Beyond the design point: when equal failure probabilities may not be equal (REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World, 2026)
In structural reliability, the probability of failure and the associated reliability index are usually treated as complete summaries of structural safety. This convention is powerful, but it hides an important distinction: two systems may have the same failure probability while exhibiting markedly different failure mechanisms and tail severities. This paper revisits the role of the classical design point and proposes two complementary quantities for interpreting failure beyond its probability. The first is the Mean Failure Point, a representative point in the standard normal space associated with the expected performance conditional on failure. It characterizes where the failure event is expected to lie, rather than where the limit-state surface is most likely to be reached. The second is the Buffered Reliability Index, obtained from the buffered probability of failure, which incorporates the tail behavior of the performance function. In the linear standard normal case, both quantities admit closed-form expressions involving the hazard rate of the standard normal distribution, clarifying their relation with the classical reliability index. The resulting triplet—failure probability, Mean Failure Point, and Buffered Reliability Index—offers a compact description of how likely failure is, how it occurs, and how severe it may be.