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This paper presents Bayesian techniques for conservative claims aboutsoftware reliability, particularly when evidence suggests the software'sexecutions are not statistically independent. We formalise informal notions of"doubting" that the executions are independent, and incorporate such doubtsinto reliability assessments. We develop techniques that reveal the extent towhich independence assumptions can undermine conservatism in assessments, andidentify conditions under which this impact is not significant. Thesetechniques - novel extensions of conservative Bayesian inference (CBI)approaches - give conservative confidence bounds on the software's failureprobability per execution. With illustrations in two application areas -nuclear power-plant safety and autonomous vehicle (AV) safety - our analysesreveals: 1) the confidence an assessor should possess before subjecting asystem to operational testing. Otherwise, such testing is futile - favourableoperational testing evidence will eventually decrease one's confidence in thesystem being sufficiently reliable; 2) the independence assumption supportsconservative claims sometimes; 3) in some scenarios, observing a system operatewithout failure gives less confidence in the system than if some failures hadbeen observed; 4) building confidence in a system is very sensitive to failures- each additional failure means significantly more operational testing isrequired, in order to support a reliability claim.

Demonstrating Software Reliability using Possibly Correlated Tests: Insights from a Conservative Bayesian Approach