for monitoring the number of waiting entities for queues. It is based on dynamic characterization of the number-in-system (NIS) data trajectory via Fourier coefficient magnitudes. Since monitoring periods are necessarily short, we investigate windowing methods for dampening the impact of the Gibbs phenomenon, which can contaminate the Fourier characterization. Secondly, we use this knowledge to present a short-window modified version of the waFm statistic, a weighted average of Fourier magnitudes, within a Cumulative sum (CUSUM) control chart. The waFm CUSUM chart works well even when only periodic NIS reports are available. The proposed method is frequently superior to the best existing methods in controlled experiments considering both non-contiguous and contiguous windows of data illustrating its use for the monitoring of both stationary and non-stationary systems. It is superior to, or competitive with, existing methods even when the nature of departure from control is known. We illustrate performance in simple queues and a more realistic scenario based on a job shop model.