Bootstrapping confidence in future safety based on past safe operation

With autonomous vehicles (AVs), a major concern is the inability to give meaningful quantitative assurance of safety, to the extent required by society - e.g. that an AV must be at least as safe as a good human driver - before that AV is in extensive use. We demonstrate an approach to achieving more moderate, but useful, confidence, e.g., confidence of low enough probability of causing accidents in the early phases of operation. This formalises mathematically the common approach of operating a system on a limited basis in the hope that mishap-free operation will confirm one's confidence in its safety and allow progressively more extensive operation: a process of "bootstrapping" of confidence. Translating that intuitive approach into theorems shows: (1) that it is substantially sound in the right circumstances, and could be a good method for deciding about the early deployment phase for an AV; (2) how much confidence can be rightly derived from such a "cautious deployment" approach, so that we can avoid over-optimism; (3) under which conditions our sound formulas for future confidence are applicable; (4) thus, which analyses of the concrete situations, and/or constraints on practice, are needed in order to enjoy the advantages of provably correct confidence in adequate future safety.