<s>
Line	B-Algorithm
sampling	I-Algorithm
is	O
a	O
method	O
used	O
in	O
reliability	O
engineering	O
to	O
compute	O
small	O
(	O
i.e.	O
,	O
rare	O
event	O
)	O
failure	O
probabilities	O
encountered	O
in	O
engineering	O
systems	O
.	O
</s>
<s>
The	O
method	O
is	O
particularly	O
suitable	O
for	O
high-dimensional	B-Algorithm
reliability	I-Algorithm
problems	I-Algorithm
,	O
in	O
which	O
the	O
performance	O
function	O
exhibits	O
moderate	O
non-linearity	O
with	O
respect	O
to	O
the	O
uncertain	O
parameters	O
The	O
method	O
is	O
suitable	O
for	O
analyzing	O
black	B-Device
box	I-Device
systems	O
,	O
and	O
unlike	O
the	O
importance	B-Algorithm
sampling	I-Algorithm
method	O
of	O
variance	B-Algorithm
reduction	I-Algorithm
,	O
does	O
not	O
require	O
detailed	O
knowledge	O
of	O
the	O
system	O
.	O
</s>
<s>
The	O
basic	O
idea	O
behind	O
line	B-Algorithm
sampling	I-Algorithm
is	O
to	O
refine	O
estimates	O
obtained	O
from	O
the	O
first-order	O
reliability	O
method	O
(	O
FORM	O
)	O
,	O
which	O
may	O
be	O
incorrect	O
due	O
to	O
the	O
non-linearity	O
of	O
the	O
limit	O
state	O
function	O
.	O
</s>
<s>
For	O
problems	O
in	O
which	O
the	O
dependence	O
of	O
the	O
performance	O
function	O
is	O
only	O
moderately	O
non-linear	O
with	O
respect	O
to	O
the	O
parameters	O
modeled	O
as	O
random	O
variables	O
,	O
setting	O
the	O
importance	O
direction	O
as	O
the	O
gradient	O
vector	O
of	O
the	O
performance	O
function	O
in	O
the	O
underlying	O
standard	O
normal	O
space	O
leads	O
to	O
highly	O
efficient	O
Line	B-Algorithm
Sampling	I-Algorithm
.	O
</s>
<s>
In	O
general	O
it	O
can	O
be	O
shown	O
that	O
the	O
variance	O
obtained	O
by	O
line	B-Algorithm
sampling	I-Algorithm
is	O
always	O
smaller	O
than	O
that	O
obtained	O
by	O
conventional	O
Monte	O
Carlo	O
simulation	O
,	O
and	O
hence	O
the	O
line	B-Algorithm
sampling	I-Algorithm
algorithm	O
converges	O
more	O
quickly	O
.	O
</s>
<s>
The	O
rate	O
of	O
convergence	O
is	O
made	O
quicker	O
still	O
by	O
recent	O
advancements	O
which	O
allow	O
the	O
importance	O
direction	O
to	O
be	O
repeatedly	O
updated	O
throughout	O
the	O
simulation	O
,	O
and	O
this	O
is	O
known	O
as	O
adaptive	O
line	B-Algorithm
sampling	I-Algorithm
.	O
</s>
<s>
The	O
algorithm	O
is	O
particularly	O
useful	O
for	O
performing	O
reliability	O
analysis	O
on	O
computationally	O
expensive	O
industrial	O
black	B-Device
box	I-Device
models	O
,	O
since	O
the	O
limit	O
state	O
function	O
can	O
be	O
non-linear	O
and	O
the	O
number	O
of	O
samples	O
required	O
is	O
lower	O
than	O
for	O
other	O
reliability	O
analysis	O
techniques	O
such	O
as	O
subset	B-Algorithm
simulation	I-Algorithm
.	O
</s>
