ML20214E450
| ML20214E450 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear, Crystal River, 05000000 |
| Issue date: | 04/23/1987 |
| From: | Richard Bright FLORIDA POWER CORP. |
| To: | Silver H Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML20214E454 | List: |
| References | |
| LFM87-0059, LFM87-59, NUDOCS 8705220091 | |
| Download: ML20214E450 (88) | |
Text
.
Power COR POR ATION April 23, 1987 LFM87-0059 Mr. Harley Silver, Project Manager PWR Project Directorate # 6 Division of PWR Licensing-B Office of Nuclear Reactor Regulation U.S. Regulatory Commission Washington, D.C.
20555
Subject:
Crystal River Unit 3 Emergency Feedwater System Review Request for Additional Information
Dear Sir:
As a result of the meetings held on March 31, 1987 through April 2,1987 on the above subj ect, the NRC personnel requested some additional information. This information is summerized and attached.
1.
CR3 Loss of Main Feedwater Event Frequency.
This data only includes challenges to the Emergency Feedwater (EFW) System resul ting from loss of main feedwater.
This data includes the detailed basis for the CR3 loss of main feedwater (LMFW) rate, data, and brief description of each event occurring from original plant startup through December 1986.
2.
EFW Pump Demand Failure Rate.
This data consists of the detailed basis for EFW pump failure rates (demands and failures) through December 1986.
3.
CR3 EFW Reliability Study utilizing NUREG-0611 Data consisting of the EFW unreliability combining the EFW model from the current CR3 EFW reliability study with the NUREG-0611 data and assumptions.
4.
The Human Error reference for the time reliability correlation (TRC) curve used in the CR3 PRA.
001 $nejs in k
8705220091 870423
]s AMC fdk P
PDR f, Q MIC GENERAL OFFICE: 3201 Thirty fourth Street South
- P.O. Box 14042 '
g=p; c s
s
..Ap il~23,-1987-
~
~
- LFM87-0059
'Page 2' 5.
The ' EFW - upgrade ~ Reliability ' Analysis. for -CR3 document numbers.
32-1125434-02: dated 6/82 and 32-1126041-00' dated 12/81.. These documents are stamped " SUPERSEDED" and have been replaced by other' documents.
~
6.
Three Pump - EFW Reliability Analysis for CR3 dated 7/81.
This document has also been' stamped '.' SUPERSEDED" and has been replaced by the current EFW reliability study.,
Sincerely, Ronald M. B i ht Assistant to the Vice President
-Nuclear Operations EMG/am attachments
RESPONSE TO NRC REQUEST FOR ADDITIONAL INFORMATION ON THE CR-3 EFW RELIABILITY ANALYSIS As a result of the meetings on March 31, April 1, and April 2,1987, the NRC requested some additional information on the EFW reliability analysis consisting of:
I.
CR-3 Loss of Main Feedwater Event Frequency Detailed basis for the CR-3 loss of main feedwater (LMFW) rate, including data and brief description of each event occurring from startup through December 1986.
II.
EFW pump Demand Failure Rate Detailed basis for.EFW pump failure rates (demands and failures) through December 1986.
III. CR-3 EFW Reliability Study (NUREG-0611 Data)
EFW unreliability combining the EFW model from the current CR-3 EFW reliability study with NUREG-0611 data and assumptions.
IV. Human Error Reference for the time reliability correlation (TRC) ' curve used in the CR-3 pRA.
Each of these items is addressed in the following sections.
j
_~
4 I
I..
CR-3 Loss of' Main Feedwater (LN W) Event Frequency
' Initia' ting event frequency for 'LMFW for CR'-3 was : then from NUREG-3862 (EGG-2373), Development of Transient Initiating Event Frequencies for Use
. in -Probabilistic Risk Assessment, May 1985. - This reference, gave the.
number of LMFW events for the first seven years of.CR-3 operation.
Data
' for the eighth year (3/13/84: - 3/12/85) 'was obtained via review of Grey -
Book (NUREG-0200) data.
The EPRI-PWR transient categories ' selected to represent ~ a LMFW event were:.
' Category Description i
15 Loss or reduction in'feedwater flow (1. loop) 16 Total loss of feedwater flow (all loops) 17 Full'or. partial. closure of_MSIV (1 loop)
^
18 Closure ofLall MSIV.
21 Feedwater flow instability - operator error 22 Feedwater_ flow instability - mechanical 23 Loss of condensate pump (1 loop) _
24 Loss of condensate pump (all loops)
.25 Loss of condenser vacuum 26 Steam generator leakage 27 Condenser leakage 28 Miscellaneous -leakage in secondary system 30 Loss of circulating water I~
Table I gives a summary of the EPRI data for CR-3.
r l
A detailed examination of the CR-3 transient history from plant startup (3/13/77) through the end of 1986 was conducted to generate _ a loss of main feedwater frequency.
Surprisingly,-
the results bear little resemblance to those shown. in Table 1 which were extracted from
-NUREG/CR-3862. A tabulation of the candidate. events for consideration in the-computation of the loss of main. feedwater frequency is given in Table 2.
There are a total of 23 events which were determined to meet-the criteria for a PRA-defined loss of main feedwater.
In eight of these events, one or both _ MFW pumps were tripped. automatically due to ' EFW actuation.
MFW pumps no. longer automatically trip upon EFW actuation.
Under the present plant design, these MFW pumps may.have served as a backup in the event EFW was lost.
In the 8/2/79 and 11/22/85 events, MFW was actually recovered shortly following the trip.- Calculation of the loss of main feedwater ; frequency based on analysis of the events in
~
Table 2 is shown in Table 3.
1 4
i TA8LE 1 7
Crystal River Unit 3 Loss of Main Feedwater Events 1-EPRI CATEGORY Total Year of Operation 15~
16 17 18 21 22 23 24 25 27 28 30 i
1 3/13/77'- 3/12/78 0
0 0
0 1-0 0
0 0-0 0
0 1-i 1
3/13/78 - 3/12/79 1
0 0
0 0
0 0
0 0
0 0
0 1
1 i 13/13/79.- 3/12/80 0
0 0
0 0
0 0.
0 0
0 l'
O 1
i 3/13/80 - 3/12/81 1
0 0
0 0-0 0
0 0
0 0-0
'l-4 1
1 3/13/81 - 3/12/82 2
0 0
0 1
1 0
0 0
0 0.
0
'4 1
i 1
l' 3/13/82 - 3/12/83 1
0 0
1 0
0 0
0 0
0 0
.0 2
l 1
}
3/13/83 - 3/12/84 1
2 0
0 2
0 0
0 0
0 0
6 2
3/13/84 - 3/12/85 1
0-0 0
0 0
0 0
0 0
0 0
1 l'- NUREG/CR-3862 i Grey Book (NUREG-0200).
l
.The total number of LOFW events for.eight years of operation is-17.
I 17 events /8 years = 2.1 events / year
.. _. _.., _. - ~ _ _.
Tabla 2 CR-3 Main Feedwater Transienta 3/13/77 - 12/31/86 Reactor MFWP Trip EFW Date Trip (Auto / Man, #) Actuation Event Description Remarks LMFW 7/17/77 Manual Auto, 2 Auto During SP-110, rod group 1 Power source for MFWPs was
- No fell into the core. Operator later permanently transferred manually tripped the reactor.
to startup transformer. No Both MFWPs tripped due to switching is now necessary.
slow transfer of power source Therefore, this event is not from aux. transformer to counted'as a LMFW.
startup transformer. EFW auto, started.
2 10/26/77 Auto Auto, 1 No "A" MFWP tripped on loss of Partial loss (1 MFWP No control power (Inverter "A").
only). No demand for EFW.
Reactor auto-tripped on high RCS pressure.
2/11/78 No Auto, 1 No "A" MFWP tripped on loss of Partial loss (1 MFWP No control power. Plant run back only). No demand for EFW.
successfully.
2/11/78 No Auto, 1 No "A" MFWP tripped on loss of Partial loss _(1 MFWP No control power due to techni-only). No demand for EFW.
cian error while trouble shoot-ing. Plant run back succcess-fully.
9/29/78 Auto Auto, 2-No During shutdown evolution, See Remarks on 7/17/77 No 4160V unit bases were left on transient.
aux. transformer. When tur-bine tripped, both MFWPs tripped.
1/6/79 Manual Manual, 2 Manual Turbine' tripped. During run-None Yes back, "A" main block valve stuck open.
"A" MFWP manually tripped by operator.
"B" MFWP remained running but pressure fell off due to loss of steam supply. Operator tripped reactor and manually started -
EFP-2.
R:rcter MFWP Trip EFW Dato Trip (Aute/ Man, #) Actu*tien Event 0:scriptien Remarks LMFW 1/17/79 Manual Auto, 2 Yes Turbine building flood caused None Yes' loss of condensate pumps which led to both MFWPs tripping on low deaerator level.
Reactor manually tripped.
EFP-2 auto.
started..EFP-1 manually started.
1/30/79 Auto No No "B" MFWP quit feeding but did Partial loss of MFW, but no Yes not trip.
In attempting to EFW actuation.
restore feed to OTSG "B",
operator overfed OTSG "B" causing a reactor trip on low pressure.
8/2/79 Auto Auto, 2 Auto "B"-MFWp slowed down causing This event will be counted Yes reactor trip and EFW actua-as a LMFW event, but it tion on low-low OTSG level.
should be noted that MFW 10 minutes following the was restored 10 minutes trip, "A" MFWP was started following the trip. The and EFW was secured.
PRA takes no credit for' this.
2/26/80 Auto Auto, 2 Manual NNI-X power was lost.
PORV None Yes opened. BTU limits ran MFW-to zero.
Reactor tripped on high pressure.
Rupture matrix actuated and auto.
tripped "A" MFWP.
EFW manually started.
"B" MFWP later auto. tripped by "B" OTSG rupture matrix actuation.
8/12/80 Auto Auto, 1 Auto "B" MFWP tripped on over-None Yes speed. Reactor tripped on high RCS pressure.
"A" MFWP recircculation valve stuck open preventing feed. EFW actuated on low OTSG' level.
.=
Rsactor MFWP Trip EFW
- Date Trip (Auto / Man, #).Actuatien Evsnt Description Remarks LMFW t
8/19/80 Auto Auto, 2 Auto Technician inadvertently None Yes tripped turbine on high FW i
heater level. Reactor auto.
tripped on ARTS.
Both MFWPs i
tripped on missing speed signal due to loss of steam supply.
EFW auto. initiated on loss of MFWPs.
9/30/80 Auto Auto, 2 Auto Technician inadvertently MFWPs.were automatically Yes grounded power to "A"~RPS tripped by EFW initiation.
channel.
RCS flow signal to This is no longer the case, ICS was lost.
Both MFW trains and MFW could now be'a ran back. Reactor tripped on useful backup to EFW innthis high RCS pressure. OTSG transient.
levels dropped to EFW initiation t
2 setpoint. Both MFWPs tripped on EFW actuation.
3/17/81 Manual Auto, 2 Auto TechnicianLerror resulted in
'See. Remarks for'7/17/77-No manually opening the "A" and transient.
"B" CRD breakers causing a-reactor trip. Due to slow transfer from aux. transformer to startup transformers, both MFWPs tripped and EFW initiated.
i 4/12/81 Auto Auto, 1 Auto During startup, turbine See. Remarks for 9/30/80.
Yes.
valves opened too far causing-transient.
OTSG levels to decrease:to the point where EFW actuated.
Reactor tripped on ARTS low-low OTSG 1evel. MFWP auto. tripped j
on EFW actuation.
5/11/81 No Auto, 1 No During SP-332, "B" MFWP suction No reactor trip. Only 1.
No valve shut far enough to trip.
MFWP trip. HNo EFW actua -
the "B" MFWP. Plant runback
' tion.
was successful.
n
.~ _
i Reactor MFWP Trip EFW Date Trip (Auto / Man. 4.1 Actuation Evsnt D scriptien
.Femarks LMFW-6/16/81 Auto Auto, 2 Auto Loss of offsite power caused-Loss of offsite power-No turbine trip and ARTS trip of modeled as separate.
l reactor. MFWPs tripped on loss initiator in PRA.
~
of control power.
EFW initia,ted on loss of MFW.
6/27/81 Auto Auto, 2 Auto MFW oscillations. led to None Yes reactor trip on high RCS 3
pressure.
Both MFWPs tripped 1
(cause unknown). 'EFW initiated on loss of MFWPs.
3 6/30/81 Auto Auto, 2 Auto MFW oscillations led to See. Remarks on 9/30/80 Yes reactor trip on high RCS transient.
pressure.
EFW started on low-low OTSG level.
Both MFWPs i
auto, tripped on EFW actuation.
i 7/14/81 Auto Auto, 2 Auto' Electrician shorted DC battery.
Loss of."A" vital bus no No and lost "A" vital bus caus-
' longer actuates EFW..EFW ing EFW actuation, tripping.
~ actuation no longer trips the MFWPs.
Reactor tripped on the MFWPs.
ARTS, loss of MFWPs.
7/31/81~
Auto Auto, 1 No Technician. error resulted in-
'Only 1 MFWP loss. No EFW No.
auto, trip' of "A" MFWP,on actuation.
e
' loss of control power.
Reactor tripped.,on high RCS pressure.
12/12/81-Auto:
Auto, 1 LAuto!
"B" MFWP s1 owed-down and None Yes quit' feeding.. OTSGLlevels
. dropped to EFW'setpoint.
-actuation tripped both MFWPs.-
Reactor. tripped on high RCS:
~~
-pressure.
1/10/82 Auto Auto, 1 No During SP-332, "A" MFWP auto.
Only:1 MFWP loss. No EFW Yes tripped due to excessive' actuation, 2
closure of suction valve.-
~y-Reactor tripped on high RCS
' pressure.
y
~
, F,
R: actor MFWP Trip EFW Dets Trip (Auto / Man, #) Actustien Event Drscriptien Remarks LMFW 3/2/82 Auto
' Auto, 1 Auto Reactor tripped on RCPPM PRA treats this event as No actuation. Approximately one a' reactor / turbine trip hour later, "B" MFWP tripped followed by failure of MFW.
for unknown reasons causing EFW actuation.
4 6/20/82 Auto Auto, 2 Auto Reactor tripped on high RCS None Yes pressure following inadver--
tent shutting of all MSIVs.
Both MFWPs tripped on loss of speed signal caused by loss of steam supply.
Loss of MFW caused EFW actuation.
7/9/82 Auto Auto, 2 Auto Turbine tripped for unknown None Yes reason causing reactor. ARTS trip. MFWPs slowed and stopped feeding.
EFW actua-ted on low-low OTSG level, tripping the MFWPs.
7/9/82 No Auto, 1-Auto Following manual turbine None Yes
-trip,'OTSGs steamed down to EFW actuation setpoint. MFWP tripped on EFW actuation.
10/14/82 Manual Auto, 1 Auto Four. hours following shut-See Remarks on 3/2/82-No down to repair'the RC drain transient.
tank, malfunction of the "B" Startup Control Valve caused low levels in both OTSGs.
EFW initiated which tripped the running MFWP.
10/29/82 No Auto, 1 Auto During startup, "A" MFWP Only 1 MFWP operating at Yes tripped due to unknown causes.
the time. Other may have EFW initiated on loss of MFW.
been available for recovery.
.10/30/82 No Auto, 1 Auto See 10/29/82 event.descrip.
See Remarks for 10/29/86' Yes tion.
l
MMMO Reactor MFWP Trip EFW
.Date Trip (Auto / Man, #) Actuation Event Description Remarks LMP4 3/19/83 Auto Auto, 1 Auto During shutdown, "A" MFWP See Remarks for 9/30/80 Yes slowed down and quit pumping.
Reactor tripped on high RCS pressure.
EFW actuated on low low OTSG level, tripping the "A" MFWP.
7/20/83 No Auto, 1 Auto During plant heatup, "B" MFWP See Remarks for 9/30/80 Yes supplied insufficient FW.
EFW actuated on low-low OTSG level, tripping the "B" MFWP.
7/20/83 No Auto, 1 Auto See 7/20/83 event description See Remarks for 9/30/80 Yes above.
7/21/83 No Auto, 2 Auto Both MFWPs supplied insuffi-See Remarks for 9/30/80 Yes cient FW.
low-low OTSG level, tripping the MFWPs.-
7/26/83 Auto Auto, 1 Auto During plant startup, low See Remarks for 9/30/80 Yes deaerator level reduced FW transient.
flow to both OTSGs.
Reactor tripped on high RCS pressure.
EFW actuated on low-low OTSG level. The operating MFWP tripped on EFW actuation.
8/22/83 Auto Auto, 1 Manual Turbine EHC malfunctioned See Remarks for 3/2/82 No and shut all governor valves.
Reactor tripped on high RCS pressure. One hour following trip, condenser vacuum was lost tripping the operating MFWP.
EFW was actuated l
manually.
l 8/26/83 Auto Manual, 1 No A MFWP malfunctioned and Loss of only 1 MFWP. No No was manually tripped, result-EFW actuation.
ing in reactor trip on high RCS pressure.
l
Reactor MFWp Trip EFW Date Trip (Auto / Man, #) Actuation Event Description Remarks LMFW 8/26/83 Auto Auto, 2 Auto Diversion of MFW led to None Yes reactor trip on high RCS pressure.
EFW actuated on low-low OTSG level. MFWPs tripped on EFW actuation.
2/28/84 Auto Auto, 2 Auto Lightning-induced failure See Remarks for 6/16/81 No of the 230 KV switchyard transient.
caused the CRDs to be depowered momentarily, tripping the reactor.
Both MFWPs tripped on loss of control power, actuating EFW.
4/26/84 Auto Auto, 1 No Loss of NNI-Y caused BTU Loss of only 1 MFWP. No No limits to run back the "B" EFW actuation.
MFWP.
Reactor tripped on high RCS pressure. The "B" MFWP tripped later for unknown reasons.
3/7/85 No Auto, 1 No During "A" MFWP lube' oil No reactor trip.
Loss of.
No testing, lube (,il pump only 1 MFWP. No EFW developed insufficient actuation.
pressure.
"A" MFWP tripped on low lube oil pressure.
10/9/85 Manual No Auto EFIC main steam line isola-No loss of MFW.
No tion circuitry failed during trouble shooting and shut 2 of 4 MSIVs.
Reactor was manually trippad.
EFIC initiated on post-trip pressure pulse phenomenon.
11/8/85 Auto Auto, 1 No "A" MFWP tripped for Loss of only 1 MFWP. No No l
unknown reason.
Reactor EFW actuation.
I tripped on high RCS pressure.
11/22/85 Auto No Auto Poor manual MFW control See Remarks for 8/2/79 Yes resulted in inadequate FW.
Reactor tripped on high RCS pressure.
Table 3 Crystal River 3 Loss of Main Feet. water Event Frequency Number of Number of Years LMFW g
Events in Data Base Frequency 23 9.8 2.3/ year While the chronology of loss of main feedwater events obtained via a detailed analysis of CR-3 operating history differs markedly from that obtained from NUREG/CR-3862, the event frequency is nearly identical.
The frequency given in Table 3 will be used in future CR-3 PRA quantifications.
l
II.
EFW pump Demand Failure Rates The data base used in generating plant-specific failure rates for the CR-3 PRA and the CR-3 EFW reliability analysis was the work request history from 9/18/78 to 6/30/84.
Work requests were reviewed for catastrophic, degraded, and incipient failures.
If there was any doubt regarding classification of a failure, a conservative approach was taken and a higher severity for the event was assumed.
Only catastrephic failures were used in the calculation of failure rates.
All classes of failures were used in determining the number of demands and maintenance unavailability of a particular component.
In the case of the EFW pumps, the number of demands was determined by summing the number of surveillance tests, demands following maintenance, and actual challenges.
The surveillance requirement for the EFW pump trains is once a month while in Modes 1, 2, 3 and once while returning to power operation after having been in Mode 4 or 5 for an extended period of time.
The number of demands for surveillance testing between 9/18/78 and 6/30/84 was 58.
The number of demands during this time due to testing following maintenance was 14 for EFP-1 and 17 for EFP-2.
The number of actual challenges of the EFW system was 15.
The total number of demands for each pump is given below in Table 4.
Table 4 EFW Pump Demand Data (9/18/78-6/30/84)
Demands EFp-1 EFP-2 Test 58 58 Actual 15 15 Maintenance-Related 14 17 Total 87 90 The total number of demands for each pump is slightly less than the figures given at the April meeting due to discovery of an incorrect assumption of monthly surveillance testing regardless of plant condition.
Review of the EFW pump failure data involved.not only the demands but also the failures.
The one EFW pump catastrophic failure during the 9/18/78 to 6/30/84 time frame was traced to installation of a new bearing in the EFP-2 turbine.
Additional research resulted in the discovery that the replacement of this bearing was prompted not by a failure of EFP-2, but by an oil analysis performed as a part of the predictive maintenance program at CR-3; therefore, this failure was reclassified as an incipient failure and removed from the calculation of the EFP-2 failure rate.
Calculation of the EFW pumps' demand failure rates are given below in Table 5.
Table 5 EFW Pumps Demand Failure Rates (9/18/78 - 5/30/84) t Number of Number of Calculation of pump Failures Demands Demand Failure Rate 0.333*/
-3 3.8 x 10 /d EFP-1 0
87 87d
=
0.333*/
-3 3.7 x 10 /d EFP-2 0
90 90d
=
- 1/3 failure assumed for 0 failures.
-3 The resultant EFP-1 failure rate is almost identical to the 4.1 x 10 per demana rate used in the _Cp-3 study.
The EFP-2 failure rate is approximately half the 6.7 x 10 per demand rate used in the CR-3 study.
The NRC also requested an update of the EFW pump failure data to include the CR-3 experience from 7/1/84 to 12/31/86, since it was known that the turbine-driven EFW pump, EFP-2, had recently experienced a failure to start. This was the only EFW pump catastrophic failure found during this period. The number of demands for this period was determined in the same manner as that for the period 9/18/78 to 6/30/84. The number of demands for the entire period of 9/18/78 to 12/31/86 is summarized in Table 6.
I Table 6 EFW Pump Demand Data I
(9/18/78 - 12/31/86)
Demands EFP-1 EFP-2 9/18/78 - 6/30/84 87 90 7/1/84 - 12/31/86 a) Test 21 21 b) Actual 19 19 c) Maintenance-Related 1
17 Total 128 147 Combining the one turbine-driven pump failure with the additional pump demand data in Table 6 yields the EFW pump failure rates given below in Table 7.
Table 7 EFW Puses Demand Failure Rates (9/18/78 - 12/31/86)-
t:
Number of Number of Calculation of pump Failures Demands Demand Failure Rate EFP-1 0
128 0.333*/123d = 2.6-x 10-3/d 1
-3 EFP-2 1
147
/147d = 6.8 x 10 /d~
- 1/3 failure assumed for 0 failures.
-3 The resultant EFP-1 failure rate is 1Sss than the 4.1'x 10 per demand rate used in the CR-3 study.
The EFP-2 failure. rate is nearly identical 3
to ths 6.7 x 10 per demand rate used in the CR-3_ study.
Using either set.(Table 5 or Table 7) of EFW pump failure rates results in a lower EFW unreliability than that given in the. Crystal River 3 Emergency Feedwater System Reliability Analysis, May 30, 1986. Using the Table 5 (9/18/78 - 6/30/84) failurerates,_gFWunreliabilitygivena1oss of main feedwater is reduced from 1.9 x 10 per demand to 1.6 x 10.4 per demand.
Using the Table 7 (9/18/78 12/31/86). failure rates, E_Fg unreliability given a ]gss of. main feedwater is reduced from 1.9 x 10 per demand to 1.7 x'10 per demand.
It should be noted that the one EFP-2 catastrophic failure which occurred during the 7/1/84 to 12/31/86 time frame was eminently recoverable.
The turbine-driven pump. tripped on overspeed due to a slug of water in a drai.' line, and was quite capable of being restarted in the event' the motor-driven EFW pump train had failed.
i 1
l' l
l
r III.~CR-3 EFW Reliability Study (NUREG-0611 Data)
The faultetree model used in the " Crystal. River 3 Emergency' Feedwater
. System Reliability Analysis," May 30,~1986, was modified to completely reflect NUREG-0611 assumptions and data.
Florida Power Corporation (FPC)
.does not wish this modification to be interpreted as an update - or revision to the original analysis._
This. modification has -been done solely at the request of the NRC.for their internal purposes., FPC believes the reliability analysis, as submitted, is the best indicator of EFW reliability.
A substantial part of the change to the model consisted of removing the
~ explicit modeling of the Emergency Feedwater Initiation and Control
-(EFIC): system from the fault tree model. and the-modular events, and replacing it with the N_UfEG-0611 assumption)of a global failure rate for EFW actuation of 7 x 10 p'er demand per train. The new fault tree model is shown in Figure 1.
The remainder of the changes involved : replacing CR-3 data with NUREG-0611 data. Where NUREG-0611~ data was not available, data was taken from the Brookhaven National Laboratory (BNL)' evaluation of the "EFW System Upgrade Reliability Analysis - for. CR-3."
In the event the BNL report did not have a failure probability for' a particular basic event, the original CR-3 data was retained.
Sources for the individual data are given in the basic event list (Table 8).
Modular event proba-bilities are given in Table 9.
The results of the quantification are given in Table 10.
The. dominant contributors to EFW unavailability remain the same: both-EFW pumps fail or unavailable; followed in importance by EFIC failure :tp4 actuate and control EFW. _ The calculated EFW unreliability is 4~ 71-x 10 per demand.
Another quantification of the modified model was made using actual CR-3 EFW component maint'enance 'unavailabilities instead of the NUREG-0611 esymates.
The resultant ' EFW -unreliability figure'-(Table 11) of. 2.36 x 10 per demand is significantly-below that obtained using aH NUREG-0611 4
data, and approximately. equal to the 1.9 - x.10
. per demand figure l
calculated in the original analysis.
The maintenance ~unavailabilities appear to be the. key difference'between the NUREG-0611 and CR-3 analyses.
I Maintenance unavailabilities for the EFW components were' generated using the work request history and the shift supervisor's log. Any maintenance which renders an EFW train unavailable causes entry.into a 72 hour8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br /> Action Statement which is recorded in the shift' supervisor's log along.with the times.of entry and exit.
Reviewing the shift ~ supervisor's log during the time periods indicated by the work request' history was'the method used to determine the CR-3 EFW component unavailabilities.
In short, the numbers assigned to the component unavailabilities in the original analysis are believed to be accurate.
l l
j -
~~
Table 8-
- FILENAME: EFW611F.BE DATEi?4/08/87 TIMES-. 7:11 lNAMEl '
lCl FACTOR -lU[0 ESC lTREESIN ^
-l SOURCE
.[LOCATlSjPROB.
l-
'1 MSRVC
'3.00E 03. TWO MAIN STEAM RELIEF VLVS FAIL TO CLOSE W OPRA-
.3.00E 2 MSTTF-5.50E 04 MAIN TURBINE STOP VALVES FAIL TO CLOSE W-OPRA
-5.50E 04-3 PAVMS09D 1 1 TURBINE BYPASS VALVE MSV 09 FAILS OPEN W
.NUREG-0611 3.10E 03 4 PAVMSiOD 1-1 TURBINE BYPASS VALVE MSV 10 FAILS OPEN' W NUREG 0611-3.10E 03
'5 FAVMS110 1 1 TURBINE BYPASS VALVE MSV-11 FAILS OPEN W NUREG 0611 3.10E 03 -
6 PAVMS140. 1 1 TURBINE BYPASS VALVE MSV-14 FAILS OPEN. W NUREG 0611 3.10E 03 7 QACEFICA 4.90E 05.EFIC FAILS ( 7E-3 PER TRAIN )
W NUREG 0611 4.90E 05~
^ 8 QAVM411C 1 1 MSIV MSV 411 FAILS 70 CLOSE W
NUREG 0611 3.10E 03 9 QAVM412C - 1 1 MSIV MSV 412 FAILS TO CLOSE W
-NUREG 0611
.3.10E-03 to QAVM413C 1 1 MS!v MSV 413 FAILS 70 CLOSE W
NUREG 0611=
3.10E 03 -
g: 111 QAVM414C - 1 1 Msiv NSV 414 FAILS TO CLOSE W
NUREG 0611 3.10E JT2 QAVMS250 1 1 ADV MSV-25 FAILS OPEN W-NUREG 0611 3.10E-03 113 QAVMS260 1-
.1 ' -ADV MSV 26 FAILS OPEN W
NUREG 0611 3.10E 03 -
14 QCVEF05N-- '1-
.1 EFV 5 FAILS TO QPEN' NUREG 0611-1.00E-04.
15 QCVEF06N 1 1-EFV 6 FAILS TO OPEN NUREG 0611 1.00E 04 16 0CVEF07N 11 1 EFV 7 FAILS TO OPEN NUREG 0611 1.00E 04-17 QCVEF00N.11 1 _.EFV-8 FAILS TO OPEN' NUREG 0611 1.00E 04 18 OCVEF15N 1 1'
EFV 15 FAILS TO OPEN NUREG 0611-1.00E 04
'.19 GCVEF16N 1 1 EFV 16 FAILS TO CPEN:
NUREG 0611 1.00E 04 20 GCVEF17N 1 1 EFV 17 FAILS TO OPEN NUREG 0611 1.00E 04 21 GCVEF18N 1 1 EFV 18 FAILS TO OPEN NUREG 0611 1.00E-04 22 QCVEF34N. 1 1 EFV 34 FAILS TO OPEN
.NUREG 0611 1.00E 041 23 QCVEF35N 1 1 EFV 35 FAILS TO OPEN NUREG 0611
=1.00E 04 24 QCVFW43M 1 1
FWW-43 FAILS TO OPEN W
NUREG 0611 1.00E 04 25 QCVFW44N 1 1-FWV 44 FAILS TO OPEN W
.1.00E 04 26 0CVM055N 1 1
MSV-55 FAILS TO OPEN NUREG-0611 1.00E 04
- 27 QCVM055x '
5.00E 04-MSV 55 LEFT UNAVAILABLE AFTER MAINT.
BNL -
5.00E 04 28 QCVM056N 1 1 MSV 56 FAILS.TO OPEN' NUREG 0611 1.00E 04 -
29 QCVM056x 5.00E 04 MSV 56 LEFT UNAVAILABLE AFTER MAINT.
BNL 5.00E 04 30 QCVM186N 1 1 MSV 186 FAILS TO OPEN NUREG 0611 1.00E 04.
31 0CVM187V 1 1 MSV 187 FAILS TO OPEN NUREG-0611 1.00E 04
.l 32 QMMEFP1 1.124E 02-MOTOR DRIVEN PUMP EFP 1 TRAIN FAILS W
1.12E 02 33 QMMEFP1M 9.971E 03 MOTOR DRIVEN PUMP EFP 1 TRAIN IN MAINT. W 9.97E-03 34 QMMEFP2 1.137E 02 TURBINE DRIVEN PUMP EFP-2 TRAIN FAILS W
'1.14E 02 35 QMMEFP2M 9.971E 03 TURB. DRIVEN PUMP EFP 2 TRAIN IN MAINT. W 9.97E 03
-36 QMMEFT2 3.56E 07 DEDICATED EFW TANK EFT 2 FAILS W
CR 3 PRA
.3.56E 07 37 QMMSGAPI 2.728E-04 INJ. LINE FROM EFP 1 TO OTSG A CLOSED W-2.73E 04 38 QMMSGAP2 2.728E 04 'INJ. LINE FROM EFP 2 TO OTSG A CLOSED W
2.73E 04 39 QMMSGAST 6.999E 04 -STEAM SUPPLY TO EFP 2 FROM OTSG A FAILS W'
7.00E 04 40 QMMSGBP1-2.728E 04 INJ. LINE FROM EFP 1 TO OTSG B CLOSED W
2.73E-04 41 QMMSGBP2 2.728E 04 INJ. LINE FROM EFP 2 TO OTSG-B CLOSED W
2.73E 04 l.
42 QMMSGBST 6.999E 04 STEAM SUPPLY TO EFP 2 FROM OTSG B FAILS -W 7.00E 04 43 QMVA0050 1 1 ASV 5 FAILS TO OPEN NUREG 0611 3.10E 03 46 QMVA005K 1 360 ASV 5 TRANSFERS CLOSED BNL.
-.4.32E-05 45 QMVA005M 2.10E 03 ASV 5 IN MAINTENANCE-NUREG-0611-2.10E 03 46 QMVA2040 1 1 ASV 204 FAILS TO OPEN NUREG 0611 3.10E 03 47 QMVA204K 1 360 ASV 204 TRANSFERS CLOSED BNL 4.32E 05
-48 QMVA204M 2.10E 03 ASV 204 IN MAINTENANCE NUREG 0611 2.10E-03 49 QMVEF01M 2.10E 03 EFV-1 IN MAINTENANCE W
NUREG 0611 2.10E 03-
.50 QMVEF02M 2.10E 03 EFV 2 IN MAINTENANCE W
NUREG 0611-2.10E 03
.51 QMVEF03K 1 360 EFV-3 TRANSFERS CLOSED BNL 44.32E 05 52 QMVEF04K 1 360 EFV 4 TRANSFERS CLOSED -
BNL -
4.32E 05 53 QMVEF110 1
1 EFV 11 FAILS TO OPEN ON DEMAND-W NUREG 0611 3.10E 03 l.
~54 QMVEF11K 1 360 EFV 11 TRANSFERS CLOSED BNL 4.32E-05 l
55 QMVEF11M 2.10E 03 ~EFV-11 IN MAINTENANCE NUREG-0611 2.10E 03 56 QMVEF11x 5.00E 04 EFV 11 LEFT UNAVAILABLE AFTER MAINT.
W BNL 5.00E 04 57 QMVEF140 1 1 EFV 14 FAILS TO OPEN ON DEMAND W
NUREG 0611 3.10E 03 58 QMVEF14K 1 360 EFV 14 TRANSFERS CLOSED BNL 4.32E 05 59 QMVEF14M 2.10E 03 EFV-14 IN MAINTENANCE NUREG 0611 2.10E 03.
40 QMVEF14x 5.00E 04 EFV 14 LEFT UNAVAILABLE AFTER MAINT.
W BNL 5.00E 04 61 QMVEF32D 1 1 EFV 32 FAILS TO OPEN ON DEMAND W
NUREG 0611 3.10E 03
63 QMVEF32M 2.10E-03 EFV-32 IN MAINTENANCE NUREG-0611 2.10E 03 64 QMVEF32X 5.00E-04 EFV-32 LEFT UNAVAILABLE AFTER MAINT.
W-BNL 5.00E 04
'65 QMVEF330 1 1 EFv 33 IAILS TO OPEN ON DEMAND W
NUREG 0611 3.10E 03 66 QMVEF33K 1 360 EFV 33 TRANSFERS CLOSED BNL 4.32E 05
' 67 QMVEF33M 2.10E-03 EFV-33 IN MAINTENANCE NUREG 0611 2.10E 03 68 QMVEF33X 5.00E 04 EFV 33 LEFT UNAVAILABLE AFTER MAINT.
W BNL 5.00E 04 69 QPMEFP1A_ 1 1 EFP 1 FAILS TO START NUREG 0611 5.00E 03
-70 QPMEFP1F 1
8 EFP-1 FAILS TO RUN BNL 2.40E-04 71 QPMEFP1M 5.80E 03 EFP-1 IN MAINTENANCE NUREG-0611 5.8CE-03 72 QPMEFP1Z 5.00E 03 EFP 1 TRAIN LEFT UNAVAIL. AFTEP MAINT, BNL 5.00E-03 73 QSVEF550 1
1 CONTROL VALVE EFV 55 FAILS ON DEMAND W
NUREG 0611 3.10E 03 74 QEVEF55K 1 1080 EFV 55 TRANSFERS CLOSED W
BNL-1.30E 04 75 QSVEF56D 1
1 CONTROL VALVE EFV 56 FAILS ON DEMAND W
NUREG 0611 3.10E 03
-76 QSVEF56K 1 1080 EFV 56 TRANSFERS CLOSED BNL 1.30E-04 77 QSVEF570 1 1 CONTROL VALVE EFV 57 FAILS ON DEMAND W
NUREG 0611 3.10E 03 78 QSVEF57K 1 1080 EFV 57 TRANSFERS CLOSED W
BNL 1.30E-04 79 QSVEF58D 1
1 CONTROL VALVE EFV 58 FAILS ON DEMAND W
NUREG 0611 3.10E 03 80 QSVEF58K 1 1080 EFV 58 TRANSFERS CLOSED W
BNL 1.30E 04 81 QTPEFP2A 1 1
EFP 2 FAILS TO START NUREG-0611 5.00E 03 82 QTPEFP2F 1 8 EFP 2 FAILS TO RUN BNL 2.40E 04 83 QTPEFP2M 5.80E 03 EFP 2 IN MAINTENANCE NUREG 0611 5.80E 03 84 QTPEFP22 5.00E 03 EFP 2 TRAIN LEFT UNAVAIL. AFTER MAINT.
BNL 5.00E 03 85 QXVAS50K 1 1 ASV 50 TRANSFERS CLOSED BNL 1.00E 04 86 QXVEF23K 1 1 EFV 23 TRANSFERS CLOSED BNL 1.00E 04 87 QXVEF24K 1 1 EFV 24 TRANSFERS CLOSED BNL 1.00E 04 88 QXVEF49K-1 1 EFV 49 TRANSFERS CLOSED BNL 1.00E 04 89 QXVEF50K 1 1 EFV 50 TRANSFERS CLOSED BNL 1.00E-04 90 QXVEF51K 1 1 EFV 51 TRANSFERS CLOSED BNL 1.00E 04 91 QXVEFS2K 1 1 EFV 52 TRANSFERS CLOSED BNL 1.00E-04 92 QXVEF53K 1 1
EFV-53 TRANSFERS CLOSED BNL 1.00E 04 93 QXVEF54K 1 1 EFv 54 TRANSFERS CLOSED BNL 1.00E 04 94 SXVS507K 1 1 SW 507 TRANSFERS CLOSED BNL 1.00E 04 95 SXVS508K 1 1
SW 508 TRANSFERS CLOSED BNL 1.00E-04 96 SXVS509K 1 1 SW 509 TRANSFERS CLOSED BNL 1.00E 04 97 SXVS510K 1 1
SW-510 TRANSFERS CLOSED BNL 1.00E 04 98 SXVS579K 1 1 SW 579 TRANSFERS CLOSED BNL 1.00E 04 99 SXVS607K 1 1
SW-607 TRANSFERS CLOSED BNL 1.00E 04 i
= _ _ _-_ _ - _ _ _ _ _ _ _
Tabb 9
- 4/08/87 7
- 09 PAGE 1 FAULT TREE / EVENT NAME DESCRIPTION RATE DURATION 8.E. PROBABILITY FAULT TREE PR08A8!LITY
.1) QMMEFP2 TURBINE DRIVEN PUMP EFP-2 TRAIN FAILS 1.14E 02
- 1) QTPEFP2A -
EFP 2 FAILS TO START 5.00E-3
.1 5.00E 03
- 2) QTPEFP2Z EFP 2 TRAIN LEFT UNAVAIL. AFTER MAINT.
5.00E 03 5.00E 03
- 3) 4TPEFP2F EFP 2 FAILS TO RUN 3.00E 05 8 2.40E 04 '
- 4) QXVEF23K EFV 23 TRANSFERS CLOSED 1.00E-4 1
1.00E 04
1.00E 04
- 6) QXVEF53K EFV 53 TRANSFERS CLOSED.
1.00E-4
.1 1.00E 04
- 7) QXVEF51K EFV 51 TRANSFERS CLOSED 1.00E 4. 1 1.00E U4
- 8) QCVEF08N EFV 8 FAILS TO OPEN 1.00E 4 1
1.00E 04
- 9) QCVEF34N EFV 34 FAILS TO OPEN 1.00E 4
'1 1.00E 04
- 10) QXVEF54K-EFV 54 TRANSFERS CLOSED 1.00E-4 1
1.00E-04.
- 11) QXVEF50K EFV 50 TRANSFERS CLOSED 1.00E 4' 1'
1.00E-04
-12) QXVASSOK ASV 50 TRANSFERS CLOSED 1.00E 4
.1 1.00E 04
- 13) QXVEF49K EFV 49 TRANSFERS CLOSED 1.00E 4 1 1.00E-04
-14) QXVEF52K EFV 52 TRANSFERS CLOSED 1.00E 4 1
1.00E 04
- 15) QMVEF04K EFV 4 TRANSFERS CLOSED 1.20E 7 360 4.32E 05
- 16) QMVA2040 ASV 204 FAILS TO CPEN 3.10E-3 1
3.10E-03 QMVA005D ASV 5 FAILS TO OPEN 3.10E 3 1 3.10E-03
- 17) QMVA204M ASV 204 IN MAINTENANCE 2.10E 03 2.10E 03-QMVA0050 ASV 5 FAILS TO OPEN 3.10E 3 1
3.10E 03 1
- 18) QMVA2040 ASV 204 FAILS TO OPEN 3.10E-3 1
3.10E-03 QMVA005M ASV 5 IN MAINTENANCE 2.10E 03 2.10E 03
- 19) QMVA204D ASV 204 FAILS TO CPEN 3.10E-3 1
3.10E 03 QMVA005K ASV 5 TRANSFERS CLOSED 1.20E-7 '360 4.32E 05
'20) QMVA204K ASV 204 TRANSFERS CLOSED 1.20E-7 360 4.32E 05
-QMVA0050 ASV 5 FAILS TO OPEN 3.10E 3 1
3.10E 03
- 21) QMVA204M ASV 204 IN MAINTENANCE 2.10E 03 2.10E 03 QMVA005K ASV 5 TRANSFERS CLOSED 1.20E 7 360 4.32E 05'
- 22) QMVA204K ASV 204 TRANSFERS CLOSED 1.20E 7 360 4.32E 05 QMVA005M ASV 5 IN MAINTENANCE 2.10E 03 2.10E 03
- 23) QMVA204K ASV 204 TRANSFERS CLOSED 1.20E 7 360 4.32E-05 QMVA005K ASV 5 TRANSFERS CLOSED 1.20E 7 360 4.32E-05
- 2) QMMEFP1 MOTOR DRIVEN PUMP EFP-1 TRAIN FAILS 1.12E 02
5.00E 03
- 2) QPMEFP1Z EFP-1 TRAIN LEFT UNAVAIL. AFTER MINT.
5.00E 03 5.00E 03
- 3) QPMEFP1F EFP 1 FAILS TO RUN 3.00E 5 8 2.40E 04
- 4) SXVS510K SW 510 TRANSFERS CLOSED 1.00E 4 1 1.00E-04
- 5) QCVEF35N EFV 35 FAILS TO CPEN 1.00E 4 1
1.00E 04
- 6) SXVS$09K SW 509 TRANSFERS CLOSED 1.00E 4 1 1.00E 04
- 7) SXVS507K SW 507 TRANSFERS CLOSED 1.00E-4 1
1.00E 04
- 8) QCVEF07N EFV 7 FAILS TO OPEN 1.00E 4 1
1.00E 04
- 9) QXVEF24K EFV 24 TRANSFERS CLOSED.
1.00E-4 1
1.00E 04
- 10) SXVS607K SW 607 TRANSFERS CLOSED 1.00E 4 1 1.00E-04
- 11) SXVS579K SW 579 TRANSFERS CLOSED 1.00E-4 1
1.00E 04
'12) QCVEF06N EFV 6 FAILS TO CPEN 1.00E 4 1
1.00E 04
- 13) SYVS508K SW 508 TRANSFERS CLOSED 1,00E 4 1 1.00E 04
- 14) QMVEF03K
. EFV 3 TRANSFERS CLOSED 1.20E 7 360 4.32E 05
- 1) QSVEF56K E'/ 26 TRANSFERS CLOSED 1.20E 7 1080 1.30E 04 l
- 2) QCVEF17N EFV-17 FAILS TO CPEN 1.00E 4 1
1.00E 04 i
- 3) QMVEF11K EFV 11 TRANSFERS CLOSED 1.20E-7 360 4.32E 05
(
- 1) QCVM187N MSV 187 FAILS TO OPEN 1.00E 4 1 1.00E-04
- 2) QCvm056N MSV 56 FAILS TO OPEN 1.00E 4 1
1.00E 04
- 3) QCVM056X MSV 56 LEFT UNAVAILABLE AFTER MAINT.
5.00E 04 5.00E 04
- 1) QCVM186N MSV 186 FAILS TO OPEN 1.00E 4 1
1.00E 04
4/08/87 7:10 PAGE 2 FAULT TREE / EVENT NAME DESCRIPTION RATE DURATION B.E. PROBABILITY FAULT TREE PROBABILITY
- 2) QCvm055N MSV 55 FAILS TO OPEN 1.00E 4 1 1.00E-04
- 3) QCvm055X MSV 55 LEFT UNAVAILASLE AFTER MAINT.
5.00E-04 5.00E 04
- 6) QMMEFP2M TUR8. DRIVEN PUMP EFP-2 TRAlN IN MAINT.
9.97E 03
- 1) QTPEFP2M EFP-2 IN MAINTENANCE 5.80E 03 5.80E 03
- 2) QMVEF11M EFV 11 IN MAINTENANCE 2.10E 03 2.10E 03
- 3) QMVEF32M.
EFV-32 IN MAINTENANCE 2.10E-03 2.10E 03
.7) QMMEFP1M MOTOR DRIVEN PUMP EFP 1 TRAIN IN MAINT.
9.97E 03
- 1) QPMEFP1M EFP 1 IN MAINTENANCE 5.80E 03 5.80E-03
- 2) QMVEF14M EFV 14 IN MA!NTENANCE 2.10E-03 2.10E-03
- 3) QMVEF33M EFV 33 IN MAINTENANCE 2.10E-03 2.10E 03
- 1) QMVEF32K EFV 32 TRANSFERS CLOSED 1.20E-7 360 4.32E-05
- 2) QCVEF18N EFV 18 FAILS TO OPEN 1.00E 4 1 1.00E 04
- 3) QSVEF55K EFv 55 TRANSFERS CLOSED 1.20E-7.
1080 1.30E 04
- 1) QCVEF16N EFV 16 FAILS TO OPEN 1.00E-4 1
1.00E 04
- 2) QMVEF33K EFV 33 TRANSFERS CLOSED 1.20E 7 360 4.32E 05
- 3) QSVEF57K EFV 57 TRANSFERS CLOSED 1.20E 7 1080 1.30E 04
- 10) QMMSGAP1 INJ. LINE FROM EFP-1 TO OTSG A CLOSED 2.73E 04
- 1) QCVEF15N EFv 15 FAILS TO OPEN 1.00E 4 1 1.00E 04
- 2) QMVEF14K EFV 14 TRANSFERS CLOSED 1.20E 7 360 4.32E 05
- 3) QSVEF58K EFV 58 TRANSFFRS CLOSED 1.20E 7.
1080 1.30E 04 l
l l
1 l
Tabla 10 4/15/87-7130
- PAGE 1 Top events 0001-Top prob.: '4.71E 04 1.278E 04 QMMEFP1-QMMEFP2 1.134E 04 QMMEFP1M
. QMMEFP2 1.121E 04 QMMEFP1 QMMEFP2M 4.900E 05.
-QACEFICA 2.388E 05-QMMEFP2
. QMVEF02M
.2.360E 05
-QMMEFP1 QMVEF01M
' 9.610E 06 QAVMS250 QAVMS260 9.300E 06 MSRVC -
.QAvMS260
'3.560E 07 QMMEFT2 3.100E 07' QAVMS250 QCVFW43N
-3.100E 07 QAVMS260 QCVFW44N
.-3.000E 07' MSRVC -
QCVFW43N 1.093E 07 QMMEFP2 QSVEF570 QSVEF58D '
1.093E 07..
QAVMS250'-
QMMEFP2 QSVEF57D 1.093E 07 QAVMS260 QMMEFP2 QSVEF580 1.080E-07 QMMEFP1 QSVEF550 QSVEF560 1.080E 07 QAVMS250 QMMEFP1 QSVEF550
~1.G80E 07 QAvMS260 QMMEFP1 QSVEF560 1.057E 07 MSAVC QMMEFP2 QSVEF57D 1.045E 07 MSAVC QMMEFP1 QSVEF550 i
E j
.~
', h
_ )
4/15/87' I7:34 IPAGE 1
. Top event: Q001-
.7op' prob.: 2.36E 04 1.278E 04 QMMEFP1
.QI04EFP2 1.005E 05 Q WEFP1M QMMEFP2
-2.551E 05
- QMMEFP1 QMMEFP2M 4.900E 05'
-QACEFICA 1.558E 06-QMMEFP2 QMVEF02M~
1.540E 06 QMMEFP1 QMVEF01M 9.610E 06 QAVMS250-QAVMS260 9.300E 06 M$RVC QAVMS260-
-3.560E 07
-QMMEFT2 3.100E 07-QAVMS250
- QCVFW43N 3.100E 07 QAVMS260 QCVFW44N
'3.000E 07-MSRVC-
-QCVFW43N i
1.093E-07~
QMMEFP2 QSVEF57D QSVEF58D l
1.093E QAVMS250 QMMEFP2 QSVEF57D 1.093E-07 QAVMS260-.
QMMEFP2 QSVEF580 1.080E 07 QMMEFP1
'QSVEF550
-QSVEF560
.1.080E 07 QAvMS250 QMMEFP1 QSVEF55D 1.080E 07 QAVMS260 QMMEFP1 QSVEF560 1.057E 07 MSRVC QMMEFP2 QSVEF57D 1.045E 07 MSRVC QMMEFP1 QSVEF550 i
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TITLE EFW RELIABILITY STUDY NUREG-0611:
DRAWING NUMBER DATE Figure 1
.4/07/87
m-9 FAILURE OF EFV-14 IN ALIGNED CLOSED POS.
G010 I)
-11 EFV-14 FAILS TO EFV-14 LEFT OPEN ON DEMAND
-UNAVAILABLE AFTER MAINT.
I QMVE'F140 1 I GMVE'F14X l 0
0 t
i TITLE' EFW'.RELIABIL'ITY STUDY.- NUREG-0611 DRAMING NUMBER DATE Figure:1
- 4/07/g7
_u
n -
INSUFFICIENT EFW FLOW FROM EFV-56
\\
100h I 0005 i
i FAILURE OF EFV-11
-INSUFFICIENT FLOW INJ. LINE FROM CONTROL VALVE IN ALIGNED CLOSED FROM EFP-2 EFP-2 TO OTSG-A
.EFV-56 FAILS ON POS.
CLOSED DEMAND i GMMS' AP2 I I QSVE'F5601 (1
Y
.O O
I 00'33 I G
II i
i EFV-11 FAILS TO EFV-11 LEFT OPEN ON DEMAND UNAVAILABLE AFTER NAINT.
I GMVE'F11D I IGMVE'F11X l C
0 TITLE EFW RELIABILITY-STUDY - NUREG-0611 DRANING NUMBER DATE-Figure 1 4/07/87
M MIJ INSUFFICIENT EFW FLOH FROM EFV-57 x
I UU 0 I 0006 I
I I
I FAILURE OF EFV-33 INSUFFICIENT FLOW INJ. LINE FROM CONTROL VALVE IN ALIGNED CLOSED FROM EFP-1 EFP-1 TO OTSG-B EFV-57 FAILS ON POS.
CLOSED DEMAND I 01' 0 l 1OMMrfG8P1l lOSVE'FS70 1 l 00' 3 l 0
5 (1
A\\
O O
II i
EFV-33 FAILS TO EFV-33 LEFT OPEN ON DEMAND UNAVAILABLE AFTER MAINT.
10MVE'F330 1 10MVE"F33XI O
O TITLE EFW RELIABILITY STUDY - NUREG-0611 DRAWING NUMBER DATE Figure 1 4/07/87
m INSUFFICIENT EFW FLOW FROM EFV-55
+
o00s FAILURE OF EFV-32 INSUFFICIENT FLOW INJ. LINE FRON CONTROL VALVE IN ALIGNED CLOSED FROM EFP-2 EFP-2 TO OTSG-B-EFV-55 FAILS ON.
POS.
CLOSED DEMAND M
T
.O-0 IGMMSG8P2I IGSVE'F550 I I
I EFV-32 FAILS TO EFV-32 LEFT OPEN ON DEMAPO UNAVAILABLE AFTER MAINT.
'IGMVE'F320 I
' I GMVE' 32X I F
O
.O
~
TITLE-EFW RELIABILITY--
STUDY NUREG-0611:
DRAWING NUMBER DATE Figure 1 4/07/87-
l l
i l
INSUFFICIENT FLOW FROM EFP-1 b
G010 00s0 i
EFP-1 TRAIN MOTOR-DRIVEN PUMP DEDICATED EFW TANK MAINTENANCE FAULTS EFP-1 TRAIN FAILS EFT-2 FAILS I Os' 1 l l GPtMdFP1 1 IGMM FT2 1-0 O
I I
MOTOR-DRIVEN PUMP '
MAINTENANCE EFV-2 IN EFP-1 TRAIN IN MAINT.
IGMME'P1Mi IGNVE'F02M l FO O
F TITLE
~EFW RELIABILITY STUDY
-NUREG-0611.
DRAWING NUMBER.
DATE-Figure'1-4/07/87-
b
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T "tr TITLE
-EFW RELIABILITY
. STUDY - NUREG-0611' DRAWING NUMBER DATE 4/07/87 Fiqure 1
LOW PRESSURE IN STEAM GENERATOR A d
9003 0182 FAILURE TO ISOLATE FAILIA?O ISOLATE ADV MSV-25 FAILS TWO MAIN STEAM STEAM LIE A2 STEAM LINE A1 OPEN MLIEF VLYS FAIL TO CL =
O U
IGAWMS25D I MSIV MSV-412 FAILS MAIN TURBINE STOP MAIN STEAM LIldE A2 MSIV MSV-411 FAILS TO CLOSE VALVE IL TD FAILS OPEN TO CLOSE I QAvt5412C I IGAVM411CI O
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O TITLE EFW RELIABILITY STUDY
'NUREG-0611 DRAWING NUMBER DATE Figure 1 4/07/87
l l
~
i LOW PRESSURE IN l
I 0004 f
Q183 FAILURE TO ISOLATE FAILURE TO ISOLATE ADV MSV-26 FAILS STEAM LINE B2 STEAM LINE B1 OPEN I G251 1 I Q252 I IGAVMS260l l
r1 (1
. O.
l l1 II l.
MSIV MSV-414 FAILS MAIN TURBINE STOP MAIN STEAM LIE B1 MSIV MSV-413 FAILS
~
TO CLOSE VALVES FAIL TO FAILS OPEN TO CLOSE l
l Q2' 5 l lGAVM413CI I
IGAVM414CI l MS TF I 5
O CD O
TWO SG B TURBIE MAIN TURBIE STOP BYPASS VALVES FAIL VALVES FAIL TO OPEN CLOSE i MSiTF I i
TURBINE BYPASS TURBIE BYPASS VALVE MSV-11 FAILS VALVE MSV-14 FAILS l
OPEN OPEN IPAVMS110I lPAVMS1401 TITLE O
O EFW RELIABILITY l
STUDY - NUREG-0611 DRANING NUMBER DATE Figure.1-4/07/87
l i
IV. Human Error The reference for the time reliability correlation (TRC) curve used in the CR-3 PRA is currently in draft form and will soon be published as a textbook on human reliability.
Its author is Mr. Ed Dougherty of Science Applications International Corporation (SAIC), who performed the human reliability analysis (PRA) for the CR-3 PRA.
One excerpt from the book addressing the TRC curve is attached.
If there are any questions, FPC will be ~ glad _ to set' up a conference call with Mr. Dougherty to resolve them.
b
1 1
5.3 DETAILEDQUANTIFICA'IION 4
A quantitadve risk analysis requires estimating the probability of human failure events. Either data peiMHy eyy.sydate to the event, of which there is woefully little, or a technique to make j
j a direct or indirect estimate of the probability is W Dree kinds of techniques are popular in nuclear power plant HRAs: a task-analytical approach such as THERP,33 ime reliability :
t j
. correladons (TRC),32 or a method that structures expertjudgment of such events, such as the f
Success i hiiW imin Methodology (SLIM).*
4 l
Choosing one or a combination of techniques is a critical step in the HRA process shown in the 1
j schematic in Figure 5-1. The choice depends on the failure modes and mechanisms that dominate the human event as represented, ne choice of the technique directs the analyst in i
identifying the characteristics of the m-t task, and human behavior that need to be factored l
Into the quantification. THERP and SLIM can accommodate numerous influences' whereas a j
TRC approach may only need the timing characteristics of the the sequence and the kind of 1
behavior that the event represents, e.g., rule based. After specifying the failure modes and mechanisms 'and the dominant influences on them, the technique allows a relatively I
I
}
straight-forward calculadon of a point estimate of the pmbability of the modes or the total event.
Some guidance relarive to'the quandtadve uncertainty that should be *Wead with the estimate f
}
is also provided.
i 5.3.1. h Onntifientian A99a=h Human failure events are quanti 5ed according to the following steps:
i
- 1. Human events are (usually) identified only in those classes indirstad by Table 5 2.
His includes latent events as contributors to component unavailabilities and may include human contributors to initiators, if ininators are modeled rather than i
quantifled directly from data. Slips may or may not be included in rule based 1
i events. Recovery failures are usuaLly attributed only to mistakes. Event specifics i
l are identified by informal or formal hterviews of operators and plant staff or observations in simulator exercises, whenever possible.
- 2. He events are represented and incery.Wd into the PRA structures either directly or indiregtly in a logic structure similar to the Operator Action Event Trees (OAET), as an adjunct to the PRA structures. An OAET is depicted in Figure 5 4 that represents the scenarios related to a reactor coolant pump seal LOCA. He 4
l figure also shows how a sequence timeline can be integrated with an OAET and the most likely human failure modes identified.
5-11 i
,_~._._y
,-,4.,_,_
m._...
.,,....,___,---,r -..
-..m.,.__
l I
RCP seals fall Inadequate core cooling symptoms arise
- SW falls Unc (0
gins
- BWST depletes SW-related Onset of RCS alarms sound core damage saturates 1 f1 f V1 f i f i f l f l f o
T, 2
3 4
5 T,
T T
T T
T
]
T 7
Mitigate Diagnose Verify Go to SW Loss LOCA Si Recire 1 Safe 2 At risk 3 Damage
+
4 At risk No 5 Damage E2 6 At risk E3 E4 7 Damage i
Event Most likelv Error Modes E1 Fall to recover SW in time E2 Cannot stop LOCA in time E3 Fall to follow ICC rule E4 Fall to respond to low level alarm Figure 5-4. Opentor Action Event Tree.
5-12
i
- 3. Slips are modeled using a simplificadon of the THERP approach; mistakes are modeled using a combinadon of TRCs and SLIM.
- 4. Probabilities are obtained from the technique chosen and the estimate is assumed to be the mean of a lognormally distributed parameter with enor factor of ten.51 j
4 i
e d
5 O
h t
5-13
=... - _ _,.
'I:
5.3.2. OnantiMne slim In Table 4-1, slips are mesnt to correlate to the failure modes of "misdetecden" and " faulty b
actions". However, in a process plant, which is fitted with considerable instrumentation and.
annunciators, Wadha is not usually credible as a mode of failure. Thus in most cases, a l
slip is an action that is not as inte'nded.52 In other words, the situadon has been diagnosed and
[
the decision or plan made, both successfully (otherwise there was a mistake). All that is left is for the person to do what was meant to be done. ' Slips occur all the time in everday acdvides -
j (and may be thought hilarious by the perpetrator if inconsequential). Slips also occur regularly
}
in routine process plant activi;ies.
f-A prototypical slip can occur when a maintainer is returning a piece of equipment to service and -
I fails to leave it in the proper state. For example, both auxiliary feedwater valves at TMI were i
apparently left closed following maintenance, which ded a vital safety system unavailable.
1 t
l In the case of a slip, there is no situation to respond to and planning is specined by procedure, j
policy, or work order. It is fair to assume, then, that the only cognidve element is that of -
1 l
control, Le., carrying out of all steps of the plan. There are so many mechanisms of slips that i
THERP assumes that each step of a particular procedure is a candidate for.a slip (i.e., an omission or commission). However, the likely candidates for slips in a control room seem to j
be:
i
- 1. Stereotype capture, i.e., a familiar, more frequently gdwmed task uses some of 2
the same steps as the intended task, and in the first case of deviance, the operator j
slips into the old task rather than continuing what is called for in the required task,
- 2. Spatia 1 reversals, e.g., two controls aie adjacent and the wrong one is manipulated.
because of a lapse in attention (or a deviation from swe@yc), and.
i
- 3. Time reversals, where the sequencing of manipuladons is critical and the order is incorrect,again due to alapse.
Assuming that the mechanisms of slips are limited, only one instance of a slip per task is 1
j modeled, which is the first difference fromTHERP. A review of the estimates for task element probabilities in Chapter 20 of NUREG/CR-1278 (THERP) shows a range from 0.0003-to 0.003 for most of the types of situadons relevant to process activities. Thus, a simple strategy is adopted of using the log-median of the bounds,0.001, as a basic probability for any slip; 0.0001 for a slip thatleaves redundant equipment inoperable. This is the screening strategy 4
5-14 a
l
........ m-.-.=
,_.__.__..____.,_,,_..,_-.,c
i i
mentioned previously. There is some aq,went for the fact that current equipment failure data
' includes human failure contribudons and often a PRA does not opt to model latent slips at all.
THERP, then, allows the basic es mata to be adjusted by so called performance shaping factors I
n (PSF) based on situational, task, or behavioralinfluences. For example in maintenance, there may be a check off policy and a PSF should give credit for this (denote this factor by f ). The t
possibility of human engineering deficiencies can also be accounted for by a PSF, f, e.g., both 2
valve operators for two trains are adjacent or rei si or otherwise could induce a reversal slip.
Table 20-22 of NUREG/CR-1278 suggests that f should be 0.1 if the checking is independent t
l of the manipulation. If a human engiaWng deficiency exists, then f could be greater than 1.0, 2
say,5.0. 'Ihe net result for the slip, then, would be:
eventprobability = basic probability
- f
- f = 0.001*0.1*5.= 0.0005.
i g
2 q
This simplified THERP approach may be used for slips whether they are latent, rule-based, or
- recovery events. The approach can be form =11'-d as depicted in Figure 5-5. A basic probability I
is chosen first (0.001 above, for example). Then three factors are chosen. Factor f accounts t
for the testing performed, with a factor of ten credit given to normal surveillance and another factor of ten credit given for effective fnardanst testing of the component or train. Factor f is a 2
j general performance shaping factor (PSF) to account for stress or other influences. Factor f is 2
generally greater than 1.0 to account for the negative effects of the influence. Factor f,0.1, 3
i accounts for the latent failure of equipment in radandant trains, e.g., where.the equipment may i
be located adjacently. In any case in which a factor is not judged relevant, its default value is I
1.0..
1 f
The product of the three factors with the basic probability produces the final point estimate of the l
probability of a slip. THERP typically assumes error factors (i.e., of the uncertainty of the estimate) that range from 3 to 30. A log median of 10 is used here; this implies that the order of magnitude of the point estimate so derived is accurate with a confidence of 90%, Le., the order l
of magnitude of such estimates can be esdmad x-aaamhly well.
1 5-15 I
1
,y,.+.mi,
--,-m-w,
,,,-,-,--.w...,-
,...--=-m--c.--
-.er--m-
-se--r,m.--
--,w---r--,--c-m-----e.,
,--ww,y-
-~~,"
e---
w,
-.-e,---
--e-,
l P= basic probability 4
Test performed?
Functional No Yes test?
No Yes t
t
( f =0.1 ) (f =0.01) i 3
4 1 P 1
Other PSFs?
)
>(
f No Yes 2
1 r l
Multiple trains?
> { f =0.1 }
'No Yes 3
1 r r lin,, =P*f
- f/1,a F
3 3
L J
Figure S-5. A Process forEstimating the Probability of Slips.
e 5-16 f
?
5.3.3. Onnntifvine mistakes A mistake is one of the failure modes - misdiagnosis, faulty decision, or faulty planning. If the strategy exhibited in Table 5-2 is correct, then these failure modes matter most in a process environment only when the process has deviated from normal or desired condidons, i.e., in an abnormal or emergency event. There is a large literature in the decision sciences but most of it attempts to discover optimum decision strategies, i.e., how decisions ought to be made. When decision science looks at decision making as it is actually performed, it is often qualitadve and set in routine, everday circumstances,83 which has little direct bearing on response to off-normal process plant events.
It is known, however, that diagnosis and the decision making of a kind needed in off-normal response is influenced by available time, perceived time (or the pace or urgency of events),
3 8
j uncertainty, complexity, and goal conflict. Dere have also been studies of simulated events that show that the response performance of crews of operators to off-normal events as distributed in response time. In fact, response times seem to fit lognormal distributions well.30 Anecdotal reviews of actual events show that individuals involved in diagnosis and decision making often exhibit hesitancy. Hesitancy can be due to uncertainty in the conditions present, 4
thus inhibiting or failing to allow diagnosis,55 or can be due to uncertainty as to which goals to pursue when in conflict.M Re fact that relatively clear procedures exist for these condidons shows that process plant operators are human and not automatons. Diagnosis and decision -
making is the critical and dominant human behavior in an abnormal or emergency situation.
Nuclear power plants have attempted to eliminnen or minimize the role of diagnosis and decision making by introducing so-called symptom-oriented emergency procedures. These procedures contain " rules" of the form:
~
IF symptoms S ' S ' ' S exist I 2 n
THEN execute actions A, A,...,A, i
2 AND do so without hesitation.
In most cases, the symptom set is kept small and each sypmtom is clearly indicated in the control room. The action set is one or two simple manipulations of controls also in the control room. Of course, it is the mandate represented by the "and" clause in the rule that is not so clear 5-17
,-,.__c
~..., _,
.-.-,---,r_.
m
,,.y
......w..-
. ~. _
r n
4 cut. In fact, no such clause is written in the procedures; it is merely the intent of the rule that it be followed without hesitation. Conflict or complexity or uncertainty of any source can introduce bestancy in the heat of a real event.
Integrating these ideas, the model of process control mistakes has the following char wdstics:
.1. Time is a de xadent variable; the probability of successful diagnosis or decision rnakmg (D&')) increases with available time. Available time is defined as the time from a clear indication for the need to act in a specified way until the time action would not produce the intended result (the point-of-no-return), minus the time it would take toimplement the dWaa-
- 2. Crew effects ar-aggregated, i.e., the failure probability ' estimates are for an anticipated crew,' such as in NUREG/CR-1278, Table 18-2, not for any individual.
- 3. Conflict, complexity, or other knowledge-based uncertainty is a prime influence on the reliability of a D&D performance. -His influence is explicitly factored. He presence of rules is explicitly factored.
- 4. Other influences, such as the quality of procedures, the adequacy of the instrumentadon and controls, and the adequacy of training, can be systematically factored into the quantification using SLIM, or some other subjective 3
j%-ant approach.
- 5. Slips are not usually dominant when D&D is necessary, and time is forgiving or multiple crew members will be present to notice and correct slips. In cases in which slips are judged to be significant, the simplified THERP approach can be applied to misactions and the THERP annunciator model (Chapter 11 of NUREG/CR-12278) can be applied to misdetections, if postulated.
- 6. Early, incorrect action based on inadequate D&D (sometimes also referred to as commission errors) is assumed to be correctable, in principle. The likelihood of the error is subsumed in the TRC value. Its effects are not modeled unless they would change the course of the sequence radically.
Mistakes are modeled by means of a family of lognormally distributed, time reliability correlations derived from the work cited previously. There are two pairs of curves in the family. One pair is to be applied to rule-based mistakes, i.e., misdiagnosis or faulty planning or 5
decision making when guided by the kind of rules specified above. One curve in this pair is to be used when hesitancy is not an important influence; the other curve is to be used when hesitancy is dominant. He second pair of curves is applied when general diagnosis must be-used to decide on a course of action in the absence of rules. His most often will be the case for recovery events. Again two curves are used to recognize hesitancy orits insignificance.
5-18
l '
Table 5-3 gives the probabilities for the four curves for several useful times. The curves are -
complementary cumulative distribution functions (CCDFs) oflognormally distributed response times. Each curre is mathematically charauW by a median response time, m, and a measure of uncertainty called the error factor, f (unrelated to human error). These parameters are indicated in Table 5-3 as <m,f> at top of the table. The carves are plotted on 1og-probability Table 5-3 Time Reliability Correlation Values General Diagnosis &
Rule-based Rule-based Recovery Time Recovery w/o hesitancy with hesitancy (min)
<4,3.2>1
<2,3.2>
<2,6.4>
<4,6.4>
5 0.4 0.1 0.2 0.4 10 0.1 0.01 0.08 0.2 20 0.01 0.0006 0.02 0.08 30 0.002 0.00006 0.008 0.04 60 0.00006 0.00002 0.001 0.008 1 <m,f> stands for A lognormal distribution with median response time of m and an errorfac:or of f.
paper in Figure 5-6 to render the curves as straight lines. The recovery curves have the same median response time and the rule-based curves also have identical medians. 'Ihe hesitancy curves have the same error factors as can be seen by their parallel slopes, as do the non-hesitancy curves. The details of the derivation of the curves are included in Appendix A.
The general diagnosis curve is a lognormal fit of the TRC used by THERP to apply to the diagnosis used to choose the approriate procedure. THERP did not include other curves, particularly for rule-based activity.
Lognormal CCDFs do not terminate at some lower probability, although probabilities that are intr.,M as human failure rates cannot meaningfully decrease without limit. The probability of unrecovered slips, even with multiple crew present, will serve as a lower threshold. That -
probability is on the order of 0.0000001 and is used as a border in Figure 5-6. It has become standard practice to truncate failure probabilities generated by TRCs at 0.0001 or 0.00001 or to 5-19
0.5 General diagnosis &
recovery with hesitancy General 0.1 diagnosis b
& recovery E
Rule-based
.o at.co 102 o.
2
.2 10-3 Rule-based with j
hesitancy 3
2 10'4 0
-5 10 10 10 1
5 10 20 30 60 100 Minutes Figure 5-6. Tune Reliability Correlations.
t truncate the available time at about an hour, as an intermediate screening process. Then only if a j
sequence event is risk significant and long term wil11ower numbers be generated.
The quantification system described so far depends on three factors: available time, the potential for hesitancy, and the error type. Other factors, such as the adequacy of the control room's instruments and controls, the applicability of procedures, the communication of the crew, etc.,
5-20
can influence the estimated probability of a human event. One way to factor in these influences is to use the Success T ikalihnad Index Methodology as an interpolation device. Each curve can be " adjusted" by success likelihood indices or a point estimate can be obtained by using such an index to interpolate between two curves in the family. For example, interpolation using SLIM can provide an estimate when hesitancy is of some significance level between negligible and dominant..
The SLIM process is based on the evidence from psychology that people are reliable in ranking j
and weighting factors related to familiar events. Using multiattribute theory, Embrey" synthesized a calculus to generate a SLI based on people's judged ranks and weights for influences on an event. The calculus is depicted in Table 5-4. De SLIis thenlogarithmically Table 5-4 SLICALCULUS
- 1. Choose influences appropriate to specific event and situation.
- 2. Rankinfluences as multiples of the least important for given situation, which is set to "10".
- 3. Sum the rankings of allinfluences and normative rankings to this sum, i.e., divide exh rank by the sum.
- 4. Assess each influence's quality, i.e., its position in a spectrum of possibilities from best (100) to worst (0). Note that " worst" means " worst licensable" not " worst conceivable".
- 5. Compute the " dot product" of the ranking and quality vectors.
- 6. Normalize this result, by dividing by 100.
- 7. His result is the success likelihood index (SLI) which can be entered into a technique that call for it.
proportional to the objective probability. The result is that a SLIM c*nlation requires a success likelihood index and two " anchor" probabilities that correspond to two known SLIs. There is no obvious way to generate the anchors, except in those unusual cases when data is available.
Thus, the TRCs can be used to provide the anchors. The next section provides an example of the use of SLIM with TRCs to produce point estimates of human events.
The two examples discussed next provide one event that is rule-based and the other that is a recovery event.
5-21
5.3.3.1 Feed and bleed. NUREG/CR-1278 includes an example analysis of the failure to use feed and bleed, i.e., high pressure injection primary cooling, to recover from a total loss of steam generator feedwater (pp. 21-1 through 21-14). This is an instance in which a recovery action was added to the B&W procedure that was to be used in case of a loss of feedwater. His was a fix, in about 1981, interim to the implementation of the B&W Abnormal Transient Operating Guidelines, which are rule-based in the manner described previously.
[
The qualitative andlysis in NUREG/CR-1278 is clearly incorrect.- Here is no reason to assume, as was, that operators will fail to notice that eregeucy (auxiliary) feedwater pumps fail to start, given a loss of main feedwater. Instead, the relisbility issue relates,to the. decision to give up on restoring secondary cooling (atleast as the first option) and to use feed and bleed. His decision presents the plant operators with a conflict, namely, using feed and bleedwill guarantee a long, costly shutdown and bring untold NRC personnel into the event followup. So the question is:
i how long will the crew delay the unpreferred opdon in trying to obtain the preferred option?
There are also plant-specific perturbations on this dilemma. Some plants, like Davis-Besse, have suspect feed and bleed capability, and plant operators may be unN1y to resort to feed and bleed even in a situation in which they should.n Other plants may have such highly radundant secondary feedwater systems that a total, unrecoverable loss is considered incredible by operators. The result could be that they delay feed and bleed initiation too long. Still other i
plants have relatively low reliability EFW systems but more than adequate HPI and their crews may actually be " feed and bleed happy", i.e., they may resort to feed and bleed too quickly or in inappropriate situations.~ All of these perturbations have been observed in actual plant settings.
PRA typically estimates that the time from the compelling signal for feed and bleed (loss of subcooling margin and initiation of a rise in core temsnue, according to most HPI rules) to the time of significant core damage is on the order of 30 to 60 minutes. The two recovery TRCs in Figure 5-6 give a range of failure probabilities of 0.04 to 0.008 when hesitancy is present and 0.002 to 0.00006 without hesitancy present. Ifinterviews with operators and operations staff reveal that hesitancy is not a problem for a particular plant, the TRC for rule-based action without hesitancy can be used. Otherwise, if hesitancy'cannot be ruled out but is not great, SLIM can be used to interpolate between the two curves.
i 5-22
e.
Assume thn in feed and bleed (F&B), the significant influences are identified in interviews with operations penannel to be:
- 1. the training awareness of the action (denoted as training),
I
- 2. the clarity of the pecek4 quidance relative to the act (procedure),
- 3. the belief that secondary cooling-auxiliary and main feedwater-f can be recovered (belief),
- 4. the lack of a direct indication of the need to act (I&C).
These are==m=1 according to the procedure listed in Table 5-4.
l i
Assume further that the influences denoted "I&C' and " procedure" are found to have least impact on the act, that " training" has 3 times the impact of these two, and that " belief "has 5 times the impactof"IAC" and " procedure". These are normali=iin the second column of Table 5-4. Finally, assume it is found that the quality of each influence, as measured by 100 for the best licensable and 0 for the worst licensable, is as in column three. (Note that " belief' in this context is a contraindicating influence, i.e., the stronger the belief in the recoverability of secondary cooling, the more likely not to use FAB.) The dot product is the sum in the fourth column and when normatiM yields a success likelihood index of 0.4. The results are listed in Table 5-5.
Table 5-5 A SLICalculation Influence Rank Normed-rank OnaHrv -
Product training 30 0.3 60 18
'xocedure 10 0.1 70 7
' belief 50 0.5 10 5
I&C 1Q.
0.1 90
.2 100 39 4
SLI = 39/100 -04 To obtain the two anchor probabilities, the data of Table 5-5 can be used. Suppose first that hesitancy is of negligible influence. Then the rank of " belief" would be zero (i.e., " belief'.
5-23 4
f
.y c.
. ~ - -
9
1 would not be in the list) and the ranks and qualities of the three other influences would remain-the same. However, their normed ranks would double, since " belief' made up 50% of the original total normed ranks. He dot product that zero hesitancy would yield is twice the sum of the other three influence products, or 68. Bus, the SLI to associate with this situation without hesitancy is 0.7. If hesitancy is dorninant among influences, on the other hand, then the dot product is solely the quality of" belief", or 10.' Thus, the SLI to associate with this situation with hesitancy is 0.10.
Putting this together, for 30 minutes, a SLI of 0.4 yields a failure probability of 0.0007. For 60 min, the failure probability is 0.0001. Dese values are quite optimistic compared to the values assuming dominant hesitancy,0.008 for 30 min and 0.001 for 60 min. If.the're were reason to assume that the feed and bleed " rule" really was not effective as a rule, as may have been the case for Davis-Besse, then the recovery curve with hesitancy could be used. In this case, the failure probability for 30 min would be assessed at 0.04 and at 0.008 for 60 min.
A residual issue is what to do with the other failure modes assessed for failing in feed and bleed recovery as depicted in Figure 12-2 of NUREG/CR-1278. These modes can be dismissed based on their low assessed probability. One exception is the dominant mode: failure to verify l
EFW pump start, assessed at a probability of 0.0016. However, since the example gives no credit for the Shift Technical Adviser nor anyone in the Technical Support Center, and because the loss of subcooling margin is so intimately associated with loss of EFW, this mode should be
&cyyed or the numbers that account for r~f= hey lowered.
5.3.3.2 BWST RefHl. Another event that can be identified in the PRA of a PWR is not rule-based. Many sequences, both LOCAs and transients, may evolve so that the ECCS is needed to maintain primary inventory and/or cool the core. Eventually the initial source of water
- referred to as the borated water sterage tank (BWST) in some plants - will deplete. Dere are two strategies to continue from that point. One is to depressurize the primary system and go onto decay heat removal (DHR) cooling (it is termed differently in different plants), which is a closed-loop system that recycles the primary inventory. This is the preferred option since it is self-contained and uses equipment in an alignment that is also used in other normal operational modes. The problem is to depressurize and cool down sufficiently fast that enough water is left 4
in the primary to use DHR. If this is not possible, e.g., for most LOCAs, then the crew can get water in a recirculation mode from the reactor building sump, a collector of water when lost from the primary system. If faults were to occur in the DHR or recirculation equipment (much 5-24 i
i of which is common to each function), then an alternadve recovery could be to refill the BWST with waterfrom otherinterconnectedsystems. The problemis thatthis recovery (1) is not specified by rule, (2) may take an hour or more to implement, and (3) its need may evolve without early indications.
One solution is to give no credit for recovery, a solution practiced in several PRAs. However, interviews with operators in some plants reveal that they are aware of the interconnections that would allow BWST refill and are aware that the implementation would take an hour or more.
Thus, they themselves do not consider the refill a viable option for LOCAs, because of the short time available in which to try to refill. However, for some variants of steam generator tube rupture (SGTR) scenarios, the time estimated in which the depressurization process can succeed is long, up to 12 hours1.388889e-4 days <br />0.00333 hours <br />1.984127e-5 weeks <br />4.566e-6 months <br />. Since depressurization is initiated immediately in response to an SGTR, this would give more than sufficient time to implement the refilt Moreover, the SGTR recovery strategy is to get to conditions that allow DHR as soon as possible, because-recirculation will not be available in an SGTR (the water being diverted out of the rupture rather than into the sump). As a result, DHR will likely be initiated many hours before the point-of-no-retum, in this case the depletion of the BWST and its initiation will" discover" faults in the DHR equipment in time to feed to the sump or refill the BWST.
The probability for this event can be estimated by using 1.0 as the upper value (i.e., a SLI of 1.0) and letting 0.008 (from the recovery with hesitancy TRC) represent a SLI of 0.9.
Assuming a SLI of 0.4 is computed for the event, the resulting probability would be 0.1; a SLI of 0.8 would yield 0.01. Plant-specific information would be required to compute a relevant SLL In any case, a means to assign non-unity probability to the failure of this and other recovery actions is available.
5-25
Babcock & Wilcox
%, % o, on a v::r : :: :a f 23:5 :: :: n- =:e-
=. : 5:n::335 April 8, 1987 f((? ail ~b-TPC-87-191 Mr.
E.E.
Froats Nuclear Project Management Engineer Florida Power Corporation Pest offic& Box 14042 St. Petersburg, F~i 33733 A :ention:
Mr. Rich Iwachow
Subject:
Trans=ittal of Requested ETW Reliability i
Calculational Packages
References:
NPMOOOO4/WA52/B&W Task 192
Dear Mr. Fronts:
Enclosed please find Calculation Packages 32-1125434-00,01,02; 32-1126041-00 and 32-1126985-00,01.
These analyses are censidered obsolete in that they do not reflect the current configuration of crystal River 3.
These packages relate to E=ergency Feedwater reliability' analyses performed for ??C.
Alse enclosed is an internal B&W memo from E.W. Swanson to J.E. Taylor that describes the purpose and limitations of the various E.~4 reliability analyses performed at B&W.
This memo is important in that it attenpts to describe the various analyses and assunpriens in an attempt to prevent the use of the results for. purposes other than those assumptions which are identified in the analysis.
i i
Please contact me if you have questions or if I may be of further assistance.
Very truly yours, L.M.
sniak Manager of Contract Engineering Nuclear Engineering Services I.ML:1s w/o attachment cc:
D E.
Porter R.J.
Finnin C.E.
Barksdale J.H.
Lander SUPERSEDED
d f
Utility Power Generation Division Babcock & Wilcox 1
J. H. TAYLOR, ENGINEERING SERVICES ew. 2asss.
e...
c......,
., File E. W. SWANSON. ANALYSIS ECHNOLOGY UNIT (26201 ANO. CR-3. 03-1. RS
- s. w..,
o...
AFW RELIABILITY MARCH 05, 1984
REFERENCE:
J. H. Taylor to Distribution, "AFW Reliability-Conversation With NRC," 02/29/84.
I have read your. letter, referenced above, and I have separately heard that the NRC is requesting or pressuring four utilities to add a third EFW pump.
0 It may be possible that the NRC is making a jucgement based on inadequate infomation and I believe that we may be able to provide some clarification of the situation to aid the owners group. The following is a discussion of the issue as I understand it.
Members of the owners group have sponsored two. separate reliability reviews of the Emergency Feedwater Systems, and I believe a good deal of confusion cxist: within the utilities, the MRC and B&W about the use of these eelia-bility reviews. Jim Lynch and I recently discussed these reports with FPC engineers and we found out that some mis-comunication exists between B&W, i
FPC, the NRC and NRC's consultant Brookhaven National Labs. The same con-fusion may apply at other utilities.
The first review was reported in " Auxiliary Feedwater System Reliability Analysis," BAW-1584, December 1979.
This review was prepared by B&W for B&W operating plants to respond to a NRC requirement for a review of all PWR plants to detemine the reliability of the EFW system. While B&W performed this study, the NRC staff performed a similar study for W and CE plants. To allow comparisons to be made, the NRC stipulated that comon assumptions about the miiability of some components be made and the NRC stipulated the nianerical values for those. assumptions (for exasple the EFW actuation logic was assigned an arbitrary failure rate value of 7 x 10 5/ demand). The numerical values assigned did not allow for plant-to-plant differences and in general oversimplified the review. How-ever, the assumptions did permit a comunon ground for comparison even though the reliability figums are unrealistic.
Furthennore, to ensure that the comparison could be made, a specific fonnat (bar chart) for presentation of the results was required. Thus a visual comparison was readily obtained for W CE, and B&W Plant EFW systems. The bar chart from BAW 1584 is attached; note that ntanerical reliability estimates were wat to be shown (I have pen-i -
cilled those in) but the results were to be presented in a " low-medium-high" fomat. BAW 1584 is now obsolete because of more recent plant changes.
If the NRC is basing current requirements for upgrade on SAW 1584, they may not be correct.
SUhiGEDED
_~
m
2-The second review was perfomed about li years later and was intended to be used as a cesign reliability evaluation to aid the design process for tne EFIC upgrade. Three plants, CR-3, ANO and RS were covered and resorted in three secarate reports, each submitted to the respective utility for their infor..ation and use as a part of the EFIC upgrade work..In addition to the EFIC upgrace, other EFW changes were also included in the analysis. These three reports did not make the oversimplifying assumptions required by the NRC fc - SAW-1584; for examole it would have been foolish and irresponsible _o assign the same simple numrical probability value to the EFIC actuation logic as was used by BAW-1584.
Obviously the benefits to be accrued by EFIC would not have been demonstrated.
In addition we did not present the results of -Jie study in the bar chart fomat recuired by the NRC for 3AW-1584; these three recorts were not intended to suo-plement the earlier study but were for design evaluation.
To give an idea of the results, however, I have shown the aooreximate imorovement to be expected by the upgrades (EFIC and other changes) on tne same bar chart. We were re-quested to do this by ANO and so those are calculated results (but not with the NRC's simplifying assumptions); the other two points shown are our uncal-culated estimates for RS and FPC.
The above gives background, now I will address my view of the confusion existing.
BAW-1584 is a " stand alone" document; it is obsolete and it should not be used to make current judgements about the design.
ne subsequent three reports were intended for design evaluation purooses and not as supplementary material to replace BAW-1584. However, each utility has provided their report to the NRC,,
. and the NRC asked its contractor, Brookhaven, w review the EFIC rwuurn. We do not know the ground rules for the review. We'believe, but do not know, that Brookhaven and/or the NRC misunderstood the purpose of these reports and thought their purpose was to supplement the earlier report BAW-1584. Our reason for this belief is that we received, through ANO, a copy of BNL questions which ANO asked us to answer. The major substance of the questions was the need to use both reporting famat (the bar chart) and the need to use simplifying assump-tions. The'latter would be incorrect, of course. We suspect, but do not know, that RS and CR-3, received the same (or similar) BNL/NRC questions; we have not been requested to review these questions, although recently FPC has discussed the EFW reliability report issue with us. And finally, NRC/BNL, has issued final reports of the reviews; they are critical but largely they reflect a mis-understanding of the purpose of the report.
Fundamentally, we think that the bulk of the EFW reliability material supplied to the NRC rests either in BAW-1584 (which is obsolete) or in the three EFIC reports. Since the three EFIC reports have apparently been misunderstood and misinterpreted by the NRC/BNL, they do not provide a good basis for judgement.
Therefore, we need to find out if the NRC's " third ptanp" pressure is based, at least in part on these reports or even on BAW-1584.
If it is, then I think the situation requirts clarification. The NRC should be advised of the purpose, content and accuracy of the information they have on hand, and the NRC should be required to clearly specify their intents and need for information to make EFW reliability evaluations. Finally, I believe the NRC's actions with these four owners should be consolidated with the USI for decay heat removal (A-45) and should consider plant reliability for decay heat removal that includes both AFW and HPI cooling.
i SUPERSEDED l
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. I suggest -J1at we followuc with the wners to provide any backgrounc ::aterial or clarification that ay be useful to them.
If-can ce af further help, p1 ease ca. :ne.
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References
~
1.
V. R. Sullive.n and.%n F. Polski. Data Fu-,arten of Liec see E': cet Re prem of M at F.
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13.
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[
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~
Interpretation &nd Sayeslaa
. L'pdating of Ealiability Data. Trsnasetion American Nuclear Society 32 (June 1979) 710.
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R. S. Enziana and J. E. tvneh. Inertency Teedsster Svmeem tSe ade Re-I liability Ansiv=1. f.r the C,v3 *.h l R:sc.r
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statius r-t: ::o a sadeock and wilcox co* Pan 7. Docu=eit t [2-11:5734-00 I.
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~ Reports o f ** -*g at t'.
F.
co---e r e t s i Nucles; F eve r
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CR-1205. EGG-EA-5.b. January 19ed.
i i 2.
Warren E. Hubole a=d Charles ? tiller. Data Su-- setes of ti:ensee Event Reaerts of "al"es at t*.
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i EUREG/CR-U65, ;GJ-EA-3125. Volures 1 throu;n J,.;u=e lido.
3.
J. F. Peloski and 7 E. Su111ran. Oaea Su-aries of 1*ee-see Event Re;* orts ef Stevel "e e ater= at t*.
S.
Cc-ere* al '.uclea r ?? er Plants. I;;;27.G/CR-U62. EGG-EA-5090, M. arch 1950.
l 4
Resete? **fe-Stufvt An Ammess-e.; of Acef der.T '.iske in ". S.
cot,eretal Ne: lear ?.-ver Flants. Appescix ;;;. 4A5n-1.CG. :it;AEG-75/014. Octot er 1973.
t 5.
Str ve, ef Tec1 Mr Detates. EFRI T7-754. Project 641 Tisal Report, April 19,6.
6.
TIEE cuide ce the cellectien and Prese-ratie-of !!ceeriesi, ricetrenic and S.n e in e A... c-t F.e11s:1.11 ata f or ' t'elea r ?cVer G* era e.
Stations, T m Std. 300-197,.
7.
J. W. Pegrs=, cc--!!stf or of Tailure Rare, fer ae * - tss a 't f e.a.t
- e
?. test ***~
Analyses Co--iiee t r:- Pue ; t ele Ava tist.1, g ure,,. 5shcock. & ".itltex Co=pany.
~
Buclear Fover Generatecu Divi.sion. I.ynchburE, Virginia. Septe=her 1975.
8 Nuclear Plane Relisb111ty Data Sysee:3, 1979 A==rual Repoets of Cu=ulative Systen and Co.=ponent Re. liability, NCREG/CR-1615. Septer.ber 1930.
9.
Military Standarditation Randbook. Reliability Frediction of Electronic i
i Equipment, 2C1.-EDE~s-217C. Depar._ent of Def ense, April 1979.
~
i
\\
10.
\\
~'i. l- ' g Report on Reliability Survey of Industrial Plants, Far:
12 Reliability 5
i of Electrical Equirnent. IEEE Co:=11ttee Report, 7" Transactiens on T-I
^-
Industry Applications, p. 212. Vol. IA-10. No. 2, !! arc 5/Apr11 1974.
11.
M. Enatyshyn, Rei taktlite Per*---- Re*ere fer T.-etraered %fa-v ' Pastures
~'-
. Actuation Systet 1 ;..7:7 t n t e s 1 and 6 Autor:s_tton Industraes, inc.,
4
- Vitao *abcratorats Division. Silver Spring Piaryland, M.sy 1979.
- f.,1,*,.
- '
-M
-jgp"
- 12. Resetor Preteetten M-* teat. Topical Report BAtt-10035P. Rev. 6. Rabcock &
'j
'.r "
Wilcox Euclear rever Generation Division. April 1979.
4 m.
A. D Swain and H. E. Gutt: san Esadbook of Human Reliability Analysis
{
~
13.
with E:2phasis on Nuclear Power Plant Applications (Dratt Repcrt)
NUREC/-CR-1278, Ceteber,1970.
.s -
\\
$5 i
I e
- C, Q" & C2 $ ;$ #
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)
I 32 (Jm 1979) 710.
f
.o 15.
S. Ah: sed. D. R. Fietcalf, and J. k. Pegram, t*ncertainty Prot agation in e'3 i
Probah11Jotic Risk Assess =ent:
A Comparative Study. ANS emi=1 2'.e e tin g.
~
ltiani. Florida. June 7-11. 1931.
- j i
jl R. S. Entiana and J. E. :.vr.ch. A*mjlj n. Teede.a r er te=ee- ' erad e Re-
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11a5111:v A stvets fer the bn-ho_ J.y-ne t.. r 4.,t.g A J
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statiei tr.1-m).1. sadco ce. an
' tis.x Cc=pany, pec.aens e y;;.11:5124-00
,1 April, 1951.
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s e
,s i
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3r
~
0 i
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d
? :.
- s:
a 1,
e
'r
- i..c '.
j i
Sjul* 5..
E
-a
.. 4
.4-j
\\
l h (a. -
g %.L..'.
W.
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.-e.
I
,e a
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" c tt :,.
r pu t
ac R
a.
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- ,,$a
- .
[, [.... MS -
- ~'
l 7
.r
.k.
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CALCULATICMAL N
i TO OSTAIM MEDIAN VALUE CF UMAVAILIM LITY
,l l
by l
~
Date R. Metcalf i-j
,7 Shahid A?sned I
-.e The generic fail re data is taken from data sources that do not take cg l t
t- (
account of specific olant data. For ernmie, in Table 1. the cor ponent
, j called battery is Itsted as havinc an upper beund of 1x10~6 failure per hour and a lower bound of 9.35x10-6 failures per hour. The estt:.ated v
4 sean re; air time is given as 232 hours0.00269 days <br />0.0644 hours <br />3.835979e-4 weeks <br />8.8276e-5 months <br />. If we assur.m the Ivwer bound i
is the 5th percentile value i.e.. '.5 = 1x10. and the upper bound as f
the 95th percentile value, i.e..
95 = 9.36x10-6 then under the assumption 4
{
of a lognoreal distrttution for the failure cate, the rnedian is obtained v
,{
u
, w
[ g
)q
( / AR f.7G+
~
r p
.r
.a i -
.h k
c
.i.
L i
t-
. C.
t-4 V
t.
..G h - '., e A corresponding value fo-unavailability is then comouted by I'
.g I
2
..f5,
I' q..
.?s.,, )g 'i' =
"J.Q X(J }.~,. y:) r 3
- O O' t
?
-where' Tis the seen time to repair to J p ji
-,-r-4 n
4 Note, in the table, a value of S.5x10 is listed.
.- C.
lI Y*
." f.?:. :
e
,e l fj 2.'
~.
A more exact method 17e obtaining the median unava11ab111ty is to use
?
l6 _
~
the plant specific data of ero failures in 68674 hours. This can be q
done conveniently through Bayesian update methods as discussed below:
.c L-q me"EDED" uw
\\
- -L-pg,~-._
_~
'L '*g
?-
J 2 - //2 4:o4/-oc f :..
O..
'% theorem for updating failure rate data takes the fom
' ~
,p
. e.'~ '.
-m
.w,.
cyJL(+ 1
?
r R.tlL(-7,.i)J A y
),
where C(i/1) = probability de9sity functi:= for A given the evidence I'
E. i.e. :ero fatturts in 66374 nours
,r-4(h/J) = the likelihood function, i.e. the probability of evidence t.
7 E given a particular failurs rate
,.I
%/ = The probability density prior to having evidence E.
[
Ed,/ lis often called t! e :csterior distribution and CU h,
is called the prior distribution.
i For rare event failure rate data, a convenient prior distribution is the 7
gasuna distribution given my y,o,,.4A k'
c g
G)) ~
I-y) le
?k' and for 4 failures in tire T, the likelihood function is often taken h
as the Poissen distribution given by f
6 //d 2,4*.~
4 t.
.r..
The parameters o*
and S in the prior distribution Eq (2). are deter =ined h'
t by solving the two ew ations g'
.A c j
Gal //l (4/
l[
i,
, g.S,
n..
.c dg t
-e ns
-7
. u: :-
).,p)).")
<ct
(
- .y.
.:;;.Q.
. as =
(
For-the specific case of the battery under study where p:
y.
N D.y l1*ii A,.'
v ?. I s' o
l j'{
.R ~s t h.
/*
M >
v.' :s.c iSy * * !fi'
/
- . S t. t / C
/.
Y I r o
~
I.l *
'S !
nee'
.g.
~
t'
.rUDc
' f-Q*s;e,::>47'Q7;%w u=.a.t' 7 g V.,.
r-c5
- - - _. _ _. ~ - _ - _. _... -.., _.
% l l
l I
. [
'd T.w-r c.' '.
<z g
^ Q, :. 4.. _=. g * %
'M rp-' ~ ~
_'z -- &_,.-
~--
I
,, - ~,, _
3
..4
.~:. u -
V'.
\\
,j
- ~. : 3
. ~.
- _f, c 1.,,
. :^-3 f:
y y
-._s
~~-r.
(
~
.3 2 1/ 7.4'O 4 l ~ 0 0 I
~ * '
n
'k l
j'.
'W
' 'f
~...
i Now to cbtain the posterior distribution. Eqs. (2) and (3) are inserted into Eq. (1) and the integral in the dencesinator is explicitly perfcM and;after sis:plification, yields the posterior distribution I
s h,,,. p. e Jr.; < I~I-
/
]
n j
s g J-
/1 C
( \\ la l g/ s.. s. )
l 4
t t
1
.I Mote that this is like the garr.a distributien in Eq. (2) excect i
f in EQ. (2) is replaced by J Jand '.s is replaced by s + d'. For the battery f
coe:ponent under discussion, we had zero failures in 68574 hot.rs, therefore, i
'rl k
At= 0 and T = 68674 and the posterior garr a distributien can l
a be written as A '.e '- !, - / N g ' $,.
W
=
ksl *
(*f.; */
'~
.q-
. h L
1 I
'3 e, ;, a $
where a
.s
.c.
.
- f
- g r
,e r/.;#::: 4. %/lY '. L
~
t
/;'.
- e r = b. u t >_
e gg
- c a
t i
Finally the median value for.4. i.e.. A is obtained by solving the g
"' )
equatica
'[
x 35
' #..- d'(,
d.'
.L i -
h Q, * /j a-
,3 d
. -. =
r...
3 a
O t"r.g T*
s, 4
y
~.
+...
~
s-
- g..
q, i
Thisvaluecfy50 obtained in E::. (8) is then cattipited by to obtain a median unavailability. i.e.
lc. '.
s:
N.
'y' h
T-J/
i 3
_ _._ m m ensa m SUygneutu
-,. ;J
~
a-
' '~~
'~
{4 31 //1Co4/-00
\\
.-m One sinole method to ebtain the plant specific median value for a
~
component unavailability is to plot the modified gs tsa distribution with parameters ' as4.I. such as shown in Figure 1. and obtain an
?
approximate median value frem the plot. The median value will divide the probability density function into dvo equal areas under the curve.
For the exa=ple under considention, we notice that the fait re rate 2
value of 30x10~7 divides the curve approximately into two halves. This k
number cultipitec by the rean tir e to failure i.e. 232 hours0.00269 days <br />0.0644 hours <br />3.835979e-4 weeks <br />8.8276e-5 months <br />, for the battery yields a median unavailability of about 3.5x10 quoted in Table 1.
l f
I 4
lt h,.
~
l
- =
O
.g g - e.'
I i*
._ j.
.w 4%
r e
'h
^ S.*%
i.'.' ' '
b.
- -.r
' ' ~
~
.g_
tt.
.j YI
.rEh 4
SUPERSEDE 7>
],
c s
1 h
--]. *.$
-.S? &:.Y YCl*h
~~
31 -1/ % d 4E*y C 5l
//
.c
{
g j
(j
~3
/. <.-
. CALC 1'LATICMA1. :"ET11005
~.,
)
s if-TO CSTAIN
' Y-
..~
M MEDIAN VALL'E OF ITdA'! AIL >SILITY i
by F1
~
Dale R. Wetcalf g
Shahid Ahned c
The generic fat ture data is tr6.en frm data sources that do not *.ska 4
account of specific ;1ar.: data. Fcr ext =;1c, in Tacle 1. the cce;onent
)
i called hattery is listed as i aving an upper beurd of 1x10-6,,g..,,
em$
per hour and a 1cwer bound of ?.3Ex1C~6 failures per hour. The esti..Ated 1@--
tean repair tic:e is given as 222 hours0.00257 days <br />0.0617 hours <br />3.670635e-4 weeks <br />8.4471e-5 months <br />. If.<e assu=e the loer *.>ound A _.
is the 5th percentile value i.e.,1 5 = 1x10. and the u:;er t*ound as the 95th percentile value, i.e.
2,ge = 9.36x10-6 then under tne assu:otion s-
' PR of a legnor=al distribution fer the failure -ate, the mectan is obtainea t-1
.as
]
f
}SJ
'\\ '
)4
-= [. 1 9,t.3" 4.7;.' 3'
= 500' 5
i
- =h.
i 7
W C
! F-55 - -
4
'.5-e
{,,
A c,rres;cnding value for uravailah1114 is then compu-d by C
~~%.-
~ ;-
?s*>.=
.l>. 7 -
2*. 7,,0.< / 0 7, S / f = 7 's 2' /d '
'..<3
~
1 y y
=
s q
A
! where T is the mean tice te reestr
.3
.~' " '.
k
+-
4 l
,. Note. in the table a.ah.e of B.Ex10 is listec.
y a
-q l.L E*d
=
.g f_
. A more e::act metbed fer :!.t2te.ta; the r.edian unavailability is tc use
'.3 i
h Il
- the plant specific *tsta of :ero failures in 63E74 hours. T"nis can be
'k s
E k
done conveniently through Cayesian update rethods as discussed belcw:
J
'.}
e e
l e.
2T
.;.Y~
. y,-
3
~.*
[
- 4
.. g.;.
y
$ i.
':*:. Mf(- mi.
'*" D f ' ~ 7,,; '
- '- w' -
lP.2.((
1 3
.3 2-//2Cd #/ - oO..
[,I.
g
-~~..
t.
J,....:..
~~
w.E 1 C 7 "' =
.. - A
- s g
,. p
. g, s
_ Bayes theorus for updating failure rate data takes the forse f
-s%~
. t s.;
cyn.(m) j.
~
~u
~
j f' 9 Qls I =
- i)
V 1. C.
-l.
f4*i.<)J.4 (y
_-l a
,2 l where
.;l CO;'C) = probability de tsity function for ' given the evidence
~[
j E. i.a.
Zero failures in 6d67.*. hours 4
+
f "
M.9} = the like11 heed 'unctien, i.e. the probability of evidence Q
E given a particular failure rate g.
f)',
h/ = The probability denstty prior to having eviden:e E.
f i I-fd[.;lis often called the posterior distribution and C 2; b
i,.. :.. '
is called the crior distributten.
s For rare event failure rate data, a convenient prior distribution is the k:
e
[
garria distribution given by g
2 (5 E,.o
.Ad r
h., _.
{')
$)
Y y.g.:
.t 4de I
h 7.'
and for E failures in ti.'e
. the likelihood function is often taken T
~~
Q, '.
as the Poissen distrioution given by f
4 g/, / --
3.)
g
't "2 -* 'y-u-
g4 g e
- r..
y',3 The parameters.4 and 8 in the prior distribution E; (2), are determined 5
w
,j-by solvieg the two ecuations 3
.,9 l fi-
..h
,4S s
!!b s"'l k' ~. 1
~ ~ i..%g'4..
Asc
.?
9
.J 1
t..:
'. - w n..-.-
,a
.u
(,
- 3 *=1
-*C
.-g.-.
s
(':.
-"N' ;f gI;)at
{
r. :'.
..c~.
s e 72&.;.. t -
,. e ~~;.ge.,.
~'
, ;f =
(gj
~
(
P(
,,t. i....
- ?.4".
E qD.W '
For-the specific ca e of the bat *.ary under study where 1
3'g.. y ggg --
l
~
i-l?
~
), r l YtY pp.a v C.I& N Id 2.
.x.
e s, n% %f h.
y u,
. b bp tY'
.%.e. K/
- N'
- g_
.w.:
.c
. it.;-
tw a*
r-
,f -- 6.
- t. :-
X!*
g.
SOPERSEUED
v
~~
g.
.e.
.... w.
n --
- .. ~< Q h
. -s.
~ Q_ g 4~'
2.
(2-
-+
~.. :....
, y
_~,
a, _.._
- }
9.. ~.,.
. __ g
~ ~
r-5
.T K - // 2 r,. e 4 / ~ C 6
~*
- ~?
'O' "~ ~ *
.. ~
Now to obtain the posterior distributton, Eqs. (2) and (3) are inserted 1
into Eq. (1) and the integral in the denominator is expli-itly performed i
and;after simplification,ytelds the posterior distribution
-,.1
- 1~ Y
(:.
,A a -r V'
~
?
\\ *[ } ~
frf e'.' J.)
- y l,
l t
I l
~
Mota that this is Itke the ge-ea distribution in Eq. (2) except
,5 l
.I I
- *Tand A is replaced by <+ i. For the battery
.. g in EQ. (2) is replaced by I
component under discusstor., w had zers failures in 68674 heurs, therefore.
~
r l
',K= 0 and T = 68674 ar/. the posterior gama distribution can be written as
?, - t[ /< !d
.e l
e
.,, 8 9
/
'1
,l.
V (t h ', = (' )~
j 1 '
M.-: 'i
,i j
y 4
m=-
- s. ;., 5 l _r.. -
,,nere..
>. j,',1jy.V *.*, ;
~
' ; f * *, * ** * ' ' ' '
_l
,. o G ' r '. <
r e
7~~
~
m,f
' );_.
Finally the median value for.4, i.e.. A is obtained by solving the
/
t j
g S -.
egnation g
c-i.,- e..
- a s.
l'.b.,
.r
('s>. < t '.
g
- 4 i
1
- 9 e
a
.d y ;
l 51 uw..
xm.
, S~a -
l z.
a
/ s.*.
L t
w.-
.a 1
f
,_~
e-Q:~
u.
~
t II ;.
l
's. ;
This value of ), g obtaired in Eq. (8) is then ruttipited by
4 to obtain a median unavailability, i.e.
l
. {.
LE
'f *
- l kN 6 '**v T
- -.,, j-
i 4,.,,,
.gg.
- - m ra.trm 4
dess g
l
= ~ ~m
. ~ --
Y A
d W-p j.
. r =4 M
'y g y
[ ?]'
-?
~
3 2.- //t g e ( /= dd
=
s
- ' ~ ~
~.
.y g,-
.,,=p P
.p *,
[.k l A.,... -
'2.
-~
'y [.
One simple eethod to obtain the plant specific median value for 4 I
8 1
+
)
component uvavailability is to plot the modified ganna distributton with i
1 parameters.s* and.'. such as shown in Figure 1. and ebtain an
)
t-approximata median value fro
- the clot. The redian value will divido i
the probability density function into two equal areas under the curve.
i i
i -
i I
For the exa=ple under ::nsideration. we nottce the: the failure rate l
value of 3Cx10 divides the curve approxinately into two halves. *his ngaber staisipited by the mean tire to failure t.e. 232 hours0.00269 days <br />0.0644 hours <br />3.835979e-4 weeks <br />8.8276e-5 months <br />. for the i }
battery yields a redian unavailahtitty of about 2.5x10 cuctsd in J
l Table 1.
i j,
I p.
w
$5
.a l
<e t
~-
.s 1
i
- i
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- 4 C I
. E!
j
.u~
-?
't c e --
~.
- y 9,q., e
. g. -
~':,$~t a:
r w,
.s.
.l t
~:
a
- l
~. :~..,
a..
v--
.g.
l.
l i
l I
i e
s
- 4. 0,-:. '.a
ggcagdEds,
+
- y l
l l
.I
~j i
. =
i 1
c
{
l
=r E
e 1
g
- = ;
5 f
i 5
5 5
e-a o
e 0 C h5 i
e s Cd la ~
44 3*
~v E
1
-.e 3t d
I e
=.: e e
..., n e w eierta m a e 7,,
1,,.,,
3,.'.P-20032A-6 (7-E-x m _ s... _ _ s..
..m.
c
.s g 2-7o 3 7 9 0 C, y,.,T
._ c_ L e. _ _
.iOTICE G'O RELEASE : ATE PA3E OCT 2 3 1931 37 d:
DART.*A:.</ TASK-3&W OOCLHENT NO.
DOCU.S.ENT TITLE
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REQL' IRE 3 NO.
COPIES INFOP?.ATION NO. ' COPIES INFOPFATICN NO. CDP!ES OISTRIBUTICN CDS ORN DOC COPIES CDS DRN DOC COPIES CDS DPJt. DC OR1*NIZATION OR TE INDIVIDUAL'S NA."E INDIVIDUAL'S NA.uE R.S. Endo,.(Rdo &, ;.. h.
TTL lohsle/
"ffe's>W.A-r%
/4/q(
on.
uni SUPERSEDED
l'4:?-20210-1 ( ;
3 '.
I C.c- _x-es :x.x - x:m:rn s=.
ll269F5
- o/
C.c_C.
3:
3e r.
re-r n a.e;5. Se rrr:
_e=, : r._-~m _u=. -1_2 mm _ =. rm. m-
_=:2.x.
_:a:2 =.:7.
- =
See ho E F iv R4t;o 67% Ae 4:a f < cps-1
??_?n z: at I N [ A i d./' R U" m - ez: ar
~
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