ML20246L186

Proposed Tech Specs to Incorporate Test Frequency Changes for Rosemount Analog Trip Unit Sys

ML20246L186
Person / Time
Site:	Brunswick
Issue date:	03/16/1989
From:	CAROLINA POWER & LIGHT CO.
To:
Shared Package
ML20246L184	List: ML20246L179 ML20246L186 ML20246L193 ML20246L198 ML20247B655
References
NUDOCS 8903230240
Download: ML20246L186 (30)

Text

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l ENCLOSURE 5  ;

BRUNSWICK STEAM ELECTRIC PLANT, UNITS 1 AND 2 NRC DOCKETS 50-325 & 50-324 )

OPERATING LICENSES DPR-71 & DPR-62 SUPPLEMENT TO REQUEST FOR LICENSE AMENDMENT }

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f 1

ENCLOSURE 7 BRUNSWICK STEAM ELECTRIC PLANT, UNITS 1 AND 2 NRC DOCKETS 50-325 & 50-324-

-OPERATING LICENSES DPR-71 & DPR-62.

SUPPLEMENT TO REQUEST'FOR LICENSE AMENDMENT 'l l

ROSEMOUNT ANAlhG TRIP SYSTEMS l

TECHNICAL JUSTIFICATION FOR CHANGING THE ROSEMOUNT ANALOG TRIP UNJJ .

l SYSTEM TECHNICAL SPECIFICATION TEST INTERVAL 'r l:

I i

1 9 .

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l l

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TECHNICAL JUSTIFICATION FOR CHANGING THE l

. ROSEMOUNT ANAIDG TRIP UNIT SYSTEM TECHNICALSPECIFICATIONTESTINTERVAL l .

e By J l' ON-SITE NUCLEAR SAFETT 1

l 1

. Principal Contributors:

'T. L. Brown M. A. Jones -

' December 24, 1986 '

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i J

CONTENTS Page

)

J i

EXECUTIVE

SUMMARY

1 BACKGROUND i

l 2 i BASIS l l

CONCLUSION .

3 (

)1

\

AFFENDICES l l

1. Surveillance Test Risk .

2. Trip Unit Failures i i

I i

j

, 3. Repeatability Data 1

]

. 1 j

Attachments: )

1. Licensing Topical Report (NED0-21617-A) . f

" Analog Transmitter / Trip Unit System For

• Engineered Safeguard Sensor Trip Inputs" I

(

2. Trip / Calibration System Model 510DU ,

(Instrument Manual 4247-1)

3. Consultant Review:

Energy Incorporated Report. December 10, 1986 C--------____-___________________e__________,__________

en . . .~ .. . s. .. _. . . .~_..#. . m ; .. . ..u... .m .

Encutivo Sunucary:

I Bec.puse of concerns expressed by Plant Maintenance and Operations personnel regarding the numerous and seemingly - unnecessary half screas. : half group isolations, and actual ECCS isolations due to

~

Rosemount Analog Trip Unit. surveillance, 'the ' Brunswick On-Site .

Nuclear Safety Unit undertook a study of these instruments (drif t and failure races).

The conclusions of' the study . are that a not reduction in risk (gain in ' safety) can be realised by increasing the surveillance interval on the Rosemount Analog Trip Units from monthly to semi-annually. ,

The basis of these ' conclusions is a study of the instrument calibration repeatability (over 6000 calibrations) and failurgs

-for over five years of operation on both plants for 192 trip units.

The study ~found..theseI-trip units -to.-be highly repeatable and to have auch lower. actual failure rates than assumed .in the design document (NEDo-21617-A) which provided Ehe basis for a monthly surveillance.

The study also qualitatively evaluated the iner, eased risk (half scrams, half group isolations and out of service " time for ECCS systems) due to the monthly surveillance test int erval . .

The study conclude s that the surveillance interval can be increased without a loss of availability.

In order to ensure the validity . of the methods and assumptions used, this study was reviewed by a consultant (G.L. Crellin, PhD -

of ENERGY INCORPORATED) for independent determination of 4 conclusions (See Attachment 3). The consultant's conclusions confirm the validity of the conclusions of this study.

e 1

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=--- 7 4 ,

.i Bru6swick Steam Electric Plant December 1, 1986 l

)

Background:

In the 1ste 1970's, General Electric Company investigated improvements in the design of the safety system instrumentation of WR's. This investigation led to proposed modificati'ons for operating plants to some instrumentation of the, Reactor Protection System . (RPS), Nuclear L

l- Steam Supply Shutoff ~ System.(NSSSS) and Emergency Core Cooling System (ECCS).. Licensing Topical Report IEDO-21617-A (See Attachment 1) is General Riectric's submittal to the NRC for justification of the design changes. NED0-21617-A was issued in late 1978 as an approved method to be used to allow improvements in safety. system ins'trumentation.

Based on past operating history and the benefits indicated in the design change ,(cont,inuous monitoring of parameters, improved testing procedures and capabilities, and improved operational ,

characteristics), the Brunswick Plant modified safety system instrumentation in the RP, NSSS and ECC systems. During the period of 1981 to 1984, the direct pressure and differential pressure switches that provided the inpu t. intgiligence to safety system logic were replaced with the Rosemount transmitters and the Rosemount analog trip system (Model 510DU) . l During ' the pas ~t five years of operations of the Rosemoun't Analog Trip l System, observations ande by both Maintenance and Operating personnel indicated the followings i

1. The system is reliable (very low failure rate).

2. The system is stable (requires little, if any calibration).

1

~

w_-________--_---__-__-_____-_______ _

J Dmis:

Based on the demonstrated reliability and stability of the Rosemount Analog Trip System it becomes apparent that the current monthly test as required by Technical Specifications and established by the design justification (NEDO-21617-A) is unnecessary and contributes adversely to the following areas related to safety: .

1. Large number of half scrans taken for testing (288/ year).

(See Appendix 1).

2. Large number of , half group isolations taken for testing (912/ year). (See Appendix 1).

3. Increased out of service time for safety systems (e.g., HPCI and RCIC). During' testing systems isolate (192/ year). (See Appendix 1).

4. Increased stroking of valves inside the drywell 'which may result in increased drywell leakage and potential valve j failures.

5. Higher potential for personnel error during testing.

As indicated 'in NEDo-21617-A, only the failure rates within the trip units and trip relays need be considered in determining the test interval. Specifically, the sua of the essential non-annunciated failure rates of the trip units and the trip relays is required to I

determine the overall system test interval.

Actual failures and failure rates (See Appendix 2) of the Rosemoun't -

Analog Trip Units (Model 510DU) experienced during the past. five years of operation, spplied to Figure 3-12 (Plot Locus of Equation 3-2) of .

~

NEDO-21617-A, indicate that a test interval in excess of six months could be use,d and still maintain an exceptional availability of -

. 0.9999.

Rosemount nnalog Trip System stability over the past five years supports an increase in test interval. In a sample of 6,177 of approximately 7,400 monthly calibration surveillance test results- (see Appendix 3), 96% fell within manufacturer's trip point repeatability specifications.

4 2

e

1 q

Conclusion:

Increasing the present monthly surveillance test interval to a six month test interval would provide the following:

o Exceptional System Availability of 0.9999 with simultaneous testing.

o Reduction of number of half scraas taken for testing (reduced from 288/ year to 48/ year). (See Appendix 1).

o Reduction of half group isolations taken for testing (reduced from 912/ year to 152/ year). (see Appendix 1).

o Reduction of out of service time for safety' systems (e.g. ,

HPCI and RCIC). , (Isolations reduced from 192/ year to 32/ year.) (See Appendix 1).

o Decreased stroking of. valves inside the, drywell.

o Lower potential for' personnel, error during testing. -

Justification 'for this change in test interval frequency is demonstrated by the operating chexacteristics of the Rosemount Analog -

Trip System over the past five years and the benefits related to l safety that will be ' gained.

. l O

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0 e

3

> .- ., . . . .. q f

Appendis 1 l

SurheillanceTestRisk 1

i A review of the forty monthly surveillance tests that cover the 192 Rosemount Analog Trip ' Units involhed in this study was_ conducted to identify testing occurrences that adversely affect safety. The following items were calculated with the assumption that both Brunswick Units. would be in operational condition one for the period specified: I L

. 24 half scrams are generated each month.

288 half scrans are generated annually.

. 76 half group isolations are generated each month.

912 half group isolations are generated annually.

. 16 RPCI and RCIC system isolations are generated each month (these systems are out of service a total of approximately 8  ;

1 i

hours a month for these tests). i l

.192, HPCI and -RCIC - system isolations are generated annually

~

l (these systems ar'e out of service a total of approximately 96 hours0.00111 days <br />0.0267 hours <br />1.587302e-4 weeks <br />3.6528e-5 months <br /> a year for these tests).

. 82 initiation or permissive occurrences are generated - each I month. l 984 initiation or permissive- occurrences are generated annually.

Surveillance testing on a six month frequency would change the above occurrences as follows:

. Half scrams reduced from 288 per year to 48 per year.

. Half group isolations reduced from 912 per year to 152 per ysar. v

. HPCI and RCIC system isolations reduced from 192 per year to 32 ,

per year (system out of service time reduced from 96 hours0.00111 days <br />0.0267 hours <br />1.587302e-4 weeks <br />3.6528e-5 months <br /> per year to approximately 16 hours1.851852e-4 days <br />0.00444 hours <br />2.645503e-5 weeks <br />6.088e-6 months <br /> per year for these tests).

. Initiation or permissive occurrences- reduced from 984 per year  !

! to 164 per year. ,

1  !

Appsndix 2 Trip Unit Failures o Sources of Failure Data Failure data for the Rosemount Analog Trip Units was compiled in the following manner:

A search of the Trouble Ticket / Work Order system to identify 4

failures of the Rosemount Analog Trip Units, and a review of those f ailures identified agnifst Stores issue records was completed.

The WOTS (Work Order Tracking System), RECO (Records portion of AQUARIUS / STAIRS), AMMS (Automated Maintenance Management System)  ;

and the CHMS (Corporate Materials Management System) computer data bases were queried for failures of the Rosemount Analog . Trip Units.

. Searches were conducted on equipment identification numbers, keywords related to equipment / failures, and by part numbers.

. Trouble Ticket / Work Orders identified were reviewed via the microfilm system and those tickets identified as failures of the Rosemount Analog Trip Units were compiled. (See Page 4 of this appendix.)

~

.' Stores issue records of Rosesiount Analog Trip Units was used to verify identified failures.

. Failurgis were classified as per NEDO-21617-A into the I following categories:

' Detected Nonessential Failures (DNF)

Detected Essential Annunciated Failures (DEAF)

Undetected Essential Nonannunciated Failures (UENF)

(See Page 4 of this appendix.)

. A review to ensure that the actual number of failures of the Trip Relays used in the Rosemount Analog System did not exceed the failure race value specified in NEDO-21617-A was conducted.

1

v. .: . - -

-)

I Seven Trip Relay failures would have had to occur to exceed the failure race value as specified in the NEDO-21617-A.

Maintenance Trouble Ticket / Work Order reports indicate that .

one trip relay was installed for. troubleshooting purposes.

(Woik Order 2-E-84-1758) . The relay removed from service was functional and had not failed.

Note: The consultant used this relay replacement as. a failure in his calculations. (See Attachment 3)

Stores records ihdicate that two other relays vers issued but not installed If all relays i'ssued were considered as failures we would have an actual failure rate 50% less than the failure rate specified in NEDO-21617-A. The conservative failure rate 4 value for the Trip Relays used in the Rosemount Analog Trip Systes,as specified in NEDO-21617-A is used in this study.

O J o Sources of Hours of Operation

]

The hours of operation for. the Rosemount Analog Trip Units was )

1' compiled as follows:

. Review of Plant Modification information with the engineer responsible for installation provided specific dates as to )

when each Rosemount Analog Trip Unit was placed into continuous service.

. The last calibration data recorded for each Analog Trip Unit in the Calibration History Data Base was used as .the end .

period for'this determination. '

. Calculation of the number of days between th'e initial in-service date and the last calibration date recorded was completed for each Analog Trip Unit in this study. .These figures were then converted to hours of operation and totaled for use in calculation of failure races. (Ske Page 4

~

of this appendix.) -

2 iin .r

o. Sturces of Friluro Rata .

.]

Point estier.as of the actual . failure rates per million hours of operation (A*) exhibited by the . Rosemount Analog Trip Units as described in NEDO-21617-A were calculated using methods described in IEEE Std 352-1975 and the results of the Failure and Operating l Hour reviews. (See Page 5 of this appendix.)

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1 ROSEMOUNT ANAIDC TRIP UNITS (MODEL 510DU)

FAILURES AT BSEP 1 Trip Unic Work Order Date classification

1. 1-321-PTS-N023D-2 1-E-82-1645 04/19/82 DEAF *-

2. 2-321-PTM-N015A-1 2-E-82-3010 07/15/82 DEAF *

3. 1-321-FDTM-N008A-1 1-E-85-2043 06/03/83- DENF*

4. 2-521-LTM-N031A-3 2-E-83-2542 07/04/83 DEAF *

5. 2-B21-LTS-NO313-3 2'E-84-1758 03/19/84 ,

DEAF *

6. 1-R21-LTM-NO36-1 1-E-84-1948 04/17/84 DNF*

2-E-84-6236 10/20/84 UENF*

)

7. 2-B21-LTM-N017D-1

8. 2-321-FTS-N023A-2 2-E-85-2441 05/10/85 UENF*

9. 2-B21'-PTS-E023A-2 2-E-85-2466 05/11/85 DEAF *

10. 1-E51-FDTM-N018-1 1-E-85-4615 10/08/85 DEAF *

11. 1-E51-FDTS-N018-2 -- 21-E-85-4615 _ . __10/08/85. . DEAF

• l l

I

12. 1-E51-PDTS-N018-2 1-E-85-4687 10/13/85 DEAF *

13. 1-B21-PTM-N023D-1 1-E-85-5211 11/05/85 DEAF *

14. 1-521-LTS-N031A-3 85-AMPG1 12/29/85 UENF*

• DNF = Detected Nonessential Failures .

• DEAF = Detected Essential Annunciated Failures

• UENF = Undetected Essential Nonannunciated Failures TOTAL OPERATING TIME IN -BOURS 70R THE BDSEMOUNT , ANAIAC TRIP SYSTEM: 6,467,784 4

(

I PLANT FAILURE RATES:

Estimate of mean failure rate n = failures

[ = r. n

.T' = hours of operation

~

k = Nonessential failures + 1 = .155/million hrs.

A -

6,467,784

' = Essential annunciated = 9 = 1.39/million hrs.

B failures 6,467,784 h = Essential nonannunciated = 4 = .618/million hrs. -

C failures 6,467,784 ,

W 9 -

h Trip Units = .618 +d Trip Relay = 1 = 1.61'8'/million hrs.

Q C ,

Total .

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x, ;.. _ _ _.

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.. .. r m- m Appendix 3 Repeatability Data i

The previous appendix concentrated on failure data. In this appendix, the concentration is on the drif t or repeatability 'of the instruments.

Operating history of the Rosemount Analog Trip Unit System was.  ;

reviewed to see if it tended to . support or confirm the stated l manufacturer's specification for Trip Point Repeatability as p,er Reference 1 of NEDO-21617-A. (See Attachment 2) This was accomplished by reviewing past calibration data. l o~ Sources of Data Calibration data for the Rosemount Analog Trip Units was compiled in the following manner:

. 1 Approximately . 7.400 calibrations haveL been conducted since the Rosemount Analog Trip Units were installed. Copies of these are maintained in the microfilm system. Of the ' total number of calibrations conducted, 84% (or 6.177 data s,e ts) were still available in hard cop'y form in Maintenance calibration folders (for egnvenience, the hard copies are purged as storage is needed, even though they have already been microfilmed). It was.

determined , therefore, that only the hard copies of the calibration sheets need be reviewed as they represented a sample size larger than necessary to lend credence to a statistical analysis of the results. -

Calibration data from the hard copy sheets was entered for each of the Rosemount Analog Trip Units in ascending order by dates.

The breakdown of data is as follows:

. 2.757 (71% of the approximately 3,900) calibrations were for '

Unit One instruments.

1 .

m ,

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. 3,420 (98% of tha cpproxt:zetoly 3,500) es11brctions wero for I

Unit Two instruments.

, . Note that although Unit One Analog Trip Units have been in s

servi'c e tihe longest, . hard copy file storage constraints for these working calibration folders necessitated purging some of the folders so as to maintain the past few years of data sheets for review. (Those purged are still retained on microfilm.)

o Data Gaps In assembliing the data base of the Rosemount Analog Trip Unit calibrations, a review was conducted to determine what gaps or

- discontinuities existed in the information by date. The results of this review were as follows: -

. Of 512 gaps identified in the data 329 (64%) were related to unit ' outages. These tests are not normally required during outages and/or when fuel has been removed from the vessel.

~

68~(13%)~ warr related- combe - removal--of -dat'a- from the- - - - - -

-~

Unit one calibration folders for storage constraints.

. 115 (23%) were identified as data sheets apparently microfilmed but not retained in the maintenance files.

It was determined that the presence of these gaps is not consequential,to the resultis for two reasons: (1) the significance .

of the sample size, and (2) the analys,is discussed below shows that 96% of the sampled surveillance (6,177 monthly surveillance tests) tes t results fell within the manufacturer's specification for trip point repeatability. .

o Data Base The assembled calibration history data base was therefore determined to be adequate for review of the drif t and setpoint repeatability of the Rosemount Analog Trip Units , installed based on the number of calibration data sheets recovered (84%) and the review of the gaps in the data entered.

I 2

r. N . , .

n. . z: ..  :: ..: . .... .

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l

)

o Repeatability Note: Data sets for each Rosemount Analog Trip Unit were. compared for setpoint/ trip point drift tiy computing the absolute value of drif t in mil 11 amperes from one calibration data se t to the next. This was completed in ascending order by comparing the as-lef t value of the previous data set to the as-found value of the next data set. .

i

,A . review of the data base was conducted to verify that the Rosemount Analog Trip Units performed within the manufacturer's specification for Trip Foint Repeatability as per Reference 1 of 1EED0-21617-A (see Attacliment 2). The most stringent tolerances for normal operating conditions and normal environment were applied to the data base (+ or .13% of span for Master Trip Units and + or

.20% of span for.8 lave Trip Units) with the following results:

. 96% of the 6.177 monthly surveillance test results fell within the manufacturer's specifications for trip point

. Review of the distribution of data indicates a normal i

1 distribution around an average drift value of -0.000959 mil 11 amperes. .

. Over their operating histcry, the Rosemount . Analog Trip j Units have exhibited a slight driit in and around their setpoint, staying well within I the manufacturer's specifications. In fact, approximately 2,400 calibrations

'showed zero mil 11 ampere drift in setpoint values.

o Conclusion ,

The results of the calibration data- review supports- the performance requirements for trip point repostability for the Master and Slave Trip Units specified in Reference 1 to NEDo-21617-A.

m. , . .

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)

Enclosure 4 To Serial: NLS-87-023

" Review of the Rosemount Analog Trip Unit Justification for Test Interval Frequency Change"

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(51248AT/bac) i

'/

Review Of The Rosemount Analog Trip Unit Justification ForTestInterva FrequencyChange l

Prepared by ,

Energyincorporated l Principal investigator: G. L Crellin 10 December,1986 I

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1 Prepared for Brunswick Steam Electric Plant Carolina Power And Ught Company e

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h (L/ J l 4 C/Q D A w__-__________-___________-__--_==_=_______________. - _- _ _- _ .__ _

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I. Summary At Carolina Power and Ught Company's request, Energy incorporated has reviewed the draft of a justification for a test interval -

change for the Rosemount Analog Trip Unit System at the Brunswick Plant, dated 14 October,1986.

The initial review generated comments that, briefly summarized, are as follows:

• The report appears to be technically correct. The availability of 3 the trip analog unit system.is based upon the same relationships employed by GE in their licensing topical report NEDO-21617-A,-

December 1978. Thus, the' appropriate' system availability model is technically acceptable by reference and precedence. In addition, NEDO-21617-A employed the methods for establishing-a test interval that is presented in the IEEE Guide for General Princioles of Reliability Analvsis of Nuclear Power Generatina Station Protection Systems (IEEE-Std-352-1975). This approach, being derived from established industry standards, is l thus founded on a credible basis and appears to be- J l appropriately used. I

• The justification thus rests principally on those data establishing that the failure rates are indeed much better than conservatively presumed in NEDO-21617-A for setting the test interval. GE anticipated lower failure rates would be demonstrated eventual!y, but initially followed a p;cdont course. Because of the importance of the supporting data, it was suggested that CP&L clearly explain the sources and rules for counting failures and operating time.

• lt was also recommended that the justification document more explicitly address and substantiate the improvement anticipated in decreased risk from half-scrams, half-group isolations and out .-

of service time for ECCS systems due to the current monthly test interval. .

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• The original failure rate' estimates were point estimates

'(maximum likelihood). It was recommended that upper l confidence interval estimates be used. This report discusses and presents both classical and Bayesian confidence interval estimates and shows the resulting availability for a semi-annual test interval.

As a result of the review, and the confidence interval calculations of this report, it is concluded that the data substantiate an increased test inte.rval while achieving or exceeding the desired level of system availability as indicated by NEDO-21617-A.

I 1I. Availability Model The trip unit system logic is established in NEDO-21617-A to be (1/2) x 2. A system with such logic has probability of failure within a time t of l

P(t)'- 2 Ar t2 , . .,

_ggy ,3) when At is small (gene, rally less than 0.05), and testing is simultaneous. -

1

- The average unavailability for a test interval, e, is the ratio of the expected time in the failed state (dudng the interval) to the interval.

Thus,

.6 (II - 2)

An"O'O P(t)dt - h(10)2 This approximation is that' cited in NEDO-21617-A and IEEE-352-1975 as applicable to (1/2) x 2 logic for simultaneous testing. It will be used to assess the unavailability of the trip unit system for the demonstrated failure rate.

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i III. Classical Confidence Intervals The classical ispper bound confidence interval for a failure rate, l when the data have been time truncated as for CP&L, is achieved by finding a failure rate that gives a probability of more failures than observed equal to the confidence level. This can be shown to be Cu=1- M* . (III - 1) l l

This can be shown equivalent to a Chi-square statistic (see for

. Instance reference 1, p.68 and p.181, or reference 2) which allows the upper interval to be determined as:

%!.e.n le= T (III - 2 ) 1 l

i l

where T is the total operating time and n = 2k+2 degrees of freedom.

Chi-square values are given in Table I.

Table II summarizes the revised failure data. These data are used in Table III which shows the upper 90% confidence interval (C = .9) for various combined failures. The table also shcws the achieved unavailability for leo assuming a test interval of 1 month ,

(730 hours0.00845 days <br />0.203 hours <br />0.00121 weeks <br />2.77765e-4 months <br />) and semi-annually (4380 hours0.0507 days <br />1.217 hours <br />0.00724 weeks <br />0.00167 months <br />). In effect, these may be thought of as 90% confidence intervals on the unavailability.

Thus, Table III shows that even with all failures counted, k = 15, an

~

interval of 4380 hours0.0507 days <br />1.217 hours <br />0.00724 weeks <br />0.00167 months <br /> will provide an unavailability of An = 137.9 x 10 e. That is, there is a 90% confidence that the availability is at least An = .999862 = 1 - An. Using only the essential nonannunciated failures and the relay failure (k = 4 + 1 = 5) gives-An = .999973'at 90% confidence.

l 4

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.. a 7  !

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These values are equivalent to the desired availabilities stated in NEDO-21617 A. Thus, based on the classical upper confidence interval, we conclude that the data substantiate increasing the test j interval.

IV. Bayesian Confidence Interval I The Bayesian Confidence Interval arises from the Bayesian process in which prior information is admitted with the data. Formally, it is not a confidence bound, but a probability interval. However, as shown in reference 2, it can be viewed as analagous to a classical confidence interval for which the prior information is admitted as

" pseudo data" The posterior upper bound probability interval is: j P(1,) = e dA=Cu (IV - 1)

'O r' a k) where the prior information is characterized by a gamma distribution.

This function is equivalent to the Chi-square and thus the Bayesian

. upper bound can be found from

%!.c.n Ac"2( +T) (IV - 2) where T is the operating time and n = 2k + 2a degrees of freedom.

Thus, posterior upper bounds may be so determined once the

)

pseudo data (a and p) are determined.

The parameters are determined with the intent of characterizing

.. the prior information as presented in NEDO-21617-A. In that document, the failure rate (for the slave trip unit with the relay) is predicted by MIL-HDBK-2178 methods and data to be 31.96 x 10-6 failures per hours.

5

y- ,. , ,

This approach, as is stated in the NEDO, is generally considered -

. to be conservative. in addition, information is offered that suggests

, that the failure rate could reasonably be as low as 3.196 x 104 These values are thus employed as approximating a 90% bound and a 10% bound, respectively. By using equation IV - 2, with k = 0 '

and T = 0, suitable values of a and p are found. The following i illustrates the approach.

Select a = f such that n = 3 degrees of freedom. For n = 3,

%.t o = 6.251 (see Table I.) .

2 Thus, since 1,'m

= E2M 2 x 31.96 x 10,, = 97794 hrs.

2$

%

• 4 As a result,ho = -=-31.96 x -10 - andi - - - -

2

'*** 4  !

.= 2.99 x 10 lo= 2s i

l This is deemed close enough to the prior information, so a = f and p = 97794 are acceptable as suitable pseuca data.

Note, the abov6 failure rates for a test interval of 730 hours0.00845 days <br />0.203 hours <br />0.00121 weeks <br />2.77765e-4 months <br /> translate into the following availabilities:

Ango = .99964 Anjo =.999997

. Table IV shows the 90% Bayesian Confidence intervals for the data summarized in Table I. The calculated failure ' rate bounds are slightly larger than the classical. Even with this increase, the -

a demonstrated failure rates are more than adequate to allow an ,

increased test interval.

a 6

_ _ _ _ _ - _ _ ________-______--______=__________ _ _ _ _ _ _ _ _ _

k Table IV shows that even with all failures counted (k = 15), an i interval of 4380 hours0.0507 days <br />1.217 hours <br />0.00724 weeks <br />0.00167 months <br /> will provide an unavailability of j

~An = 141.1 x 10-6. That is, there is a 90% probability that the availability is at least An = .999859. More appropriately, using only the essential non-annunciated failures and the relay failure (k = 4 +1

= 5) gives An = .999971 at the 90% level. As the original NEDO-21617-A based its selection on essential non-annunciated modes of failure, it seems most appropriate to use the latter value.

V. Conclusion The original selection of a 730 hour0.00845 days <br />0.203 hours <br />0.00121 weeks <br />2.77765e-4 months <br /> test interval appears to be based on having an availability of 0.999 at a high confidence and  !

with an anticipation of achieving 0.9999. The observed data indicate i a high confidence (both classically and Bayesian) that for worse case l

. failure counts 0.999 can be achieved with semi-annual testing. . l

-- - . Furthermorerrealistic. failure counting.would. indicate _that.0.9999 is . .. .___ _.._ - l achieved with high confidence. This, thus, represents a substantial-improvement over the original conservative interval selected.

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1 Table II Failure Data i

Nonessential Failures = 1 T = 6,467,748 hrs.  !

Essential Annunicated Failures = 9 T = 6,467,748 hrs.

l Essential Non-Annunicated Failures = 4 T = 6,467,748 hrs.

- Trip Relay Failures = 1 T = 6,467,748 hrs. l

./ 4 1

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Table III

]

-Classical I i

Simultaneous Test '

Unavalabity 2 (per106)

Failures Degrees T A90" 'f7 0=730 0-4380 l (k) (n - 2k + 2)  %.2 1, n (106 hrs) (per106 hrs) (hrs) (hrs) 1 4 7.7779 6.467784 .601 .129 4.23 4 10 15.987 1.236 .543 19.4 5 12 .549 1.434 .731 26.3 9 20 28.412 2.196 1.714 61.7 14 30 40.256 3.112 3.441 123.9 15 32 42.479* 3.284 3.831 137.9

• Determined from %.1, n " 2 {i90 + 20*l} "2[l*20+ 211-1] for n > 30.

9

, . . .. . . . .... , , ~ .. : 2. . ;.

Table IV Bayesian Simultaneous Test 2

W 4

'(per tos) x A90 Failures Degrees 2 = 2(p +T) e = 730 - e=4380

.M - (n = 2k + 2a)*

.1, n (@ +T)* (per10s hrs) (hrs) (hrs) l 1 5 9.236 6.565578 .730 .176 6.327 4 11 17.275 1.316 .615 22.14 5 13 19.812 1.509 .809 29.11 9 21 29.615 2.255 1.807 65.05 14 31 41.316t 3.146 - 3.517 126.62 15 33 43.639t .

• 3.323 3.924 .141.13 -

l

• From selected prior distribution, a gamma distribution with a - 3/2, S = 97794.

t Determinedfrom % . { [tgo+ 42n - 1 ] = { [1.28 + V2n - 1 }* for n > 30. ,

1 1

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j References

1. Mann, N.R., Schafer, R.E., and N.D. Singpurwalla, Methods for Statistical Analysis of Reliability and Life Data, John Wiley and Sons, Inc,1974.

2. Ballard, B.E., and G.L Crellin, " Quality Confidence of infrequent Preventive Maintenance", Proc. of the American Society for Quality Control,11th Annual Energy Division Conference, Sept.1984.

i 1

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