Analysis of the Robustness and Recovery of Critical Infrastructures by Goal Tree–Success Tree: Dynamic Master Logic Diagram, Within a Multistate System-of-Systems Framework, in the Presence of Epistemic Uncertainty

In this paper, we evaluate the robustness and recovery of connected critical infrastructures (CIs) under a system-of-systems (SoS) framework taking into account: (1) the dependencies among the components of an individual CI and the interdependencies among different CIs; (2) the variability in component performance, by a multistate model; and (3) the epistemic uncertainty in the probabilities of transitions between different components states and in the mean values of the holding-times distributions, by means of intervals. We adopt the goal tree success tree–dynamic master logic diagram (GTST–DMLD) for system modeling and perform the quantitative assessment by Monte Carlo simulation. We illustrate the approach by way of a simplified case study consisting of two interdependent infrastructures (electric power system and gas network) and a supervisory control and data acquisition (SCADA) system connected to the gas network. This article is available in the ASME Digital Collection at http://dx.doi.org/10.1115/...

[1]  Lev V. Utkin,et al.  Processing unreliable judgements with an imprecise hierarchical model , 2002 .

[2]  Scott Ferson,et al.  Arithmetic with uncertain numbers: rigorous and (often) best possible answers , 2004, Reliab. Eng. Syst. Saf..

[3]  G. Apostolakis.  The concept of probability in safety assessments of technological systems. , 1990, Science.

[4]  Bernd Möller,et al.  Safety assessment of structures in view of fuzzy randomness , 2003 .

[5]  Klemens Szaniawski,et al.  Formal methods in the methodology of empirical sciences : proceedings of the Conference for Formal Methods in the Methodology of Empirical Sciences, Warsaw, June 17-21, 1974 , 1976 .

[6]  G. Apostolakis.  Bayesian Methods in Risk Assessment , 1981 .

[7]  David I Blockley,et al.  Analysing uncertainties: Towards comparing Bayesian and interval probabilities' , 2013 .

[8]  M. Beer,et al.  Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method , 2013 .

[9]  Distribution type uncertainty due to sparse and imprecise data , 2013 .

[10]  James J. Buckley,et al.  Fuzzy Probabilities and Fuzzy Sets for Web Planning , 2003, Studies in Fuzziness and Soft Computing.

[11]  W. T. Tucker,et al.  Sensitivity in risk analyses with uncertain numbers. , 2006 .

[12]  Enrico Zio,et al.  Goal Tree Success Tree–Dynamic Master Logic Diagram and Monte Carlo simulation for the safety and resilience assessment of a multistate system of systems , 2014 .

[13]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[14]  Yu-Shu Hu.  Evaluating system behavior through dynamic master logic diagram modeling , 1995 .

[15]  Durga Rao Karanki,et al.  Uncertainty Analysis Based on Probability Bounds (P‐Box) Approach in Probabilistic Safety Assessment , 2009, Risk analysis : an official publication of the Society for Risk Analysis.

[16]  Luis G. Crespo,et al.  Reliability analysis of polynomial systems subject to p-box uncertainties , 2013 .

[17]  V. Kreinovich,et al.  Imprecise probabilities in engineering analyses , 2013 .

[18]  V. Kreinovich,et al.  Experimental uncertainty estimation and statistics for data having interval uncertainty. , 2007 .

[19]  Stuart G. Reid,et al.  Probabilistic confidence for decisions based on uncertain reliability estimates , 2013 .

[20]  Philipp Limbourg,et al.  Uncertainty analysis using evidence theory - confronting level-1 and level-2 approaches with data availability and computational constraints , 2010, Reliab. Eng. Syst. Saf..

[21]  Michael Kaliske,et al.  Solutions to problems with imprecise data—An engineering perspective to generalized uncertainty models , 2013 .

[22]  Mohamed Sallak,et al.  Reliability assessment for multi-state systems under uncertainties based on the Dempster–Shafer theory , 2013 .

[23]  Enrico Zio,et al.  Some considerations on the treatment of uncertainties in risk assessment for practical decision making , 2011, Reliab. Eng. Syst. Saf..

[24]  S. Ferson,et al.  Different methods are needed to propagate ignorance and variability , 1996 .

[25]  Timothy A. Wheeler,et al.  Guidance on the Treatment of Uncertainties Associated with PRAs in Risk-Informed Decision Making , 2009 .

[26]  Enrico Zio,et al.  The Monte Carlo Simulation Method for System Reliability and Risk Analysis , 2012 .

[27]  Andy Hart,et al.  Application of Uncertainty Analysis to Ecological Risks of Pesticides , 2010 .

[28]  Bruce R. Ellingwood,et al.  Serviceability of earthquake-damaged water systems: Effects of electrical power availability and power backup systems on system vulnerability , 2008, Reliability Engineering & System Safety.

[29]  Enrico Zio,et al.  Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[30]  Mark A. Turnquist,et al.  Assessing the performance of interdependent infrastructures and optimising investments , 2005, Int. J. Crit. Infrastructures.

[31]  Scott Ferson,et al.  Special issue of Mechanical Systems and Signal Processing “Imprecise probabilities—What can they add to engineering analyses?” , 2013 .

[32]  Christophe Bérenguer,et al.  Reliability analysis for new technology-based transmitters , 2011, Reliab. Eng. Syst. Saf..

[33]  B. M. Hill,et al.  Theory of Probability , 1990 .

[34]  R. Wasserstein.  Monte Carlo Methods, Volume 1: Basics , 1989 .

[35]  A. Sofi,et al.  Bounds for the stationary stochastic response of truss structures with uncertain-but-bounded parameters , 2013 .

[36]  Enrico Zio,et al.  Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model , 2013 .

[37]  V. Kreinovich,et al.  Estimating correlation under interval uncertainty , 2013 .

[38]  Christopher H. Mehl.  P-boxes for cost uncertainty analysis , 2013 .