OS-C501

Offshore Standard DNV-OS-C501, November 2013
Sec.10 Component testing – Page 164
reflecting uncertainties in the underlying material property estimates as well as uncertainties in the applied
analysis models.
3.4.4 If the results of an analysis by means of the available analysis models are unbiased, the mean of the
estimate of µ R is to be taken as:
µ µ ’=µ RA
3.4.5 If the results of an analysis by means of the available analysis models are encumbered with a bias, the
mean of the estimate of µ R is to be taken as:
µ µ ’=µ RA +∆
in which ∆ represents the effect of the conservatism implied in the analysis leading to µ RA . ∆ is sometimes
referred to as the bias and needs to be estimated.
3.4.6 An estimate of the characteristic value of the resistance, prior to any component testing, can now be
obtained with 95% confidence as:
x C ’=µ µ ’-1.64σ µ ’-2σ R
3.4.7 After component testing is performed, the characteristic value of the component should be updated based
on the test results (and Bayesian updating theory).
3.4.8 When a total of n tests are performed, leading to n resistance values x 1 ,…x n , the sample mean is defined as
3.4.9 Based on the test results, the following updated values of the mean and the standard deviation of the
estimate of the mean resistance m R can be obtained:
µ µ ” = [n ⋅ µ test ⋅σ µ ’ 2 + µ µ ’ ⋅ σ R 2 ]/( n ⋅ σ µ ’ 2 + σ R 2 )
and
σ µ ” = [(σ µ ’ 2 ⋅ σ R 2 )/( n ⋅ σ µ ’ 2 + σ R 2 )] 1/2
3.4.10 Based on this, the following updated estimate of the characteristic resistance can be obtained with a
confidence of 95%:
x C ”=µ µ ”-1.64σ m ”-2σ R
3.4.11 When the standard deviation σ µ ’of the mean resistance estimate prior to testing is not available, and
when a significant, conservative bias ∆ in the resistance estimate is implied by the available analysis models,
then σ µ ’ may be approximated by ∆/2, unless a better approximation can be estimated. This approximation is
not valid when the bias ∆ is small or zero.
Guidance note:
The present note gives some more details related to the derivations above (see [3.4.1]-[3.4.11]). Assume that an
estimate of µ R is sought. The estimate can be based on a prediction by means of available engineering models. Such
models are usually encumbered with uncertainty owing to simplifications and idealisations, so the estimate becomes
uncertain. The combined effect of simplifications and idealisations are on the conservative side, such that they imply
systematic errors in the predictions, i.e., the estimator µ R ’* applied in the estimation of µ R comes out with a bias and
is thus not a central estimator. The bias is denoted ∆ and is defined as:
∆=µ R -E[µ R ’*]
where E[µ R ’*] = the mean value of the estimator µ R ’* for µ R .
The bias ∆ has to be estimated based on all available information and a best possible engineering judgement. This
estimation of ∆ is a very crucial stage. Once the bias ∆ has been estimated, an unbiased central estimate of the mean
resistance can be established with mean value:
µ µ ’=E[µ R ’]= E[µ R ’*]+∆
The standard deviation of the unbiased central estimate of the mean resistance is taken as:
σ µ ’=D[µ R ’*] where D[µ R ’*] = standard deviation of the estimator µ R ’* for µ R .
3.5 Specimen geometry - scaled specimen
---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e---
3.5.1 The specimen geometry for testing may be chosen to be different from the actual under certain
conditions.
3.5.2 Scaled specimens may be used if analytical calculations can demonstrate that:
µ
=
— all critical stress states and local stress concentrations in the critical part of the scaled specimen and the
1
n
∑
test
x i
n i=
1
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