A nonparametric online control chart for monitoring crowd density using relative density-ratio estimation

Abstract

With the increasing incidence of fatal crowd stampede disasters at public events due to rapid urbanization and escalating population density, there is an urgent need for real-time monitoring of crowd flow to prevent such tragic incidents. This paper proposes a novel nonparametric online control chart for crowd density monitoring, called the RDR-CUSUM chart. This chart utilizes a new statistic based on the principles of cumulative sum (CUSUM) and relative density ratio (RDR). We present an RDR estimation method for deriving this statistic, which is enhanced by an S-M Invertor algorithm to ensure the efficiency required for real-time application. Numerical analyses demonstrate that the proposed chart can quickly respond to the distribution’s mean, variance, pattern, and different distribution parameter shifts. Moreover, the effectiveness of the method has been validated through two application examples, which illustrate its proficiency in detecting changes in crowd density and providing early warnings of potential crowd stampede disasters.