Environmental Engineering Reference
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if
(
n k T
−
)
≥t − <t
,
t kT
;
l
b
+
1
bb b
+
1
+
1
q kT t
(
,
)
=− −
1
exp
0
(
−
t kT
)
−−
(
n k
)
T
,
b
+t
Here λ
0
is the intensity of random failures,
T
is the interval of periodic
testing, τ is the beginning of ageing,
B
is the shape parameter for the
Weibull distribution.
The uniform wear model, proposed in Ref. 38, belongs in the same
class of models.
Random failures (not time-dependent) are characterised by a constant
flow rate of failures λ
0
, and it is assumed that in case of failure the element
returns to the usable state without improving the reliability characteristics
('as bad as old'). Failures associated with ageing occur when the element
reaches a limited number of states
N
, for example, start/stop, start, etc. It
is assumed that each loading results in partial and uniform degradation of
the element and when the
N
states are reached the element is completely
degraded and changes to a failure state.
The unavailability of such an element can be expressed as
(
b
1)
2
qt
( )
= −
1
exp(
−l
t
) 1
− c
H
(2
w N
, 2
) ,
[2.24]
0
where
w
is the frequency of loading of the element;
N
is the maximum
number of loads,
H
χ
2
is the distribution function χ
2
with 2
N
degrees of
freedom.
The main factor limiting the use of all proposed models is the availability
of representative and inexpensive initial data.
Comparative analysis of models in terms of information necessary for
calculating the parameters of the model was carried out in Ref. 45. Some
of the results of the comparison are presented in Table 2.2. In addition,
certain difficulties are experienced in selecting algorithms for calculating
the parameters depending on the structure and completeness of primary
reliability data.
For example, in Ref. 44 and 46 it is reported that in most cases the data
on the reliability of safety equipment in nuclear power plants are heavily
censored. The examples considered in Ref. 35 show that the censorship on
the right is a typical case where data are available for the entire period of
operation of the unit. If the data were collected for a certain limited period
of operation, we can speak of interval censoring, i.e. right and left. In
practice, many PSA use the data collected for a limited period of operation.
An obligatory step in choosing a model is the validation stage, validation
of the model. The use of parametric chi-square tests, Fisher, Kolmogorov-
Smirnov tests, etc., is proposed in Refs. 34, 35, 37, 38. Since there are no
requirements for testing the hypothesis for the constancy of the intensity of
failures in the procedures to implement PSA and because of the specificity
of data on the reliability of equipment in nuclear power plant the statistical
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