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Title  A statistical analysis of fullscale fracture propagation test data  
Author(s)  Dr Andrew Cosham, Dr Ronald Koers, Dr Robert M Andrews, and Tanja Schmidt  
Abstract  A PIPE IN A FULLSCALE fracture
propagation test is classified as either a
propagate pipe or an arrest pipe. The
semiempirical methods, such as the AISI
Formula, the Battelle Short Formula or the
Two Curve Model, for predicting the
toughness required to arrest a running
ductile fracture do not necessarily
correctly predict the results of the full
scale tests. In some cases, the fracture
has propagated through a pipe joint in
which it was predicted to arrest (a non
conservative error), and in other cases it
has arrested in a pipe joint through which
it was predicted to propagate (a
conservative error). A statistical
analysis of these errors, based on the
principles of discrimination and
classification, and Bayesâ€™ theorem, can be
used to estimate the probability that a
pipe is a propagate pipe given the ratio
of the measured toughness to the predicted
toughness. The probability that a pipe is
a propagate pipe can then be used to
estimate an upper bound to the length of a
running fracture in a pipeline.
A data set of fullscale fracture propagation tests conducted using air or lean natural gas has been compiled, based on the earlier data sets compiled by Re et al., 1995 [1] and Vogt et al., 1983 [2] for the European Pipeline Research Group, but with reference back to the original (published) sources. The total number of data points in the revised data set, excluding tests conducted using line pipe of Grade L625 (API 5L X90) and above, is 226.
The European Pipeline Research Group has used this data set to conduct a statistical analysis of the Short Formula. Four correction factors have been considered: Leis, 1997 [10]; Eiber, 2008 [13, 14]; Wilkowski et al., 1977 [9]; and Wilkowski et al., 2000 [15].
A multiplier to be applied to the toughness predicted using the Short Formula with a correction factor to, for example, ensure that at least half of the pipe in a pipeline is predicted to be arrest pipe, or that there is a 95% probability of arrest within five pipe joints, is calculated. 

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