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f ser ( G,X )

v. G. G. f. Total Common Cause Failures. G. X. f ser ( G,X ). Pr( X = x 1 ) = 1  v , Pr( X = x 2 ) = v. Nested Common Cause Groups. Single element. u m ( z ). Operators over d -functions. d j ( z ). d i ( z ). d j (z). d i (z). v m. d m (z). v 1. 1. 2. v 4. v 5. 3. 5.

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f ser ( G,X )

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  1. v G G f Total Common Cause Failures G X fser(G,X) Pr(X = x1) = 1v, Pr(X = x2) = v

  2. Nested Common Cause Groups Single element um(z)

  3. Operators over d-functions dj(z) di(z) dj(z) di(z) vm dm(z)

  4. v1 1 2 v4 v5 3 5 v3 v2 4 A v1 8 7 v5 v4 v4 v4 v5 v5 5 5 5 9 3 3 v3 v3 v3 v2 v2 v2 4 4 4 B D C v4 v4 v5 v4 v5 v5 9 5 9 5 12 5 v3 11 10 E F G v5 v5 14 15 13 12 H J I RBD method for nested CCG

  5. Limitations of the d-function method Impossible CC groups Impossible nesting

  6. Modified UGF 2 Um(z,x) = (1x1x2x3) um(z) + x1x2x3z0 um(z) 1 xm=1 protection m is destroyed xm=0 protection msurvives 3

  7. Multilevel protection solutions v2 v1 v1 9 9 1 1 v1 6 6 v2 v2 3 10 10 2 v2 v2 7 7 11 11 4 v1 v2 v2 8 8 5 12 5 12 B A v1 v1 9 9 1 1 v1 6 6 3 10 3 10 2 7 7 v1 11 11 4 v1 8 8 5 12 5 12 D C

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

  9. Different destructive factors 2 xm=1 protection m is destroyed xm=0 protection msurvives um(z) 1 3 Um(z,x) = (1x1x2) (1x3) um(z) + (x1x2+x3-x1x2x3)z0

  10. Multilevel protection solutions for multiple DF 1 5 8 3 7 4 6 9 2 4 4 1 1 3 3 6 6 2 5 5 2 7 7 A 4 3 1 8 5 A 7 6 9 2 B

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