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# Event and fault tree analysis, RRW importance measure

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1. Calculate the expected (mean) value of the total risk of the system described by the event tree and fault trees below. Assume up indicates True in the event tree. The random variable distributions are specified in the table as: Normal (mean, standard deviation), Exponential (mean), Weibull (eta, beta), Uniform (lower bound, upper bound).

2. Using the mean of each random variable, calculate the Risk Reduction Worth of components C1, C2, and C3. Note that there are random variables for which you do not calculate an importance!

3. Given the results of a Monte Carlo importance ranking shown (attached), give the relative ranking of the three components.

4. Assume that you talk to two experts about component C2. they tell you that the failure rate should be 3.5 yr^-1 and 4.2yr^-1 respectively. You trust your original failure rate twice as much as you trust the independent experts. you also have six C2 components operating in the field. You see failures at 2.5 months, 6.2 months, 8.7 months, and 12.1 months; at the end of 14 months the remaining two components are still running. Using a Bayseian approach to combine the three prior values and six data points, find a point estimate for the failure rate of component C2.