ML19312C746
| ML19312C746 | |
| Person / Time | |
|---|---|
| Site: | Oconee  |
| Issue date: | 08/18/1969 |
| From: | Ross D US ATOMIC ENERGY COMMISSION (AEC) |
| To: | Long C US ATOMIC ENERGY COMMISSION (AEC) |
| References | |
| NUDOCS 7912190957 | |
| Download: ML19312C746 (5) | |
Text
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UNITED STATES b4 A.
ATOMIC ENERGY COMMISSION d
WASHINGTON. D.C. 20545
%n8 August 18, 1969
-Charles G. Long, Chief, Reactor Project Branch No. 3, Division of Reactor Licensing PERIODIC TESTS AS RELATED TO OCONEE TECH SPECS (DOGET NOS. 50-269, 50-270, and 50-287)
We will be analyzing the requirements for periodic tests as part of our tech spec review for Oconee's POL.
No mathematical basis for testing is provided in the FSAR and perhaps one should be sought. My comments follow in the attachment.
~
.L.8 y( ; -lC'.,
D. F. Ross Reactor Project Branch No. 3 Division of Reactor Licensing
Enclosure:
Attachment:
Mathematical Basis for Periodic Tests cc:
A. Sc'.twencer D. Ross (5)
'R.
DeYoung V. Moore Docket files (3)
RPB-3 Reading W
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WASHINGTON, D.C. 20545 s,,, /
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%n e August 18, 1969 Charles G. Long, Chief, Reactor Project Branch No. 3, Division of Reactor Licensing
\\ 60 PERIODIC TESTS " "TJTED TO OCONEE TECH SPECS (DOCKET NOG. 50 50-270, and We will be analyzing the requirements for ' periodic tests as part of our tech spec review for Oconee's POL. No mathematical basis for testing is provided in the FSAR and perhaps one should be sought. My comments follow in the attachment.
')
C'51 D. F. Ross Reactor Project Branch No. 3 Division of Reactor Licensing
Enclosure:
Attachment:
Mathematical Basis l
for Periodic Tests cc:
A. Schwencer D. Ross (5)
R. DeYoung V. Moore Docket files (3)
RPB-3 Reading 9
9
/
4 Mathematical Basis for Periodic Tests 4
Probability techniques may be applied to the periodic testing of components with the result being an e' stimate of the long-run availability. $he "mean life" of the item must be known, and an inspection and repair model must be postulated.
For introductory purposes suppose that the follouing terns are used:
t = time A = failure rate, (time units)~
f(t) = a function 7hich describes the probability distribution of the length of life F(t) = ff(t) dt
_ x.
As an example let f(t) = Ac
'3 t3o This function la shown by:
x s\\A hs DN'd-J L
=
m o'
f(t)dt = o[ e '
dt = 1 This distribution is known as the exponential distribution.
The treanlife, ML, is found by:
~
11 =
,/ t f(t)dt o'
f(t)dt = 1 L
D
i
- ~
ML = A!/ te dt = 1 O
A Hence A may be fixed if the mean life is knowa and conversely.
Suppose it is desired to find a survival function T(t) that expresses the probability that an item will " live" at Least t { and perhaps longer)
The function fCt) gives life at t (but no longer).
The 1
. probability of failure is the interval o<t < t is found frem 1
1 T(t) = /E(t )dt l
T(t)=e e
de 1
T(t) = Cfl l g' T(t) = 1 - e~
The probability of survival, labeled A(t) is 1 - T(t) llence A(t) = E Consider the first test interval at time t = x
--- A i
r t.
t
, - A?
d f(f) ' A e' O
t t
t t
Tae probability of failing at t, in the increment dt, is f(t )dt t
The unavailable time is (x-t ).
The probability of being unavailable (x - t ) is t
I f
r = (x - t ) f (t ) d t The sum probability of being unavailable in time frem o to x is R, uhere
}*
t E
t R=
I (x-t )f(t )dt time = x
. 1
-A t R=
/X( x - t')f\\e dt' O
-x X
R=
AX/ - At'dt, o/ te At'dt X-o
-A e
X At'(t+ 1) l 7' R=
Av e
8 j.
-A e
-^
O A
7,\\
f Jo X
it =
x[ l - eAx]
+[e-Ax(x + b 1
]
I X
-Ax
-Ax
-Ax e
+y2 R=
x-xc-
+ xc 3
s X
Ax ~
R = I +2 C e
-1) -
XA e
+
L e
9 e
.. The available probability A=1-R 4
^
-Ax 1
A = '_ -
1+
e L
Ax Ax A = 1 -e _
Ax Some valuas are Ax A
.01
.995
.02
.99
.03
.935
.06
.9706
.1
.9516
.2
.9063
.4
.8242
.7
.7192 1
.6321 As an e:< ample, the Duke FSAR >roposes. [ page 15-47, T.S.15.4.2.1 -Bla]
to test the HP, LP, and SU pumps every t' gree months.. Suppose the mean life is 10 years.
Then A
=1 months 120 With a test interval of 3 months, 3
Ax =
=.025 and A N.987 120 h
Note:
for small Ax, A N 1-h =.012 The unavailability R=
2 The probability that both EP pumps uould be unavailable would bc.012 or
- 1. 4:<10".
In accordance uith our desire for Duke to present some basis for tach specs, let us invite thp. to comment on thic as an e:: ample.
t