A new perspective on precursors and rare events from a systematic review

Estimating the probability of ultra-rare but catastrophic events, such as core melts, offshore blowouts, or chemical explosions, poses a fundamental challenge due to the lack of observed failures. To overcome this “zero-failure dilemma,” safety researchers have turned to accident precursors: abnormal conditions that share causal pathways with potential disasters. This paper presents the first cross-sector systematic review of 72 peer-reviewed studies on precursor-based probability estimation, spanning nuclear, chemical, offshore, rail, and autonomous systems. This study classifies existing methods into four methodological families, including frequency-based rules, Bayesian estimators, Accident Sequence Precursor (ASP) logic trees, and Bayesian networks (BNs). Moreover, to address key gaps such as multi-precursor interaction and recurrence modeling, this study proposes a novel Logistic–Exponential (LE) framework. This model captures how accident risk grows with increasing types of precursors and how repeated signals contribute less over time, using a compact and analytically manageable form. This study concludes by identifying future research directions to improve the model's interpretability, cross-domain applicability, and potential for integration into real-time safety monitoring systems.