Fault Tree Analysis of Software-Controlled Component Systems Based on Second-Order Probabilities

Software is still mostly regarded as a black box in the development process, and its safety-related quality ensured primarily by process measures. For systems whose lion share of service is delivered by (embedded) software, process-centred methods are seen to be no longer sufficient. Recent safety norms (for example, ISO 26262) thus prescribe the use of safety models for both hardware and software. However, failure rates or probabilities for software are difficult to justify. Only if developers take good design decisions from the outset will they achieve safety goals efficiently. To support safety-oriented navigation of the design space and to bridge the existing gap between qualitative analyses for software and quantitiative ones for hardware, we propose a fault-tree-based approach to the safety analysis of software-controlled systems. Assigning intervals instead of fixed values to events and using Monte-Carlo sampling, probability mass functions of failure probabilities are derived. Further analysis of PMF lead to estimates of system quality that enable safety managers to take an optimal choice between design alternatives and to target cost-efficient solutions in every phase of the design process.

[1]  Barbara Paech,et al.  Developing and applying component-based model-driven architectures in KobrA , 2001, Proceedings Fifth IEEE International Enterprise Distributed Object Computing Conference.

[2]  Vladik Kreinovich,et al.  Optimal choice of granularity in commonsense estimation: Why half‐orders of magnitude? , 2006, Int. J. Intell. Syst..

[3]  Mario Trapp,et al.  Integrating Safety Analyses and Component-Based Design , 2008, SAFECOMP.

[4]  Vasant Honavar,et al.  A Software Fault Tree Approach to Requirements Analysis of an Intrusion Detection System , 2002, Requirements Engineering.

[5]  Dominik Domis,et al.  Safety Concept Trees , 2009, 2009 Annual Reliability and Maintainability Symposium.

[6]  Ronald Fagin,et al.  Uncertainty, belief, and probability 1 , 1991, IJCAI.

[7]  Vladik Kreinovich,et al.  From [0,1]-Based Logic to Interval Logic (From Known Description of All Possible [0,1]-Based Logical Operations to a Description of All Possible Interval-Based Logical Operations) , 2002 .

[8]  Peter Liggesmeyer,et al.  A New Component Concept for Fault Trees , 2003, SCS.

[9]  David Wright,et al.  Assesing dependability of safety critical systems using diverse evidence , 1998, IEE Proc. Softw..

[10]  Lavon B. Page,et al.  Standard deviation as an alternative to fuzziness in fault tree models , 1994 .

[11]  Simon Parsons,et al.  Qualitative Probability and Order of Magnitude Reasoning , 2003, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[12]  Timothy M. Barry,et al.  Monte Carlo modeling with uncertain probability density functions , 1996 .

[13]  Ralf Kalmar,et al.  Efficient Safety Analysis of Automotive Software Systems , 2009 .

[14]  Hideo Tanaka,et al.  Fault-Tree Analysis by Fuzzy Probability , 1981, IEEE Transactions on Reliability.

[15]  Marie-Christine Bansse.  Comité européen de normalisation électrotechnique (CENELEC) , 1989 .

[16]  P. Pandurang Nayak,et al.  Order of Magnitude Reasoning using Logarithms , 1992, KR.

[17]  Katerina Goseva-Popstojanova,et al.  Architecture-based approach to reliability assessment of software systems , 2001, Perform. Evaluation.

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

[19]  Claude E. Shannon,et al.  A symbolic analysis of relay and switching circuits , 1938, Transactions of the American Institute of Electrical Engineers.

[20]  Michael A. S. Guth.  A probabilistic foundation for vagueness and imprecision in fault-tree analysis , 1991 .

[21]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[22]  Winfrid G. Schneeweiss,et al.  On the Polynomial Form of Boolean Functions: Derivations and Applications , 1998, IEEE Trans. Computers.

[23]  C. Y. Lee.  Representation of switching circuits by binary-decision programs , 1959 .

[24]  Weldon A. Lodwick,et al.  Constrained Interval Arithmetic , 1999 .

[25]  Norman E. Fenton,et al.  Software metrics: roadmap , 2000, ICSE '00.

[26]  Z W Birnbaum,et al.  ON THE IMPORTANCE OF DIFFERENT COMPONENTS IN A MULTICOMPONENT SYSTEM , 1968 .

[27]  J. A. Cooper,et al.  New Mathematical Derivations Applicable to Safety and Reliability Analysis , 1999 .

[28]  J. Arlin Cooper.  Constrained mathematics evaluation in probabilistic logic analysis , 1998 .

[29]  Ian D. Walker,et al.  Interval methods for fault-tree analysis in robotics , 2001, IEEE Trans. Reliab..

[30]  K. Sentz,et al.  Fault tree uncertainty quantification using probabilities and belief structures on basic and non-basic events , 2005, NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society.

[31]  J. D. Andrews.  To not or not to not , 2000 .

[32]  Michael Brickenstein,et al.  POLYBORI: A Gröbner basis framework for Boolean polynomials , 2007 .

[33]  Septavera Sharvia,et al.  Non-coherent Modelling in Compositional Fault Tree Analysis , 2008 .

[34]  Peter Neumann,et al.  Safeware: System Safety and Computers , 1995, SOEN.

[35]  S.G. Miremadi,et al.  A fuzzy-monte carlo simulation approach for fault tree analysis , 2006, RAMS '06. Annual Reliability and Maintainability Symposium, 2006..

[36]  Swapna S. Gokhale,et al.  Reliability simulation of component-based software systems , 1998, Proceedings Ninth International Symposium on Software Reliability Engineering (Cat. No.98TB100257).

[37]  Benjamin Kuipers,et al.  Qualitative and Quantitative Simulation: Bridging the Gap , 1997, Artif. Intell..

[38]  Vladik Kreinovich,et al.  Optimal choice of granularity in commonsense estimation: Why half-orders of magnitude?: Research Articles , 2006 .

[39]  Josh Dehlinger,et al.  Software fault tree analysis for product lines , 2004, Eighth IEEE International Symposium on High Assurance Systems Engineering, 2004. Proceedings..

[40]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[41]  Saburo Muroga,et al.  Binary Decision Diagrams , 2000, The VLSI Handbook.

[42]  S. Skelboe.  Computation of rational interval functions , 1974 .

[43]  Vladik Kreinovich,et al.  Computing best-possible bounds for the distribution of a sum of several variables is NP-hard , 2006, Int. J. Approx. Reason..