Advanced Analysis for Evaluating the Efficiency of Multivariate MCUSUM Charts Using Kernel Functions in Air Pollution Monitoring"

Abstract

Air pollution is considered one of the major environmental challenges in Baghdad Province due to the continuous increase in the concentrations of gaseous pollutants resulting from various human activities. Since environmental data are often multivariate and do not follow a normal distribution, the use of nonparametric statistical methods becomes more appropriate for representing their actual characteristics. Among these methods, the Kernel Estimator is a flexible and effective tool for estimating probability distributions without requiring strict distributional assumptions. This study aims to evaluate the efficiency of Multi-Chart MCUSUM control charts based on the Kernel Estimator in monitoring multivariate air pollution data by comparing the performance of three common kernel functions: Gaussian, Laplace, and Epanechnikov. The practical aspect of the study was implemented using R version 4.5.1 due to its advanced capabilities in statistical analysis. The evaluation was based on the ability of the charts to detect small shifts while reducing false alarms, using the proposed Composite Average Run Length (CARL) criterion, which balances chart performance under in-control and out-of-control conditions by integrating the two indicators ARL₀ and ARL₁ into a unified evaluation measure. The results showed that the Gaussian and Laplace functions outperformed the others in terms of speed and sensitivity in detecting small changes, whereas the Epanechnikov function demonstrated lower efficiency in identifying small shifts.