Adaptation of the Rules of the Models of Games with Nature for the Design of Safety Systems

  • Adrian GillEmail author
  • Piotr Smoczyński
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 516)


The article presents a manner of formulating the problem of designing safety systems in terms of decision-making problems solved with the use of the models of the so-called games with nature. The models of this type are very frequently used to make decisions under conditions of uncertainty. The situation also occurs in the process of designing safety systems. For the purposes of solving the problem, the appropriate understanding of the basic components of the models of games with nature, i.e. the game strategy and the state of nature, was assumed. In this context, a definition of a system and a safety system was provided, along with an interpretation of the relationships between safety system elements (risk reduction measures) and domain elements (hazard factors/sources, hazards), on account of which these systems are designed. The specificity of the functioning of safety systems also required a modification of the decision rules applied within the models used. The modification was illustrated with the example of Wald’s rule. A general concept of formulating the problem of designing safety systems as a decision-making problem was presented, along with the general algorithm of selecting risk reduction measures for safety systems with the use of the modified rules of the models of games with nature. Next, a mathematical model of the research problem was provided, including: creation of the risk reduction measure efficacy matrix, creation of the hazard source – hazard relationship matrix, determination of the payoff matrix, and the modification of decision rules. Usually, there is a need to select more than one risk reduction measure. An already developed original concept of sequential selection of these measures was used. The application of the rule adaptation proposed here was illustrated with an example of a fire protection system for railway vehicles. Hazard sources were identified and hazards related to electrical systems in railway vehicles were formulated. A list of examples of risk reduction measures which may form a safety system was presented.


Safety systems Games with nature Risk reduction measures 



The research work financed with the means of statutory activities of Faculty of Machines and Transport, Poznan University of Technology, 05/52/DSPB/0280.


  1. 1.
    Adger, W.N.: Vulnerability. Glob. Environ. Chang. 16(3), 268–281 (2006)CrossRefGoogle Scholar
  2. 2.
    Aven, T.: Risk Analysis (2015)Google Scholar
  3. 3.
    Aven, T., Heide, B.: Reliability and validity of risk analysis. Reliab. Eng. Syst. Saf. 94(11), 1862–1868 (2009)CrossRefGoogle Scholar
  4. 4.
    Cempel, C.: Teoria i inżynieria systemów-zasady i zastosowania myślenia systemowego. ITE Radom, Radom (2008)Google Scholar
  5. 5.
    Gill, A.: Koncepcja zastosowania reguł decyzyjnych w doborze środków redukcji ryzyka zagrożeń. Pr. Nauk. Politech. Warsz. Transp, pp.181–190 (2013)Google Scholar
  6. 6.
    Gill, A., Kadziński, A.: Hazard identification model. In: Proceedings of 20th International Scientific Conference. Transport Means (5–7 October 2016, Juodkrante, Lithuania), pp. 885–890. Kaunas University of Technology (2016)Google Scholar
  7. 7.
    Gill, A., Smoczyński, P.: Layered model for convenient designing of safety system upgrades in railways. Saf. Sci., in press.
  8. 8.
    Girdner, N.: An integrated system safety model of the national airspace system. In: Proceedings of the Annual Reliability and Maintainability Symposium (2016)Google Scholar
  9. 9.
    Harms-Ringdahl, L.: Analysis of safety functions and barriers in accidents. Saf. Sci. 47(3), 353–363 (2009)CrossRefGoogle Scholar
  10. 10.
    Harms-Ringdahl, L.: Guide to safety analysis for accident prevention. IRS Riskhantering AB (2013)Google Scholar
  11. 11.
    Hughes, B.P., et al.: System theory and safety models in Swedish, UK, Dutch and Australian road safety strategies. Accid. Anal. Prev. 74, 271–278 (2015)CrossRefGoogle Scholar
  12. 12.
    Jędrzejczyk, Z., et al.: Badania operacyjne w przykładach i zadaniach. PWN, Warszawa (2002)Google Scholar
  13. 13.
    Kadziński, A.: Studium wybranych aspektów niezawodności systemów oraz obiektów pojazdów szynowych (2013)Google Scholar
  14. 14.
    Kadziński, A., et al.: The concept of method and models for risk management of hazards generated at railway crossings. In: Proceedings of 20th International Scientific Conference. Transport Means (5–7 October 2016, Juodkrante, Lithuania), Kaunas, Lithunania, pp. 297–302 (2016)Google Scholar
  15. 15.
    Majchrzyk, D., Tarka, I.: Kable i przewody elektryczne przeznaczone do taboru szynowego. Pr. Inst. Kolejnictwa. 149, 14–21 (2016)Google Scholar
  16. 16.
    Meyer, T., Reniers, G.: Engineering Risk Management. De Gruyter (2016)Google Scholar
  17. 17.
    Sikora, W.: Badania operacyjne. Polskie Wydawnictwo Ekonomiczne (2008)Google Scholar
  18. 18.
    Sun, Y., et al.: Multilayered impact evaluation model for attacking missions. IEEE Syst. J. 10(4), 1304–1315 (2016)CrossRefGoogle Scholar
  19. 19.
    Tsenina, E.V., et al.: Indication of competitiveness of the potential of the region through hurwitz and wald criteria. Glob. J. Pure Appl. Math. 12(1), 325–335 (2016)Google Scholar
  20. 20.
    Turskis, Z., et al.: Multi-criteria optimization system for decision making in construction design and management. Eng. Econ. 1(1), 7–17 (2009)Google Scholar
  21. 21.
    Vincoli, J.W.: Basic Guide to System Safety, 3rd edn. Wiley, Hoboken (2014)Google Scholar
  22. 22.
    Wald, A.: Statistical decision functions which minimize the maximum risk. Ann. Math. 46(2), 265–280 (1945)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Wu, X., Du, R.: A solution to decision making under uncertainty. J. Theor. Appl. Inf. Technol. 45(1), 320–324 (2012)Google Scholar
  24. 24.
    Yemets, O.A., Ustian, N.Y.: Games with combinatorial constraints. Cybern. Syst. Anal. 44(4), 575–581 (2008)CrossRefGoogle Scholar
  25. 25.
    Zavadskas, E.K., et al.: Development of software for multiple criteria evaluation. Informatica 14(2), 259–272 (2003)MathSciNetzbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2019

Authors and Affiliations

  1. 1.Poznan University of TechnologyPoznańPoland

Personalised recommendations