On designing EWMA charts to model demographic trends with generalized extreme value distribution

Demography and policy depend on monitoring life course events such as fertility and mortality rates in various countries. The commonly used measure to establish whether a nation is replacing its population is the total fertility rate or TFR. In contrast, the crude death rate (CDR) provides insight into the overall mortality trend. A recent study suggests that the most suitable model for TFR is the Generalized Extreme Value (GEV) distribution. In this study, the Exponentially Weighted Moving Average (EWMA) chart based on the GEV distribution is proposed for monitoring TFRs and CDRs across different Middle East and North Africa (MENA) countries, with the discovery that CDR also follows the GEV distribution. Furthermore, we introduce an innovative performance metric, the Expected Absolute Loss (EAL), to assess the effectiveness of the control chart; various quality metrics such as Average Run Length (ARL), Standard Deviation Run Length (SDRL), Median Run Length (MDRL), and EAL have been used to evaluate the performance of the newly proposed GEV-EWMA control chart. The result indicates that the ARL bias is due to the GEV shape parameter, which is influenced by the nature of asymmetric distribution. When symmetric limits are used, the bias still prevails, but the bias is significantly reduced when applying asymmetric limits. The findings indicate that the GEV-EWMA chart performs better than the Gumbel chart, particularly in detecting signals that exhibit increasing extremeness.