Conservative confidence bounds in safety, from generalised claims of improvement & statistical evidence

“Proven-in-use”, “globally-at-least-equivalent”, “stress-tested”, are concepts that come up in diverse contexts in acceptance, certification or licensing of critical systems. Their common feature is that dependability claims for a system in a certain operational environment are supported, in part, by evidence – viz of successful operation – concerning different, though related, system[s] and/or environment[s], together with an auxiliary argument that the target system/environment offers the same, or improved, safety. We propose a formal probabilistic (Bayesian) organisation for these arguments. Through specific examples of evidence for the “improvement” argument above, we demonstrate scenarios in which formalising such arguments substantially increases confidence in the target system, and show why this is not always the case. Example scenarios concern vehicles and nuclear plants. Besides supporting stronger claims, the mathematical formalisation imposes precise statements of the bases for “improvement” claims: seemingly similar forms of prior beliefs are sometimes revealed to imply substantial differences in the claims they can support