Bounds on survival probability given mean probability of failure per demand; and the paradoxical advantages of uncertainty

We explore effects of uncertainty on parameters of convex reliability functions.

Given uncertainty about a parameter, using its mean ensures pessimistic reliability predictions.

We show that, given this mean, more uncertainty can surprisingly yield higher reliability.

We discuss consequent practical implications for decision making in reliability and safety.

These may be counter‐intuitive and require scrutiny of the underlying principles.