The South Asian summer monsoon (SASM) exerts a profound influence on South Asia and the southern Tibetan Plateau. The timing of its onset and withdrawal significantly impacts regional rainfall, a critical water source for agriculture and the economy. Various SASM indices, employing different variables, have been employed to gauge monsoon onset and withdrawal, each demonstrating distinct characteristics. This study provides a comprehensive comparison of prominent SASM indices related to onset and withdrawal, revealing similar timing but varying magnitudes. Across nearly all indices, a consistent pattern emerges, indicating a trend towards earlier onset and delayed retreat during 1979-2018, marked by pronounced interdecadal variability, with a notable turning point around 1997. The earlier onset and later retreat are likely to enhance rainfall and potential water resources for South Asia and the Tibetan Plateau. Delving into the mechanisms revealed a delayed connection between the SASM onset to the large-scale sea surface temperature (SST) anomalies characterized by the Oceanic Niño Index (ONI) in the preceding spring, but a simultaneous connection between SASM withdrawl and ONI in autumn. Current index definitions, relying on single or dual variables, may fall short in accurately depicting monsoon onset and withdrawal. To address this, we introduce a novel monsoon index derived from multiple large-scale circulation variables, offering improved trend capture and enhanced representation of interannual variability in SASM onset and withdrawal. This study advances our understanding of SASM indices and their correlation with monsoon rainfall, providing insights into the dynamics of SASM onset and withdrawal.