Conservative Software Reliability Assessments Using Collections of Bayesian Inference Problems

2025-11-10

AI Summary

To address conservative reliability assessment for safety-critical software under prior uncertainty, this paper proposes a robust Bayesian framework that computes the worst-case posterior predictive probability of fault-free operation—thereby yielding a conservative estimate of future reliability. Methodologically, software failures are modeled as a Bernoulli process, and the approach integrates set-based Bayesian inference with asymptotic analysis. Key contributions include: (1) the first closed-form analytical solution for the worst-case posterior predictive probability; (2) characterization of its asymptotic convergence properties; and (3) an extension of robust Bayesian theory, providing a rigorous mathematical foundation for quantifying worst-case behavior under prior uncertainty. The framework balances theoretical rigor with practical applicability, enabling high-assurance software reliability certification.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Determining worst-case posterior predictive probabilities for software reliability
• Modeling software failures using Bernoulli process Bayesian inference
• Extending robust Bayesian methods for safety-critical software assessments

Innovation

• Collections of Bayesian inference problems for reliability
• Bernoulli process models software failure occurrences
• Asymptotic analysis of conservative posterior probabilities