Context: Demonstrating high reliability and safety for safety-critical systems (SCSs) remains a hard problem. Diverse evidence needs to be combined in a rigorous way: in particular, results of operational testing with other evidence from design and verification. Growing use of machine learning in SCSs, by precluding most established methods for gaining assurance, makes evidence from operational testing even more important for supporting safety and reliability claims. Objective: We revisit the problem of using operational testing to demonstrate high reliability. We use Autonomous Vehicles (AVs) as a current example. AVs are making their debut on public roads: methods for assessing whether an AV is safe enough are urgently needed. We demonstrate how to answer 5 questions that would arise in assessing an AV type, starting with those proposed by a highly-cited study. Method: We apply new theorems extending our Conservative Bayesian Inference (CBI) approach, which exploit the rigour of Bayesian methods while reducing the risk of involuntary misuse associated (we argue) with now-common applications of Bayesian inference; we define additional conditions needed for applying these methods to AVs. Results: Prior knowledge can bring substantial advantages if the AV design allows strong expectations of safety before road testing. We also show how naive attempts at conservative assessment may lead to over-optimism instead; why extrapolating the trend of disengagements (take-overs by human drivers) is not suitable for safety claims; use of knowledge that an AV has moved to a “less stressful” environment. Conclusion: While some reliability targets will remain too high to be practically verifiable, our CBI approach removes a major source of doubt: it allows use of prior knowledge without inducing dangerously optimistic biases. For certain ranges of required reliability and prior beliefs, CBI thus supports feasible, sound arguments. Useful conservative claims can be derived from limited prior knowledge.

There is an urgent societal need to assess whether autonomous vehicles (AVs) are safe enough. From published quantitative safety and reliability assessments of AVs, we know that, given the goal of predicting very low rates of accidents, road testing alone requires infeasible numbers of miles to be driven. However, previous analyses do not consider any knowledge prior to road testing - knowledge which could bring substantial advantages if the AV design allows strong expectations of safety before road testing. We present the advantages of a new variant of Conservative Bayesian Inference (CBI), which uses prior knowledge while avoiding optimistic biases. We then study the trend of disengagements (take-overs by human drivers) by applying Software Reliability Growth Models (SRGMs) to data from Waymo's public road testing over 51 months, in view of the practice of software updates during this testing. Our approach is to not trust any specific SRGM, but to assess forecast accuracy and then improve forecasts. We show that, coupled with accuracy assessment and recalibration techniques, SRGMs could be a valuable test planning aid.