Environmental Engineering Reference
In-Depth Information
Determination of the total probability of failure (formation of open
defects, or large-scale destruction) of the structure is reduced to the
summation of the total probabilities of failure of elements in accordance
with the structural scheme designed in the initial stage of analysis:
I
(
)
i
P
()=1- 1
t
Π− t
P
(),
[4.62]
l
l
i
=
1
where
I
is the the number of elements that make up the structural model of
the structure.
To determine the reliability parameters, it is necessary to determine the
following distribution functions:
- To determine the indicators of reliability and suitability for repair-
distribution functions of time to failure
[4.63]
where
t≤
is the probability determined using [4.58] and [4.61], of
the formation of stable through-wall defects in the
i
i-th element which can
be repaired
- to determine the parameters of durability - the distribution function
of time to transition to the limiting state.
i i i
Pl l
[ ( )
]
T
per
}
{
i
i
i
i
i
i
i
i
i
i
i
F
()
t=
Pl l P a a
[ ()
t≤
]+
()
t>
1
Pl P l
−
()
− t≤
,
I
T
per
unst
per
T
T
per
i
i
i
i
i
i
iF PP l
()
t=
+ ()
()
t t>
l
1- () ,
P
t
[4.64]
II
cr
T
per
cr
i i i
Pl
t
is the probability, determined using [4.58] and [4.61],
of the formation of stable through-wall defects in the
i
i-th element which can
not be repaired;
P
i
cr
(τ) is the probability of large-scale destruction of the
i
-th
element determined by the formula [4.61].
If the functions of distribution of time to failure
where
[ ( )> ]
T
per
i
F
t
and to transition
to the limit state
F
i
II
(τ)are determined, then the corresponding rates of
failure
()
I
i
lt
and the transition to the limit state λ
i
II
(τ) are defined in the
same manner
71,72
:
I
()
i
dF
()
t
i
I
i
[4.65]
lt
()=
/ 1
− t
F
() ;
I
I
d
t
dF
i
()
t
i
i
lt
()=
II
/ 1
− t
F
().
[4.66]
II
II
d
t
The flow diagram of equipment or piping has usually the form of a series
connection of elements for which the failure rate [4.65] and transition to
the limiting state are determined [4.66].Therefore, the reliability indices of
equipment or piping are defined as follows:
- mean service life to failure
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