Why is the probability of failure referred to as a notional probability?

In structural reliability analysis, the probability of failure is conditional on the underlying probabilistic model and on the current state of knowledge. Some events that will occur in the future might be unforeseeable at the time of modeling and, therefore, not accounted for in the model. Also, certain causes for failure might be excluded from the model on purpose. This often includes human errors, gross errors and deterioration. Moreover, it is important to remember that any model is by definition only a simplification of reality.

The probability of failure is referred to as notional, because the probability obtained through a structural reliability analysis cannot be observed in the real world and, therefore, should not be interpreted in an absolute sense. Nevertheless, relative comparisons of the probabilities of failure of different designs or situations are still possible. However, working with notional probabilities, one has to be careful with the interpretation of the results, when it comes to cost optimization or risk-based system-level decisions.

Probabilistic design does not attempt a perfect simulation of the real world. Probabilistic design provides a formal procedure to decide whether or not a structural design meets the reliability requirements. Compared to classical deterministic design methods, probabilistic design provides additional information and offers advanced options to perform an in-depth analysis.

This work is based on the discussion in [Vrouwenvelder et al., 2025, section 4].

Literatur

[Vrouwenvelder et al., 2025]: Vrouwenvelder, T., Beck, A., Proske, D., Faber, M., Köhler, J., Schubert, M., Straub, D. & Teichgräber, M.: Interpretation of probability in structural safety – A philosophical conundrum. Structural Safety, 113, 102473, 2025.