Analyzing Ballistic Missile Defense System Effectiveness Based on Functional Dependency Network Analysis

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1 Send Odes fo Repints to 678 The Open Cybenetics & Systemics Jounal, 2015, 9, Open Access Analyzing Ballistic Missile Defense System Effectiveness Based on Functional Dependency Netwok Analysis Yao Jian *, Huang Qiwang and Wang Weiping College of Infomation System and Management, National Univesity of Defense Technology, Hunan, Changsha, , P.R. China Abstact: Recent engineeing expeiences highlight the Ballistic Missile Defense System (BMDS as a System of Systems (SoS, and taditional pobability models wee limited in captuing the complex inteactions between component systems. A novel appoach was poposed to evaluate the effectiveness of the whole BMDS fom the aspect of functional inteactions, athe than the functions of components. Fist, Functional Dependency Netwok Analysis (FDNA was intoduced to build the analysis model though integating the component systems in multi-layeed kill chains of BMDS. The key metics wee poposed to measue the effectiveness fom both pobability of aid annihilation and system esponse time. Finally, the application of this method was demonstated though a case study, and the esult shown the holistic chaactes of BMDS at SoS level. The case shown that FDNA was a pomising way to analyze SoS at high level. Keywods: Ballistic missile defense system, effectiveness analysis, functional dependency netwok analysis, system of systems. 1. INTRODUCTION Ballistic Missile Defense System (BMDS being developed, tested and deployed by the United States povides initial capability to counte ballistic missiles in multi-layes, othe counties (e.g., Russian and China also achieve geat pogess in missile defense capability. Taditionally, the effectiveness analysis of BMDS was based on the simplified pobability models of both intecept missiles and suppot sensos [1-3]. With continued attention to achitectue integation of sensos with shootes, specifically to implement launch-on-emote (LOR and engage-onemote (EOR fiing doctines [4], ecent engineeing expeiences focus on the numeous inteactions between component systems of the BMDS in the view of system of systems(sos [5, 6]. The most citical inteactions in SoS ae functional dependencies between component systems, as the mission of SoS is completed by the whole not a single o seveal component systems, that functional dependencies integate the components as a whole. Theefoe, it is necessay to evaluate the effectiveness of BMDS fom the aspect of functional dependencies. To assess the effectiveness of BMDS at the level of SoS, we built the functional dependency netwok (FDN of BMDS though integating the kill chains in the multilayeed defense system, and make the metics to assess and measue the effectiveness of BMDS. The pape is oganized as follows: in section 2, we eview the cuent pactice in the effectiveness analysis of BMDS. In Sections 3, functional dependency analysis model of BMDS is poposed. In section 4, a case study is pesented to show how the outputs of the method can be used to quantify metics of effectiveness in BMDS. In section 5, we daw the conclusions and give ecommendations fo applications and futue wok. 2. RELATED WORK 2.1. BMDS Oveview The BMDS consists of a netwok of satellites, adas, Aegis ships, missile launches and missiles, and povides intecepting capabilities in thee phases of flight: boost phase, midcouse phase, and teminal phase, that pefomances multi-layeed missile defense [4]. Wheeas the cuently deployed BMDS pefoms missile defense with elements acting independently, the next geneation BMDS focuses on the capability of distibuted engagements: EOR and LOR [4]. LOR concept, the missile launching ship eceives senso input fom off-boad sensos (fo example, land-based AN/TPY-2 ada of sufficient quality to launch an intecepto and does not need to acquie the taget tack on its onboad sensos at the time of launch. EOR is an extension of LOR, that the intecepto can be launched using any available taget tack and engagement is contolled fom in-flight taget updates that can be povided to the intecepto missile fom any Aegis AN/SPY-1 o AN/TYP-2 ada [5] BMDS Effectiveness Analysis Pobabilistic model is widely applied in the analysis the effectiveness of BMDS fom the aspects of configuation and doctine [3]. Menq intoduced a discete time Makov X/ Bentham Open

2 Analyzing Ballistic Missile Defense System Effectiveness The Open Cybenetics & Systemics Jounal, 2015, Volume pocess model to multi-layeed BMD system [1]. Wilkening poposed a simple Benoulli tials model to detemine the size of equied BMDS [2]. The effectiveness of BMDS was pesented by the pobability distibution of the numbe of penetating waheads, and optimal fie doctines wee poposed based on these models. Pobabilistic model focused on the capability of intecepto, howeve, the suppot systems (e.g. ada sensos, communications netwoks wee ignoed o simplified, and failed to captue the intenal dependency between component systems. Due to the complexity of BMDS, system of systems engineeing is applied to study the effectiveness [6]. Tomme built suogate models of components in BMDS, and povided an M&S envionment fo eal-time, high-level BMDS achitectue tade studies at the SoS level [7]. Gaett poposed a SoS famewok to managing the intestitials, in which Gaph Theoy was applied to analysis infomation flowing between component systems [5]. Agent Based Modeling (ABM was poposed to as a technique to exploe and quantify the intestitial behavios [8]. Most of system of systems engineeing adopted M&S appoach to model the complex inteactions and focused on high-fidelity component models. Howeve, inteaction as a key facto to fom SoS capability was not studied independently at high level. 3. FUNCTIONAL DEPENDENCY NETWORK OF BMDS 3.1. Basic of FDNA Functional Dependency Netwok Analysis (FDNA was oiginally fomulated by Gavey [9], who applied it to capability potfolio analysis and isk assessment. FDNA has been applied in SoS analysis fo wide domains. Guainiello extended FDNA in both opeational and development netwoks to analysis the complex dependencies between systems and capabilities in SoS, which is applied in the aeospace SoS design and achitectue [10]. Dabble [11] applied the dependency netwok analysis to identify the key dependent nodes and conduits within the infomation popagation netwok fo emegency esponse. Wang [12] and Zhang [13] analyzed the SoS secuity of Global Navigation Satellite Systems (GNSS based on FDNA technique. Accodingly [9, 10], in the FDN, the nodes epesent systems o capabilities, while the links epesent the opeational dependencies between the systems o between the capabilities. Each dependency is chaacteized by stength (Stength of Dependency, SoD and citicality (Citicality of Dependency, CoD, that affect the behavio of the whole SoS in diffeent ways. As in the SoS, CoD quantifies the opeational independence of the components, while SoD epesents the effect of inteactions between components. Those inputs can come fom expet judgment and evaluation, o the esult of statistics of simulations and expeiments. The fomation of FDN is given as follows: Define 1. A Functional Dependency Netwok (FDN is a tuple <V, E, C, OE>, with G = (V, E epesenting a diected-acyclic gaph, Whee V : set of nodes epesenting eithe the component systems o the capability to be acquied, E : set of edges epesenting the opeational dependencies between nodes, C : epesents the dependencies attibutes : E { SoD,CoD}, SoD [0,1] is the stength of dependency faction, CoD [0,100] is the citicality of dependency constaint. OE : epesents the opeate effectiveness level: CoD [0,100] Fig. (1. An example of functional dependency netwok. We pesented an Beadth-Fist-Seach algoithm to solve the FDNA, and the detail calculation on the FDNA, which can be found in [9], was also in the algoithm. Algoithm 1. FDNA algoithm. Pocedue FDNA<V, E, C, OE> Function Analysis(V while V do fo all vi V do if P( v i = then V = V v i // P( v i is the paent nodes set of v i else if P( v i else Analysis ( P( v i V = then V SoD _ P i = 1 (SoD K ki OE k + (1 SoD ki *OE i v k P(v i CoD _ P i = Min (CoD v k P(v i ki + OE i OE i = Min(SoD _ P i,cod _ P i //K is the numbe of nodes in P( v i end if end fo end while end Function end Pocedue 3.2. Integate BMDS Kill Chains into FDN As ou study focuses on the effectiveness of the whole system of systems, we built the FDN of BMDS though integating multi-layeed kill chains. In ou FDNA model, the

3 680 The Open Cybenetics & Systemics Jounal, 2015, Volume 9 Jian et al. Fig. (2. Multi-layeed kill chains in BMDS. Table 1. Paametes of the functional dependency. Systems S1 S2 S3 S4 S5 S6 S7 S1 \ (0.3,80 a (0.4,60 (0.3,60 \ \ \ S2 \ \ \ (0.4,60 \ (0.7,0 \ S3 \ \ \ (0.3,50 \ (0.8,0 \ S4 \ \ \ \ (0.6,80 (0.9,0 \ S5 \ \ \ \ \ \ (0.9,0 a. (SoD ij,cod ij and \ epesents no functional dependency components in BMDS wee epesented as nodes while the links in C4ISR (Command, Contol, Communications, Computes, Intelligence, Suveillance, Reconnaissance wee epesented as edges. In BMDS, most component systems ae able to wok independently, howeve the function dependency futhe exploit the capabilities of the components. Fo an instance, data fom SBIRS elieves AN/TYP-2 of unnecessay volume o fan seach, and fee the fie contol adas to focus on tacking and discimination at longe distance and get eady fo the launch against time-sensitive tagets. Fo the SoS of BMDS, pobability of aid annihilation ( P is the final Measue of Effectiveness (MoE. The capability of inteceptos was defined as pobability of kill, while that of senso was defined as the time to detect the taget. In the combat field, assume P i is the pobability of kill fo intecepto P i at ideal situation that the opeate effectiveness is 100, howeve, the P i is effected by many exta factos such as the quality of tack data and the level of the taining. Thus, the actual kill pobability is PKi = OEi * Pi /100, then P is n P = 1 (1 P i=1 Ki (1 System esponse time is also suggested by the authos as a MoE in the time-sensitive intecept task. Assume senso S s to detect the taget within T s at the effectiveness of 100, given the actual OE s, the esponse time is modified as T = 100* T / OE, the esponse time of the fist shoot is s s s T = mint (2 s 4. CASE STUDY To test the applicability of ou method, thee notional BMDS achitectues wee built which took the US and Japanese BMDS as a efeence [14]. Although these data wee notional, the geneal pinciples and tends eflect those of eality, the notional BMDS was shown in Fig. (1. Act A is the base-line achitectue that an Aegis destoye and a PAC- 3 battey woked independently without suppot fom othe systems. Act B is the cuent achitectue, while Act C is the achitectue updated based on Act B with AN/TPY-2 ada being added to fom the capabilities of EOR and LOR. In Table 1, the independent opeational effectiveness means the system woks without the suppot fom othes,

4 Analyzing Ballistic Missile Defense System Effectiveness The Open Cybenetics & Systemics Jounal, 2015, Volume and max capability fo the sensos means the least time to acquie a tack with full suppot, which fo inteceptos means the highest pobability of kill with high quality tack. The functional dependency netwoks of BMDS achitectues wee pesented in Fig. (2, and the notional values of SoD and CoD wee given in Table Effectiveness Analysis Fist, initial OE of systems and dependency paametes wee fed into the FDN to compute the actual OE of each system. Fig. (3. showed the impovement in component OE due to the functional dependencies, especially in detect and tack systems. With the suppot of sensos, inteceptos came into wok ( OEi 0. Due to the netwoked senso achitectue, in Act B the P inceased by 24.2%, while T was almost the same at about 224s, as the AN/SPY-1 was the key senso to launch SM-3. Fig. (3. Opeational effectiveness of component systems. In Act C the land-based AN/TPY-2 was integated in the SOS to povide the EOR and the FPS-3 adas was updated with LOR. The BMDS made a geat impovement with two intecept oppotunities at 123s with pobability of 61% and at 166s with 54%, as was shown in Fig. (4. Fig. (4. Intecept oppotunities System Degadation Analysis In the battle field, the advesay would destoy o disable the components in the BMDS, fo example, the anti-satellite weapons to destoy the SBIRS. On the othe hand, opeational effectiveness might decease due to the bad envionment. Theefoe, it is meaningful to analysis the effectiveness of BMDS unde attack and system degadation. A seious scenaio was that the SBIRS being disabled by anti-satellite weapons, othe scenaios consideed the degadation of AN/SPY-1 at thee levels -30%, -50%, -70%. The P and T wee compaed between Act B and Act C. The esult was shown in Table 3, the SBIRS contibuted lots to T, while made few effect on P, only about 10%. The ealy waning was citical to EOR engagement conducted by AN/TPY-2, as the T inceased by 23.9% (Act B and 38.9% (Act C. Fo the degadation of AN/SPY-1, Act C woked moe effectively than Act B both in P and T. Act C was not affected at 30% degadation of AN/SPY-1, Table 2. Paametes of the component systems. Systems S1 S2 S3 S4 S5 S6 S7 Independent OE Max Capability 80s 160s 120s 220s s 0.7 Table 3. Pefomance of BMDS unde attack and system degadation. Metic fo BMDS Situation Act B Act C P T P T SBIRS (-100% -11.2% 23.9% -9.3% 38.9% AN/SPY-1 (-30% -7.9% 18.2% 0 0 AN/SPY-1 (-50% -13.5% 19.3% -5.3% 9.7% AN/SPY-1 (-70% -25.5% 22.3% -7.3% 12.3%

5 682 The Open Cybenetics & Systemics Jounal, 2015, Volume 9 Jian et al. because the land based AN/TPY-2 shaed the wokload of AN/SPY CONCLUSION AND FUTURE WORKS We poposed a new appoach based on the functional dependency netwok to analysis the effectiveness of BMDS in the view of system of systems. Ou appoach ovecomes the limits of taditional pobability models and simulations by the analysis on the functional dependences between the components which built up the multi-layeed kill chains. The notional case study demonstated that it was a useful appoach to assess the BMDS unde diffeent scenaios. The futue woks would focus on the methods to fom the paametes of functional dependency which epesent the effectiveness of the C4ISR, and an exploe analysis would be made to get a full knowledge of the BMDS in diffeent situations. CONFLICT OF INTEREST The authos confim that this aticle content has no conflict of inteest. ACKNOWLEDGEMENTS The eseach was suppoted in pat by the National Natual Science Foundation of China though Gant Numbe ( , REFERENCES [1] J. Menq, P. Tuan, and T. Liu, Discete Makov ballistic missile defense system modeling, Euopean Jounal of Opeational Reseach, vol. 178, no. 2. pp , [2] D.A. Wilkening, A simple model fo calculating ballistic missile defense effectiveness, Science & Global Secuity, vol. 8, no. 2, pp , [3] B.U. Nguyen, Assessment of a ballistic missile defense system, Defense & Secuity Analysis, vol. 30, no. 1, pp. 4-16, [4] National Reseach Council. Making Sense of Ballistic Missile Defense: An Assessment of Concepts and Systems fo U.S. Boost- Phase Missile Defense in Compaison to Othe Altenatives. Washington, DC: The National Academies Pess [5] R.K. Gaett, A. Steve, N. T. Baon, and J. D. Moeland J., Managing the intestitials, a system of systems famewok suited fo the ballistic missile defense system, Systems Engineeing, vol. 14, no. 1, pp , [6] S. Sommee, M.D. Guevea, M.A. Landis, J.M. Rizzuto, J.M. Sheppad, and C.J. Gant, Systems-of-systems engineeing in ai and missile defense, Johns Hopkins APL Technical Digest, vol. 31, no. 1, pp. 5-20, [7] T. Ende, R.F. Leuck, B. Weave, and P. Miceli, Systems-ofsystems analysis of ballistic missile defense achitectue effectiveness though suogate modeling and simulation, Systems Jounal, IEEE vol. 4, no. 2, pp , [8] O.T. Holland, and S.E. Wallace, Using agents to model the kill chain of the ballistic missile defense system, Naval Enginees Jounal, vol. 123, no. 3, pp , [9] P. Gavey, and A. Pinto, Intoduction to functional dependency netwok analysis. in the MITRE copoation and old dominion, 2 nd Intenational Symposium on Engineeing Systems, Massachusetts Institute of Technology, Cambidge, Massachusetts, [10] C. Guainiello, and D.A. DeLauentis, Maintenance and ecycling in space: functional dependency analysis of on-obit sevicing satellites team fo modula spacecaft, In: Confeence, The Ameican Institute of Aeonautics and Astonautics, [11] B. Dabble, Infomation popagation though a dependency netwok model, Collaboation Technologies and Systems (CTS, Intenational Confeence on, IEEE, [12] Y. Wang, X. Z. Wang and Q. Li, Functional dependency netwok analysis of secuity of navigation satellite system, Applied Mechanics and Mateials, vol. 522, pp , [13] W. X. Zhang, Y. Wang, and Q. Li. An impoved functional dependency netwok model fo SoS opeability analysis, Applied Mechanics and Mateials, vol. 602, [14] Japan Ministy of Defense, Japan' s BMD, Japan, Received: Apil 02, 2015 Revised: May 23, 2015 Accepted: June 06, 2015 Jian et al.; Licensee Bentham Open. This is an open access aticle licensed unde the tems of the Ceative Commons Attibution Non-Commecial License ( licenses/by-nc/3.0/ which pemits unesticted, non-commecial use, distibution and epoduction in any medium, povided the wok is popely cited.