We examine the prediction of real accident and event probability in the absence of prior data and/or with partial knowledge, when the human contribution is properly included. We now know that the major cause of all real accidents (not postulated ones) is actually the unforeseen human contribution, as an integral and inseparable part of the technological system. The real events we actually will experience or observe in our lives may be spectacular plane, train, space shuttle or stock market crashes. In every case, they are unexpected occurrences, they seemingly appear randomly, and how often they happen, or the rate of such events, covers the whole spectrum from frequent to rare. Because so-called rare events do not happen often, they are also widely misunderstood and do not follow the expectations or the same “rules” governing many or frequent events, and are always due to some apparently unforeseen combination of circumstance, conditions, and combination. Usually in safety analysis, a distinction is made between “probabilistic” safety analysis (PSA), based on examining so-called risk dominant accident sequences, and “deterministic” safety analysis (DSA). Intended to be complementary, PSA provides insights into risk scenarios and allowing numerical estimation of outcomes for transients, such as loss of offsite power (LOOP) or station blackout (SBO), and the resulting core damage frequency (CDF) or large early release frequency (LERF) with some estimated uncertainty in the calculated probabilities of occurrence. In contrast, the DSA provides a standard set of stylized events, such as large breaks (LOCA) and transients (ATWS), as a means of setting safety margins and design criteria, as also proposed in Theofanous’s ROAMM, where extremes of knowledge are postulated as a test of the robustness of the design and safety systems. These methods can produce statements of margins and uncertainties, and converge in the area known as “risk informed regulation” (RIR), where the insights gained are proposed to derive limiting Farmer-type “tolerable risk” boundaries or frequency-consequence (F-C) curves. Conversely, real accidents are often unknown sequences, with no priors or precursors, and/or include possibly unforeseen initiators (for example, undetected pressure vessel corrosion) and the key role of the human. In this paper, we address the question of the quantitative prediction of such real and rare events, their occurrence probability and hence the risk.

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