Environmental Engineering Reference
In-Depth Information
1. 19
Variation of the normalising factor
c
0
.
[
]
Qt
( )
= −
1
c
0.5
−Φ
( ) ;
x
0
[
]
l=l=
()
t
()
t ft S
()/
−Φ =l =−
0.5
( )
x
(),
t x t T S
(
)/ .
0
Changes of the normalising factor
c
0
depending on the ratio
T
0
/
S
are
shown in Fig. 1.19.
A
t
T
0
=
S
,
T
0
/
S
= 1
c
0
= max (≈1.2), at
T
0
/
S
≥ 2.5
c
0
= 1.0,
ft t f t
( ) ( ) = ( ).
i.e.
1.2.6 Binomial distribution (Bernoulli distribution)
To conclude this section, another distribution that arises in cases where
the question: how many times some event occurs in a series of a certain
number of independent observations (experiments) performed under identical
conditions, will be described. For convenience and clarity, it is assumed that
we know the value of
p
- the probability that the component (part) taken out
of production is defective, and (1 -
p
) =
q
is the probability that the part
will not be rejected.
If
X
is the number of rejected parts from the toal number
n
of items,
then probability that among
n
parts
k
parts will be defective is equal to:
n
!
k nk
−
k k nk
n
−
PX k
(
=
)
=
pq
=
Cpq
,
where
k
= 0,1,...
n
[1.56]
knk
!(
−
)!
Equation [1.56] is called the Bernoulli formula. With a large number of tests
the binomial distribution tends to normal.
1.3 Safety of nuclear power stations.
Active and passive safety features
The nuclear power plant consists of a large number of elements. All the
elements of nuclear power plants can be classified in several groups: the
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