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Motivation: Recap - estimating Pf with basic MCS, variance of estimate vs. sample size for IID samples, graphical example of ... Flowchart; Redo Example D1 with importanc sampling - choice of sampling density, estimated value vs. sample size - comparison ... Original sampling density fX and biased sampling density fV; estimated Pf seen as an expectation of a function of V that includes a ... Example E1: Cantilevered Beam in deflection limit state, 3 RVs, solved by basic MCS and by Importance Sampling - comparison ... Recap: Cumulative vs Overload Type Failure and first passage time, Case 1 formulation; Description of C(t) and D(t) in terms of ...
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