Representing Confidence in Assurance Case Evidence

  • Lian Duan
  • Sanjai Rayadurgam
  • Mats P. E. Heimdahl
  • Oleg Sokolsky
  • Insup Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9338)


When evaluating assurance cases, being able to capture the confidence one has in the individual evidence nodes is crucial, as these values form the foundation for determining the confidence one has in the assurance case as a whole. Human opinions are subjective, oftentimes with uncertainty—it is difficult to capture an opinion with a single probability value. Thus, we believe that a distribution best captures a human opinion such as confidence. Previous work used a doubly-truncated normal distribution or a Dempster-Shafer theory-based belief mass to represent confidence in the evidence nodes, but we argue that a beta distribution is more appropriate. The beta distribution models a variety of shapes and we believe it provides an intuitive way to represent confidence. Furthermore, there exists a duality between the beta distribution and subjective logic, which can be exploited to simplify mathematical calculations. This paper is the first to apply this duality to assurance cases.


Opinion triangle Beta distribtion Subjective logic 


  1. 1.
    Safety management requirements for defence systems. Defence Standard 00–56 4, Ministry of Defense (2007)Google Scholar
  2. 2.
    Hawkins, R., Kelly, T., Knight, J., Graydon, P.: A new approach to creating clear safety arguments. In: Advances in Systems Safety (2011)Google Scholar
  3. 3.
    Denney, E., Pai, G., Habli, I.: Towards measurement of confidence in safety cases. In: 2011 International Symposium on Empirical Software Engineering and Measurement (2011)Google Scholar
  4. 4.
    Fenton, N., Neil, M., Caballero, J.G.: Using ranked nodes to model qualitative judgements in Bayesian networks. In: IEEE Transactions on Knowledge and Data Engineering (2007)Google Scholar
  5. 5.
    Ayoub, A., Chang, J., Sokolsky, O., Lee, I.: Assessing the overall sufficiency of safety arguments. In: Safety-Critical Systems Club (2013)Google Scholar
  6. 6.
    Jøsang, A.: Artificial reasoning with subjective logic. In: Proceedings of the Second Australian Workshop on Commonsense Reasoning (1997)Google Scholar
  7. 7.
    Cyra, L., G\(\acute{o}\)rski, J.: Supporting expert assessment of argument structures in trust cases. In: 9th International Probability Safety Assessment and Management Conference PSAM (2008)Google Scholar
  8. 8.
    Duan, L., Rayadurgam, S., Heimdahl, M., Ayoub, A., Sokolsky, O., Lee, I.: Reasoning about confidence and uncertainty in assurance cases: a survey. In: Software Engineering in Health Care (2014)Google Scholar
  9. 9.
    Kerr, O.: Why courts should not quantify probable cause. In: Klarman, S., Steiker (eds.) The Political Heart of Criminal Procedure: Essays on Themes of William J. Stuntz. GWU Law School Public Law Research Paper No. 543 (2012)Google Scholar
  10. 10.
    Druzdzel, M.J., van der Gaag, L.C.: Elicitation of probabilities for belief networks: combining qualitative and quantitative information. In: UAI 1995 Proceedings of the Eleventh Conference on Uncertainty in Artificial Intellingence (1995)Google Scholar
  11. 11.
  12. 12.
    Hobbs, C., Lloyd, M.: The application of Bayesian belief networks to assurance case preparation. In: Achieveing Systems Safety: Proceedings of the Twentieth Safety-Critical Systems Symposium (2012)Google Scholar
  13. 13.
    Cozman, F.: Axiomatizing noisy-or. In: Proceedings of the 16th European Conference on Artificial Intelligence (2004)Google Scholar
  14. 14.
    Toulmin, S.: The Uses of Argument. Cambridge University Press, Cambridge (1958)Google Scholar
  15. 15.
  16. 16.
    Górski, J., Jarzębowicz, A., Miler, J., Witkowicz, M., Czyżnikiewicz, J., Jar, P.: Supporting assurance by evidence-based argument services. In: Ortmeier, F., Daniel, P. (eds.) SAFECOMP Workshops 2012. LNCS, vol. 7613, pp. 417–426. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  17. 17.
    Choi, W., Kurfess, T.R., Cagan, J.: Sampling uncertainty in coordinate measurement data analysis. Precis. Eng. 22, 153–163 (1998)CrossRefGoogle Scholar
  18. 18.
    Merkle, E.: The disutility of the hard-easy effect in choice confidence. Psychon. Bull. Rev. 16(1), 204–213 (2009)CrossRefGoogle Scholar
  19. 19.
    Bishop, P., Bloomfield, R., Littlewood, B., Povyakalo, A., Wright, D.: Towards a formalism for conservative claims about the dependability of software-based systems. IEEE Trans. Softw. Eng. 37(5), 708–717 (2011)CrossRefGoogle Scholar
  20. 20.
    Jøsang, A., Haller, J.: Dirichlet reputation systems. In: Proceedings of the 2nd International Conference on Availability, Reliability and Security (2007)Google Scholar
  21. 21.
    Jøsang, A., Hayward, R., Pope, S.: Trust network analysis with subjective logic. In: 29th Australasian Computer Science Conference (2006)Google Scholar
  22. 22.
    Whitby, A., Jøsang, A., Indulska, J.: Filtering out unfair ratings in Bayesian reputation systems. In: Proceedings fo the Workshop on Trust in Agent Societies, at the Autonomous Agents and Multi Agent Systems Conference (2004)Google Scholar
  23. 23.
    Ettler, P., Dedecius, K.: Probabilistic reasoning in service of condition monitoring. In: Proceedings of the 11th International Conference on Condition Monitoring and Machinery Failure Prevention Technologies (2014)Google Scholar
  24. 24.
    Han, S., Koo, B., Hutter, A., Stechele, W.: Forensic reasoning upon pre-obtained surveillance metadata using uncertain spatio-temporal rules and subjective logic. In: 2010 11th International Workshop on Image Analysis for Multimedia Interactive Services (WIAMIS), pp. 1–4 (2010)Google Scholar
  25. 25.
    Chilenski, J., Miller, S.: Applicability of modified condition/decision coverage to software testing. Softw. Eng. J. 9, 193–200 (1994)CrossRefGoogle Scholar
  26. 26.
    Renooij, S.: Probability elicitation for belief networks: issues to consider. Knowl. Eng. Rev. 16, 255–269 (2001)CrossRefGoogle Scholar
  27. 27.
    O’Hagan, A.: Eliciting expert beliefs in substantial practical applications. J. Roy. Stat. Soc. Series D (Stat.) 47, 21–35 (1998)CrossRefGoogle Scholar
  28. 28.
    van der Gaag, L.C., Renooij, S., Witteman, C., Aleman, B.M.P., Taal, B.G.: How to elicit many probabilities. CoRR abs/1301.6745 (2013)

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Lian Duan
    • 1
  • Sanjai Rayadurgam
    • 1
  • Mats P. E. Heimdahl
    • 1
  • Oleg Sokolsky
    • 2
  • Insup Lee
    • 2
  1. 1.University of MinnesotaMinneapolisUSA
  2. 2.University of PennsylvaniaPhiladelphiaUSA

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