When Adding Epistemic Uncertainty To a Lognormal Fragility Function, How Should We Increase the Median?

Abstract eng:
Probabilistic seismic risk analyses use fragility functions that relate the probability of an asset exceeding specified limit states to the seismic excitation to which the asset is subjected. The fragility function is commonly idealized with the twoparameter lognormal cumulative distribution function (CDF). One may wish to add uncertainty to such a fragility function to account for epistemic uncertainties. For example, one may want to recognize that the fragility function was derived from too-limited data that might inadequately represent the population of assets in question. Or one may want to counteract the decrease in uncertainty resulting from some other modeling simplification. Engineers commonly increase the uncertainty by taking the standard deviation of the natural logarithm of the capacity (the combined or total uncertainty) to be the square root of the sum of the squares of the initial uncertainty (often called aleatory) and epistemic uncertainty. Some engineers have recognized that, if one does not also increase the median, one tends to bias loss estimates high. They advocate rotating the fragility function about the 10th percentile. I found the available evidence supporting the use of the 10th percentile unsatisfying, so I studied how different values of the rotation point might bias long-term failure rate. This work examines how the long-term rate is sensitive to the rotation point, median, aleatory and epistemic uncertainties, and site hazard. It appears better to rotate fragility functions about the 20th percentile if one is concerned with long-term failure rate and expected annualized loss. If one is more concerned with extrema, it can be better to rotate about the 10th or 50th percentiles.

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