Conservative Software Reliability Assessments Using Collections of Bayesian Inference Problems

TL;DR

This paper develops a method for conservative software reliability assessment by analyzing collections of Bayesian inference problems to find worst-case posterior predictive probabilities, especially useful for safety-critical software.

Contribution

It introduces a framework for using collections of Bayesian problems to determine worst-case reliability estimates, extending robust and conservative Bayesian inference methods.

Findings

Explicitly determines worst-case posterior predictive probabilities.

Provides asymptotic properties of conservative posterior probabilities.

Illustrates application to safety-critical software assessments.

Abstract

When using Bayesian inference to support conservative software reliability assessments, it is useful to consider a collection of Bayesian inference problems, with the aim of determining the worst-case value (from this collection) for a posterior predictive probability that characterizes how reliable the software is. Using a Bernoulli process to model the occurrence of software failures, we explicitly determine (from collections of Bayesian inference problems) worst-case posterior predictive probabilities of the software operating without failure in the future. We deduce asymptotic properties of these conservative posterior probabilities and their priors, and illustrate how to use these results in assessments of safety-critical software. This work extends robust Bayesian inference results and so-called conservative Bayesian inference methods.