On the probability of perfection of software-based systems

The probability of perfection becomes of interest as the realization of its role in the reliability assessment of software-based systems. It is not only important on its own, but also in the reliability assessment of 1-out-of-2 diverse systems. By “perfection”, it means that thesoftware will never fail in a specific operating environment. If we assume that failures of a software system can occur if and only if it contains faults, then it means that the system is “fault-free”. Such perfection is possible for sufficiently simple software. While the perfection can never be certain, so the interest lies in claims for the probability of perfection. In this thesis, firstly two different probabilities of perfection – an objective parameter characterizing a population property and a subjective confidence in the perfection of the specific software of interest – are distinguished and discussed. Then a conservative Bayesian method is used to claim about probability of perfection from various types of evidence, i.e. failure-free testing evidence, process evidence and formal proof evidence. Also, a “quasiperfection” notion is realized as a potentially useful approach to cover some shortages of perfection models. A possible framework to incorporate the various models is discussed at the end. There are generally two themes in this thesis: tackling the failure dependence issue in the reliability assessment of 1-out-of-2 diverse systems at both aleatory and epistemic levels; and degrading the well-known difficulty of specifying complete Bayesian priors into reasoning with only partial priors. Both of them are solved at the price of conservatism. In summary, this thesis provides 3 parallel sets of (quasi-)perfection models which could be used individually as a conservative end-to-end argument that reasoning from various types of evidence to the reliability of a software-based system. Although in some cases models here are providing very conservative results, some ways are proposed of dealing with the excessive conservatism. In other cases, the very conservative results could serve as warnings/support to safety engineers/regulators in the face of claims based on reasoning that is less rigorous than the reasoning in this thesis.