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Correction to: Improving FEMA P-58 non-structural component fragility functions and loss predictions

  • Gemma CremenEmail author
  • Jack W. Baker
Correction
  • 56 Downloads

1 Correction to: Bulletin of Earthquake Engineering  https://doi.org/10.1007/s10518-018-00535-7

Unfortunately, Eqs. 2, 4 and 5 of the associated paper are published incorrectly. We apologize for these errors.

2 Equation 2

Instead of:

The likelihood that an arbitrary component is damaged at a level of demand that caused damage (\(edp_i\)) is the normal distribution probability density function (PDF) evaluated at the fragility function defined by Eq. 1, i.e.,
$$\text{Likelihood} = \phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right) $$
(2)
where \(\phi (.)\) is the normal distribution PDF.

Equation 2 should be:

The likelihood that an arbitrary component is damaged at a level of demand that caused damage (\(edp_i\)) is the fragility function defined by Eq. 1, i.e.,
$$\text{Likelihood} = \Phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right) $$
(2)

3 Equation 4

Instead of:
$$\text{Likelihood} = \left[ \prod _{i=1}^{m}\phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right) \right] \left[ 1-\Phi \left( \frac{\ln {(edp_{max}/\theta )}}{\beta }\right) \right] ^{n-m} $$
(4)
Equation 4 should be:
$$\text{Likelihood} = \left[ \prod _{i=1}^{m}\Phi \left( \frac{\ln {(edp_i/\theta )}}{\beta }\right) \right] \left[ 1-\Phi \left( \frac{\ln {(edp_{max}/\theta )}}{\beta }\right) \right] ^{n-m} $$
(4)

4 Equation 5

Instead of:
$$\{\hat{\theta }, \hat{\beta }\} = \mathop{{\mathrm{argmax}}}\limits_{\theta ,\beta }\sum _{i=1}^m\left[ \ln \phi \left( \frac{\ln (edp_i/\theta )}{\beta }\right) \right] + [n-m] \ln \left[ 1-\Phi \left( \frac{\ln (edp_{max}/\theta )}{\beta }\right) \right]$$
(5)
Equation 5 should be:
$$\{\hat{\theta }, \hat{\beta }\} = \mathop{{\mathrm{argmax}}}_{\theta ,\beta }\sum _{i=1}^m\left[ \ln \Phi \left( \frac{\ln (edp_i/\theta )}{\beta }\right) \right] + [n-m] \ln \left[ 1-\Phi \left( \frac{\ln (edp_{max}/\theta )}{\beta }\right) \right] $$
(5)

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA
  2. 2.Stanford UniversityStanfordUSA

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