Survivability of systems under multiple factor impact Edward Korczak , Gregory Levitin

1. Survivability of systems under multiple factor impactEdward Korczak, Gregory Levitin Adviser: Frank,Yeong-Sung Lin Present by Sean Chou

2. Agenda • Introduction • Assumptions and model • MSS survivability evaluation • Computational example • Conclusions

3. Agenda • Introduction • Assumptions and model • MSS survivability evaluation • Computational example • Conclusions

4. Introduction • Many technical systems operate under influence of external factors that may cause simultaneous damage of several system elements and lead to degradation or even termination of the mission/ function performed by the system. • Survivability, the ability of a system to tolerate intentional attacks or accidental failures or errors

5. Introduction • In order to mitigate the impact of external factors, a multilevel protection is often used. • The multilevel protectionmeans that a subsystem and its inner level protectionare in their turn protected by the protection of the outerlevel. • Numerous studies were devoted to estimating the impactof external factors on the system’s survivability

6. Introduction • In the recent paper [1], a newalgorithm for evaluation of the survivability of series-parallelsystems with arbitrary (complex) structure of multilevelprotection was presented, extending applicability of previousworks. • [1] Korczak E, Levitin G, Ben Haim H. Survivability of series–parallelsystems with multilevel protection. Reliab Eng Sys Safe 2005;90:45–54.

7. Introduction • In many real situations the impacts can be characterizedby several destructive factors (DF) affecting the system orits parts simultaneously. • The groups of elements protected bydifferent protections can overlap. Each protection can beeffective against single or several DFs. However this factwas not considered in [1].

8. Agenda • Introduction • Assumptions and model • MSS survivability evaluation • Computational example • Conclusions

9. Assumptions and model

10. Assumptions and model

11. Assumptions and model • Gj : : random performance rate of MSS element j • The element can have Kj different states (from total failure up to perfect functioning) with performance rates gjk (1pkpKj). • The performance distribution of each element when it is not affected by any DF is given as

12. Assumptions and model • Single elements or groups of elements can be protected.All the elements having the same protection compose aprotection group (PG). • Any PG or its part can belong to another PG. • Oj :set of numbers of DFs that can destroyelement j • Yj, d :set of numbers of protections that protectelement j against DF d

13. Assumptions and model • The system survives if its performance rate is not lessthan the minimal allowable level w. The MSS survivabilityis the probability that the system survives:

14. Assumptions and model • The presented model in which the system is alwaysexposed to all the DFs can be directly used for two cases: • The system survivability is evaluated under assumptionthat the system is under single multifactor impact. • The system survivability is evaluated when external threats are continuously present.

15. Agenda • Introduction • Assumptions and model • MSS survivability evaluation • Computational example • Conclusions

16. MSS survivability evaluation • The conditional performance distribution (1) of anysystem element j when it is not affected by any DF isrepresented by the u-function: • When the element j is destroyed its performance is zeroedwith probability 1. Therefore, the conditional performancedistribution of destroyed element is represented by the u-functionz0.

17. MSS survivability evaluation • Let xm be the state of protection m( xm =1 if protectionm is destroyed and xm =0 if it survives). • This condition can be represented by Boolean functionbj,d(x): • By convention the product over the empty set is equal to 1.Therefore bj;d ex=0 if Yj;d ?+.

18. MSS survivability evaluation • Element j survives if it is not destroyed by any DF fromOj. This condition can be represented by Boolean functionBj(x):

19. MSS survivability evaluation • If all of the protections belonging to Yj,d for any DF d 2 Oj are destroyed element j is also destroyed and its performance distribution in this case can be represented by the u-function z0. • The element performance distribution as a function of the states of the protections as

20. MSS survivability evaluation • Applying these rules recursively, oneobtains the final u-function of entire system:

21. Agenda • Introduction • Assumptions and model • MSS survivability evaluation • Computational example • Conclusions

22. Computational example • A chemical reagent supplysystem consists of seven multi-state elements. • Three DFs can incapacitate the system in the case of explosion: fire (DF 1) corrosion active gases (DF 2) voltage surge (DF 3).

23. Computational example • Nine different protections are used to protect differentgroups of the elements.

24. Computational example • The element protectionsets Yj,d corresponding to different configurations

25. Computational example

26. Computational example

27. Computational example

28. Computational example • Fig. 2 presents the MSS survivability as a function ofthe demand for each configuration.

29. Computational example • Observe that configurationA provides greater system survivability in the rangeof small demands while configuration B outperformsconfiguration A in the range of greater demands. • Thisshows that when different protection configurations arecompared the expected system demand should be takeninto account.

30. Agenda • Introduction • Assumptions and model • MSS survivability evaluation • Computational example • Conclusions

31. Conclusions • This paper presents an adaptation of the numericalgorithm for evaluating the survivability of series-parallelsystems with multilevel protection [1] to the case ofmultiple factor impacts.

32. Thanks for your listening.