Environmental Engineering Reference
In-Depth Information
Function of density distribution
f
(
t
) of the time to failure has the form:
(
)
dP
cc
*;
t
D
mt
()
def
[5.38]
ft
()
=
=
,
M t
D
dt
where Δ
m
(
t
) is the increase in the number of failures over time Δ
t
.
The failure rate λ(
t
)
D
mt
()
f t
()
1
(
)
l=
()
t
or
()
t
l
=
=
P
*
[5.39]
; .
t
c c
def
M t
D
Pt Pt
()
()
p
Hence, the probability of failure-free operation can be determined by
the formula which is one of the basic equations of the mathematical theory
of reliability:
t
∫
P t
()
=
exp
−l
()
t dt
,
[5.40]
0
t
1
d
(
)
∫
P t
( )
=
exp
−
P
c ≥c
*
;
t dt
.
[5.41]
(
)
def
1
−
P
c ≥c
*;
t dt
0
def
The technical result of the method is that the indicators of failure-free
operation of the product according to the criteria for defects, leaks or failure
are determined before the start operation without preliminary tests with or
without prior service of the product based on the results of non-destructive
testing of products, the reliability characteristics of the NDT method used
and the growth rate of possible defects during operating time
t
.
5.3.4 Methods of determining gamma-percentile life
The duration of safe operation in the reliability aspect can be defined as the
time during which the probability of the product maintaining its strength is
P
f
[
P
f
]
P
in
τ
TM(1)
τ
TM(2)
τ
TM(3)
τ
s
5.49
Determination of operating life in the probabilistic aspect.
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