Date of download 3 12 2018 Copyright ASME All

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: An otherwise linear structure with nonlinear elements between nodes 5 and 21

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: Histogram of 30 loads and 25 strengths. The histograms are each normalized to integrate to one.

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: Multiple distributions fitted to the available load and strength realizations. The load and strength data are indicated by blue and red tick marks, respectively.

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: Probability of failure (Po. F) calculated using multiple distributions fitted to the shifted load and strength data

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: A notional depiction of the translation of load realizations that causes the top 5% of the revised load to extend beyond the bottom 5% of the strengths. The abscissa represents load and strength data.

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: The load realizations translated by M 95∕ 5, their approximating PDFs, the strength realizations, and their approximate strength PDFs

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: Contours of the joint PDF, f. Xf. Y (ellipses) and integration domains of Eq. (1. 3) (lower, green cross-hatched region) and (2. 1) (blue and green cross-hatched regions)

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: The TIM/PFM margin and uncertainty approach embodied in Eq. (2. 1) is suggested by the statistical statement about flood levels that have actually been observed (50 -yr flood mark) and the distance (30 m) between rare, high flood levels and the base of the house shown

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: The TIM can be approximated using a combination of the empirical cumulative distribution function of load and a delta function approximation for the PDF of strength. The blue curve is the ECDF of load.

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: The probability of failure including margin (PFM) can be estimated by integrating the product of the KDE approximations for the PDF (f. Y) for strength and the complementary CDF for translated load (1 − FX(x − M)), where M is the tail independent margin (TIM). To put both plots in the same figure, the PDF of strength is normalized by its peak value.

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: Bootstrap resampling is used to obtain 1000 other plausible sets of realizations of load and of strength. The low 20% load and the high 20% strength distributions are shown in thick blue and red lines, respectively. Abscissas are load (left) and strength (right), and ordinates are cumulative probabilities.

Date of download: 3/12/2018 Copyright © ASME. All rights reserved. From: A Robust Approach to Quantification of Margin and Uncertainty J. Verif. Valid. Uncert. 2017; 2(1): 011005 -10. doi: 10. 1115/1. 4036180 Figure Legend: KDE estimates for CDFs for load (left) and strength (right) from 1000 resamplings each. The low 20% load and the high 20% strength distributions are shown in thick blue and red lines, respectively. Abscissas are load (left) and strength (right), and ordinates are cumulative probabilities.