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Example of Weighted Voting System Undersea target detection system

Example of Weighted Voting System Undersea target detection system. ?. Weighted Voting System. - system output (0,1,x). D ( I ). t. - threshold. - weights. w 1 w 2 w 3 w 4 w 5 w 6.

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Example of Weighted Voting System Undersea target detection system

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  1. Example of Weighted Voting System Undersea target detection system ?

  2. Weighted Voting System - system output (0,1,x) D(I) t - threshold - weights w1 w2 w3 w4 w5 w6 d1(I) d2(I) d3(I) d4(I) d5(I) d6(I) - voting units outputs (0,1,x) unit 3 unit 4 unit 1 unit 2 unit 5 unit 6 - system input (0,1) I

  3. Decision Making Rule Total weight of units voting for the proposition acceptance Total weight of units voting for the proposition rejection System output

  4. (1-t)Wn1 tWn0 Accept Reject Decision Making Rule if (1-t)Wn1-tWn0<0 if Wn1=Wn0=0 otherwise

  5. Entire WVS: Multiple states characterized by different scores (1-t)Wn1-tWn0 WVS as a Multi-state System Voting unit j: 3 states: 4 failure modes: dj(0)=1; dj(1)=0; dj(0)=x; dj(1)=x. 3 possible outputs: 4 failure modes: D(0)=1; D(1)=0; D(0)=x; D(1)=x. InputI

  6. D(I) t - threshold w01 w02 w03 w04 w05 w06 w11 w12 w13 w14 w15 w16 d1(I) d2(I) d3(I) d4(I) d5(I) d6(I) unit 3 unit 4 unit 1 unit 2 unit 5 unit 6 - system input (0,1) I Asymmetric Weighted Voting System - system output (0,1,x) - rejection weights - acceptance weights - voting units outputs (0,1,x)

  7. Decision Making Rule Total weight of units voting for the proposition acceptance Total weight of units voting for the proposition rejection System output

  8. System Parameters Types of Errors dj(0)=1 (unit fails stuck-at-1) too optimisticq01(j) dj(1)=0 (unit fails stuck-at-0) too pessimisticq10(j) dj(I)=x (unit fails stuck-at-x) too indecisiveq1x(j), q0x(j) Voting unit parameters Decision making time tj Rejection weight wj0 Acceptance weightwj1 adjustable System threshold t

  9. Universal generating function technique Score distribution for a single voter Composition operator Score distribution for m voters

  10. Optimization problems System Success Probability )w01,w11,…,w0n,w1n, t) = arg{R(w01,w11,…,w0n,w1n, t)max} Optimal adjustment problem

  11. Optimal grouping R(w,e,t)max t0 e1e2e3 t1 t2 w1 w4 w5 w2 w6 w3 1 4 5 2 6 3

  12. D(P) t w1 w2 w3 w4 w5 w6 d1(P) d2(P) d3(P) d4(P) d5(P) d6(P) VU 1 VU 2 VU 3 VU 4 VU 5 VU 6 PG1 PG2 PG 3 P Optimal distribution among protected groups v

  13. Optimal distribution among protected groups M-number of groups Group vulnerability

  14. Order of voting decisions tn … tm … t2 t1 Total weight of units with tjtmvoting for the proposition acceptance Total weight of units with tjtmvoting for the proposition rejection

  15. Accelerated Decision Making tV0m+1 (1-t)V1m+1 (1-t)Wm0 tWm0 tWm0 (1-t)Wm0 Reject Accept

  16. System reliability and expected decision time Qijm probability of making the decision D(i)=j at the time tm p0, p1 -input distribution

  17. T R Voting system optimization problem R max Two-objective problem: T min Constrained problem: R max | T<T* )w01,w11,…,w0n,w1n, t) = arg{R(w01,w11,…,w0n,w1n, t)max} subject to T(w01,w11,…,w0n,w1n, t)T*

  18. Numerical Example Parameters of voting units Reliability vs. expected decision time Parameters of optimal system for T*=35

  19. References 1. Weighted voting systems: reliability versus rapidity, G. Levitin, Reliability Engineering & System Safety, 89(2) pp.177-184 (2005). 2. Maximizing survivability of vulnerable weighted voting systems, G. Levitin, Reliability Engineering & System Safety, vol. 83, pp.17-26, (2003). 3. Threshold optimization for weighted voting classifiers, G.Levitin, Naval Research Logistics, vol. 50 (4), pp.322-344, (2003). 4. Asymmetric weighted voting systems, G.Levitin, Reliability Engineering & System Safety, vol. 76, pp.199-206, (2002). 5. Evaluating correct classification probability for weighted voting classifiers with plurality voting, G.Levitin, European Journal of Operational Research, vol. 141, pp.596-607, (2002). 6. Analysis and optimization of weighted voting systems consisting of voting units with limited availability, G.Levitin, Reliability Engineering & System Safety, vol. 73, pp. 91-100, (2001). 7. Optimal unit grouping in weighted voting systems, G.Levitin, Reliability Engineering & System Safety vol. 72, pp. 179-191, (2001). 8. Reliability optimization for weighted voting system, G. Levitin, A. Lisnianski, Reliability Engineering & System Safety, vol. 71, pp. 131-138, (2001).

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