A spatio-temporal CUSUM chart for detecting spatially coherent shifts in sensor networks

Modern sensor networks generate observations with both spatial and temporal dependence, creating challenges for conventional control charts based on independent observations. Existing adaptive CUSUM procedures can improve sensitivity to small and moderate shifts, but they generally adapt the reference parameter from local process information and therefore do not explicitly exploit spatially coherent disturbances. This study proposes a Spatio-Temporal Adaptive CUSUM (ST-ACUSUM) chart that combines a spatio-temporal autoregressive residual model with a spatially informed adaptive reference mechanism based on both local standardized residuals and neighborhood deviation. The formulation is deliberately parsimonious so that the contribution of the adaptive monitoring mechanism can be isolated and evaluated under controlled dependence structures. Monte Carlo simulations show that the chart maintains the target in-control performance and provides substantially faster detection of small and moderate global, cluster, and local shifts than the ANN-RA-CUSUM and conventional CUSUM benchmarks. For example, at a global shift of δ = 0.1, the ARL is 110.56 for ST-ACUSUM compared with 237.02 for ANN-RA-CUSUM and 286.09 for conventional CUSUM, corresponding to reductions of approximately 53.4% and 61.4%, respectively. The relative advantage decreases for large shifts, for which all methods signal rapidly. A temperature-data case study from ten monitoring sites in Pakistan illustrates implementation after seasonal adjustment. The proposed framework is therefore intended primarily as a shift-agnostic monitoring procedure for early detection of spatially coherent changes in spatio-temporally dependent processes.