Approach: Fault tree analysis E0E0 E2E2 E1E1 E3E3 E 0 – Top event: operational failure or life-safety failure (two trees) E i – Basic event: damage of individual equipment “or” - gate “and” - gate E 23 (E 0 occurs) if and only if (E 1 occurs OR both E 2 and E 3 occur)

Fault tree analysis (continued) Mathematical equivalent of gates (independent events): I1I1 ININ O I1I1 ININ O For the example fault tree: E0E0 E2E2 E1E1 E3E3 E 23

Decision variables and top-event definitions n Life safety failure: DV LS =P(LSF | T), where LSF is u Occurrence of a life-threatening event, T = planning period (alternatively: DV LS =P(LSF|IM)) n Operational Failure: DV O =P(OF | T) or P(OF | IM), where OF is u Repair or replacement time of critical equipment exceeds some threshold value DT 0. u Research products lost and the time to repeat the study is greater than some threshold value RT 0. Events of interest and proposed Decision Variables (DV): Required performance level is specified by DV LS, DV O, DT 0, RT 0

Fault tree illustration for an LSA laboratory To be refined upon consulting Comerio’s database, Comerio and LSA occupants Operational Failure Subject DieCritical Equipment FailureData Lost Env. FailureTrauma Temp. Changes Hazmat Release Containment Failure Microscope is broken Data storage device is broken Tube is broken Basic event (Damage State)

Expected Results n Result of calculation of DV=P(E 0 | EDP) IM DV Each point corresponds to a particular value of the vector of EDP at the given level of IM IM DV n Result of calculation of DV=P(E 0 | IM) by applying theorem of total probability x1x1 x2x2 x3x3 x1x1 x2x2 x3x3 Where N – is number of simulations at the level IM=x i, and the right part probabilities are all conditioned on IM= x i

What we would like from structure modeler (Mosalam) SIM # GM ID EDP ID EDP Value Files in formats: CSV, MDB, XLS.

What we would like from fragility testers Assembly ID DS EDP Type Files in formats: CSV, MDB, XLS. Assembly Name Fragility Parameters P 1 (e.g.  )P 2 (e.g.  )

n Result of simulation of E 0 | EDP, using generated E l events IM E0E0 n Generate basic event E i according to distribution P(E l | EDP = V k ) n Follow Boolean logic of the fault tree to know if E 0 has happened n Repeat for all V k, and get n i, m i for each level of excitation IM= x i IM DV n P(E 0 | EDP), using generated E l events x1x1 x2x2 x3x3 x1x1 x2x2 x3x3 Where m i – is number of simulations when E 0 has happened, and n i – is number of simulations when E 0 has not happened m1m1 n1n1 m2m2 n2n2 m3m3 n3n3 Expected Results (Simulation Technique)