1 / 30

Optimal Survivability Enhancement in Complex Vulnerable systems Gregory Levitin

The Israel Electric Corporation Ltd. Optimal Survivability Enhancement in Complex Vulnerable systems Gregory Levitin. Pr{w>W*}. S(W*). w. W*.

tasha-blackwell
Download Presentation

Optimal Survivability Enhancement in Complex Vulnerable systems Gregory Levitin

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Israel Electric Corporation Ltd. Optimal Survivability Enhancement in Complex Vulnerable systems Gregory Levitin

  2. Pr{w>W*} S(W*) w W* Survivable system - system that is able to “complete its mission in a timely manner, even if significant portions are incapacitated by attack or accident”. Multi-state system with different performance rates Reliability + vulnerability analysis

  3. SYSTEM OUTPUT PERFORMANCE DISTRIBUTION … P 0.1 0.05 0.1 0.05 0.70 0.85 0.75 G W1 W2

  4. System survivability enhancement by element separation

  5. Basic Definitions lowest-level part of system, which is characterized by its inherent value, availability and performance distribution ELEMENT quantitative measure of task performing intensity of element or system (capacity, productivity, processing speed, task completion time etc.) PERFORMANCE COMPONENT collection of elements with the same functionality connected in parallel in reliability logic-diagram sense

  6. Basic Definitions technical or organizational measure aimed at reduction of destruction probability of a group of system elements in the case of attack PROTECTION action aimed at preventing simultaneous destruction of several elements in the case of single attack (can be performed by spatial dispersion, by encapsulating different elements into different protective casings, by using different power sources etc.) SEPARATION group of system elements separated from other elements (and possibly protected) so that a single external impact destroying elements belonging to a certain group cannot destroy elements from other groups PROTECTION GROUP object that imitates protected group of system elements, but does not contain any element (the total damage caused by the destruction of any false target is much lower than the damage caused by the destruction of any protection group) FALSE TARGET

  7. S R=Pr( w>W*) Optimal element separation problem wq ... v q

  8. 11 12 13 14 15 16 PARAMETERS OF SYSTEM ELEMENTS 1 8 6 2 9 3 7 4 10 5

  9. OPTIMAL SEPARATION SOLUTION FOR v=0.05 11 15 2 8 6 3 13 9 14 1 7 4 10 12 5 16

  10. System survivability enhancement by element protection

  11. S R=Pr( w>W*) Survivability optimization problem wqc vc ... v q

  12. Functional scheme of system List of available elements with given performance distributions List of chosen elements Separation and protection of elements Survivability and cost of possible protections Desired system performance and survivability W, S* Optimal system structure

  13. Parameters of available system elements Producing units Protection

  14. Optimal structure for W=5, S*=0.85 3 3 3 3 2 1 1 2 3 1 1 1 3 3 1 1 1 3 1 3 1 2 1 2 3 2 2 SMSS=0. 8504 CMSS=152.2

  15. Multilevel protection s3 s6 5 1 s5 s4 s2 6 3 2 s1 7 4

  16. sn ... s3 s2 s1 a s1 s2 s3 sn a ... s1 a s2 s3 ... sn Protection survivability importance in simplest binary systems

  17. s3 s6 4 3 1 6 5 2 7 s4 s2 s5 s1 Protection survivability importance and relevancy in multi-state system

  18. Structure of series-parallel system Performance distribution of system elements 6 3 6 4 4 10 12 3 5 12 5 8 10 8 2 1 7 11 1 2 7 9 11 9 Survivability and cost of possible protections cm, sm Desired system performance and survivability W, S* Optimal multilevel protection problem List of chosen protections

  19. 3 7 1 10 4 8 5 2 11 12 9 6 Parameters of a system to be optimized

  20. 6 3 4 12 5 8 10 7 2 1 11 9 w=7, S*=0.85 Optimal multilevel protection solutions

  21. Protection against multiple factor impacts Destructive factors Protections Complex protections

  22. 4 4 3 3 1 1 6 6 2 5 5 2 7 7 Example of two different protection configurations 1 5 8 3 SA<SB 7 4 6 9 2 A SA>SB 4 3 1 8 5 A 7 6 9 2 B

  23. Unintentional vs. intentional impacts No impact strategy Attacker’s strategy maximizing the expected damage

  24. Expected damage model Protection vulnerability Attack probability p v g Equipment losses Cumulative performance of the group Expected damage System performance reduction Failures

  25. Defense strategy Separation Damage g Destruction probability Protection v False targets Impact probability p Disinformation

  26. Single attack strategy p=1/N p p Perfect knowledge about the system p=1 No knowledge about the system Imperfect knowledge about the system p Spi=1

  27. Multiple attack strategy p=1 p=1 p p Unlimited resource Limited resource + perfect knowledge about the system Limited resource + imperfect knowledge about the system p Spi>1

  28. Universal generating function technique uj(z) ui(z) Tools for solving the problems Evaluating system performance distribution Solving optimization problems Universal simulated evolution technique Genetic Algorithm

  29. References 1. Optimal separation of elements in vulnerable multi-state systems,G. Levitin, A. Lisnianski,Reliability Engineering & System Safety, vol. 73, pp. 55-66, (2001). 2. Optimizing survivability of vulnerable series-parallel multi-state systems, G. Levitin, A. Lisnianski, Reliability Engineering & System Safety, vol. 79, pp.319-331, (2003). 3. Optimal multilevel protection in series-parallel systems, G. Levitin, Reliability Engineering & System Safety, vol. 81, pp.93-102, (2003). 4. Optimizing survivability of multi-state systems with multi-level protection by multi-processor genetic algorithm, G. Levitin, Y. Dai, M. Xie, K. L. Poh, Reliability Engineering & System Safety, vol. 82, pp.93-104, (2003). 5. Protection survivability importance in systems with multilevel protection, G. Levitin, Quality and Reliability Engineering International, vol. 20, pp.727-738, (2004). 6. Survivability of series-parallel systems with multilevel protection, E. Korczak, G. Levitin, H. Ben Haim, Reliability Engineering & System Safety, vol. 90, pp.45-54, (2005). 7. Incorporating common-cause failures into series-parallel multi-state system analysis, G. Levitin, IEEE Transactions on Reliability, vol. 50, No. 4, pp. 380-388 (2001). 8. Maximizing survivability of vulnerable weighted voting systems, G. Levitin, Reliability Engineering & System Safety, vol. 83, pp.17-26, (2003). 9. Maximizing survivability of acyclic transmission networks with multi-state retransmitters and vulnerable nodes, G. Levitin, Reliability Engineering & System Safety, vol. 77, pp.189-199, (2002). 10. Survivability maximization for vulnerable multi-state system with bridge topology, G. Levitin, A. Lisnianski, Reliability Engineering & System Safety, vol. 70, pp. 125-140, (2000). 11. Universal generating function in reliability analysis and optimization, G. Levitin, Springer-Verlag, 2005. 12. Multi-state system reliability. Assessment, optimization and applications, A. Lisnianski, G. Levitin, World Scientific, 2003.

  30. Contents: • Basic Tools and Techniques. • UGF in Reliability Analysis of Binary Systems. • Introduction to Multi-state Systems. • UGF in Analysis of Series-parallel MSS. • UGF in Optimization of Series-parallel MSS. • UGF in Analysis and Optimization of Special Types of MSS. • UGF in Analysis and Optimization of Consecutively Connected Systems and Networks. • UGF in Analysis and Optimization of Fault-tolerant Software.

More Related