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

2. 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 w Pr{w>W*} W* S(W*)

3. SYSTEM OUTPUT PERFORMANCE DISTRIBUTION G P 0.70 0.05 0.1 0.05 0.1 W2W2W2W2 0.75 … W1W1W1W1 0.85

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 collection of elements with the same functionality connected in parallel in reliability logic-diagram sense quantitative measure of task performing intensity of element or system (capacity, productivity, processing speed, task completion time etc.)

6. Basic Definitions technical or organizational measure aimed at reduction of destruction probability of a group of system elements in the case of attack 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.) 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 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)

7. ... Optimal element separation problem

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

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

10. System survivability enhancement by element protection

11. ... Survivability optimization problem

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

13. Producing units Protection

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

15. 5 7 s2s2 6 3 4 s1s1 s3s3 s5s5 s4s4 s6s6 2 1 Multilevel protection

16. Protection survivability importance in simplest binary systems s1s1 s2s2 s3s3... snsn a s1s1 s2s2 s3s3 snsn a s2s2 s1s1 snsn s3s3 a

17. Protection survivability importance and relevancy in multi-state system 5 7 s2s2 6 3 4 1 2 s1s1 s3s3 s5s5 s4s4 s6s6

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

19. Parameters of a system to be optimized 7 9 8 5 6 2 3 4 1 12 10 11 654321No of element (j) g jk p jk g jk p jk g jk p jk g jk p jk g jk p jk g jk p jk State (k) 40.754 4 4 7 7 1 20.152 2 2 5 5 2 00.10 0 0 30.053 3 --------0 0 4 121110987No of element (j) g jk p jk g jk p jk g jk p jk g jk p jk g jk p jk g jk p jk State (k) 100.8580.9580.8060.1050.855 1 70.1000.0550.1540.7030.053 2 0 --0 20.1500.100 3 ------00.05----4 protection cost protection survivability set of protected elements No of protection 1.50.9511 1.50.9522 1.00.9033 … 5.20.657,8,9,10,11,1228 7.00.701,2,3,4,5,6,7,8,9,10,11, 12 29

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

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

22. A 5 7 6 3 4 1 2 1 2 3 4 5 6 7 8 9 5 7 6 3 4 1 2 4 2 3 1 5 67 8 9 A B Example of two different protection configurations S A >S B S A <S B

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

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

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

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

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

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

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.