ML20215L757

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

ML20215L757
Person / Time
Site:	Brunswick
Issue date:	12/10/1986
From:	Crellin G ENERGY, INC.
To:
Shared Package
ML20215L691	List: ML20215L687 ML20215L724 ML20215L741 ML20215L757 ML20215L780
References
NLS-87-023, NLS-87-23, NUDOCS 8705120362
Download: ML20215L757 (12)

Text

Enclosure 4 To Serial: NLS-37-023

" Review of the Rosemount Analog Trip Unit Justification for Test Interval Frequency Change" yyDIfdh 3

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Review Of The Rosemount Analog Trip Unit Justification For Test interval Frequency Change Prepared by Energyincorporated Principal Investigator: G. L. Crellin 10 December,1986 4

Prepared for Brunswick Steam Electric Plant Carolina Power And Light Company l

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p I. Summary At Carolina Power and Light 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 availablility of 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 Princiales of Reliability Analysis of Nuclear Power Generatino Station Protection Systems (IEEE Std 352-1975). This approach, being derived from established industry standards, is thus founded on a credible basis and appears to bo appropriately used.

• The justification thus rests principally on those data establishing that the failure rates are Indood much bottor than conservatively presumed in NEDO 21617 A for settin0 the test interval. GE ant!cipated lower failuro rates would be demonstrated eventually, but initially followed a prudent course. Because of the importance of the supporting data,it was suggestod that CP&L clearly explain the sources and rules for counting failures and operating time.

• lt was also recommended that tho justification document more explicitly address and substantiato tho improvement anticipated in decreased risk from half scrams, half group Isolations and out of service timo for ECCS systems due to the curront monthly test Interval.

2

The original failure rate estimates were point estimates (maximum likelihood). It was recommended that upper 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 interval while achloving or exceeding the desired level of system availability as indicated by NEDO 21617 A.

II. Availability Model The trip unit system logic is established in NEDO 21617 A to bo (1/2) x 2. A system with such logic has probability of failuro within a timo t of P(t) = 2 A t22, (g;,3)

I when At is small (generally loss than 0.05), and testin0 S simultaneous.

The average unavailability for a tost interval,0,is the ratlo of the expected timo in the failed state (during the interval) to the interval.

Thus,

.0 An = h'O P(t)dt - f(A0)2 (11 - 2) l This approximation is that cited in NEDO 21017 A and IEEE 352-1975 as applicable to (1/2) x 2 logic for simultaneous testin0. It will be used to assess tho unavailability of tho trip unit system for tho demonstrated failuro rato.

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III. Classical Confidence Intervals The classical uppor bound confidence interval for a failure rate, 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-(III ' l) d d=0 This can be shown equivalent to a Chl square statistic (see for instanco referenco 1, p.68 and p.181, or reference 2) which allows the upper interval to bo datormined as:

Ae" (III 2) where T is the total operating timo and n = 2k+2 degrees of freedom.

Chl squaro values are glvon in Tablo I.

Tablo 11 summarizos the revised failuro data. Those data are used in Tablo !!! which shows the upper 90% confidenco interval (C =.9) for various combined failuros. The table also shows tho achloved unavailability for loo assumin0 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 offect, those may bo thought of as 00% confidenco intervals on the unavailability.

Thus, Tablo III shows that oven with all failuros counted, k = 15, an interval of 4380 hours0.0507 days <br />1.217 hours <br />0.00724 weeks <br />0.00167 months <br /> will provido an unavailability of 3n = 137.9 x 10 6. That is, thoro is a 90% confidenco that the availability is at least An =.999802 = 1 An. Using only tho essential nonannunclated failuros and tho rolay failuro (k - 4 + 1 = 5) givos An =.000073 at 90% confidenco, e

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O 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 substantiato increasing the test interval.

IV. Bayoslan Confidence Interval The Bayoslan 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 referenco 2, it can bo viewed as analagous to a classical confidenco Interval for which the prior Information is admittod as

" pseudo data". The postorlor upper bound probability interval is:

0 dA =C (IV 1)

"+

+

P(A,) =.

r(a k) u whoro the prior information is charactorized by a gamma distribution.

This function is equivalent to the Chi squaro and thus the Bayoslan uppor bound can be found from

%!.c,n Ac" 2 (p + T)

(IV 2) whoro T is the operating timo and n = 2k + 2a degroos of froodom.

Thus, posterior uppor bounds may bo so datormined once the psoudo data (a and p) are datormined.

The paramotors are datormined with tho intont of charactorizing the priorinformation as prosented in NEDO 21617 A. In that document, tho failuro rato (for the slavo trip unit with the relay)is prodicted by MIL HDDK 2170 methods and data to bo 31.00 x 10 0 failuros por hours.

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4 This approach, as is stated in the NEDO, is generally considered to be conservative. In addition, information is offered that suggests that the failuro rato could reasonably be as low as 3.196 x 104 Those values are thus employed as approximating a 90% bound and a 10% bound, respectively. By using equation I V - 2, with k = 0 and T = 0, suitable values of a and p are found. The following illustratos the approach.

Sofoct a = f such that n = 3 degrees of freodom. For n = 3,

%.io = 6.251 (soo Tablo I.)

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6.251 Thus, since Ae = 2 0, p = 2 x 31.96 x 10'8 = 97794 hrs.

4 As a result, Ago =

31.96 x 10 and Ago

= 2.09 x 10 '8 This is doomed closo enough to the prior information, so a = l and p = 97794 are acceptablo as cultablo pseudo data.

Noto, tho abovo failuro ratos for a tost interval of 730 hours0.00845 days <br />0.203 hours <br />0.00121 weeks <br />2.77765e-4 months <br /> translato into tho following availabilitlos:

An

=>.00004 Anio = 999997 oo Tablo IV shows tho 90% Dayoslan Confidenco intervals for tho data summarized in Tablo I. The calculated failuro rato bounds are slightly larger than the classical. Evon with this increase, the demonstrated failuro ratos aro moro than adoquato to allow an increased test Interval, m

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Table IV 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

%n = 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 a high confidence (both classically and Bayesian) that for worse case failure counts 0.999 can be achieved with soml annual testing.

Furthermore, realistic failure counting would Indicate that 0.9999 is achieved with high confidence. This, thus, represents a substantial Improvement over the original conservative Interval selected.

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3.364 2.408 3.219 4.eas 5.993 7.424 9.214 2

4.0201 0.0404 e.185 0.211 0.446 S.713 3

2.3e6 3.665 4 642 S 251 7.815 9.837 31.341 3

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0.257 9 425 8.711 1.064 3.449 2.tS5 5

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8 572 3.134 1 Et1 2 204 3 G29 3 328 7

a.344 8 3e3 9.est 12.617 14.887 to 622 IS 475 7

1.215 1.564 2 187 2.833 3.s22 4.671 8

7.344 9.524 31.030 13.362 15.50t 14.188 SS See 3 646 2 812 2 733 3.498 4.544 5.527 9

S.343 le sa 12.342 14.584 14 919 19.679 21 884 j

9 2 ess 2.532 3.325 4.166 5.348 s.303 le 9.342 11.781 13.442 15.957 14.307 21.161 23.300 te 2_558 3.000 3 948 4.865 S.179 7 267 11 18.348 12.3e8 14 833 17.275 19.675 22.418 24.725 11 3.053 3 ees 4 575 5 578 s tat S.tsg 12 11.348 14.C11 15.812 IS See

21. 0M 24.954 28 217 12 3 571 4 17s 5 226 6 304 7.saff 9 est g3 12.348 15.I19 to 906 19.832 22.362 25.472 27.888 13 4 167 4 765 5 es2 7.e42 S.634 9 32s 14 13 338 14.222 IS.151 21.064 23 665 24 873 29.141 to 4.088

5. Es a 571 7.7se 9.4s7 to 321 15 14.339 17.322 19 311 22,387 24 984 28.254 38.578 15 5.223 5 Ses 7 263 4 547 19,3e7 33,721 to 15 338 34.414 28.466 23.542 26.296 29 633 32.000 14 5 412 6 614 7.962 9.312 11.152 12 624 I7 14.336 IS 513 21.615 24 700 27.557 38 995 33.400 17 4 408 7 255

& 672 14,085 12 ek2 13.331 18 17.338 28.481 22.708 2593 28.000 32.344 34.805 16 7.et5 7.908 9 308 IS 865

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38.813 21 S 387 9 915 11.561 13 244 15.445 17 182 22 21.337 24 938 27.38t 32.0 7 35.172 38 988 41.438 22 9.542 to E=ht 12.334 14.941 14.314 18.103 yt 22.337 26.814 28.438 23 18 ISS 11.253 13.881

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24 23.337 27.8p6 38 553 33.3s6 36 415 44.274 42.908 24 IS E4 11 982 13 M 4 15 654 18 e62 39.943 25 24.337 28.372 38 575 34.382 37.652 41.586 44.314 i

25 II 124 12 687 Is 451 14.473 1s 948 38.067 28 25 336 29.246 31.786 36.563 38.985 42.GM 45.442 2e 12 198 13.4e9 15 379 17.362 19.u28 21.792 27 24 336 38.389 22.912 36.741 48.113 44.148 44.983

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27 12.329 14 125 16 151 ts 114 24.795 22.719 28 27.336 31.361 34.827 27.914 41.337 45.419 44.278 28 13.545 14 647 54 928 16 939 21 5e8 23.647 29 28.336 32.461 15.139 38.es7 42.557 44 483 48.588 29 14 254 15.574 17.738 19 764 22.475 24 577 M

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Table II Failure Data Nonessential Failures = 1 T = 6,467,748 hrs.

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

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

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

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Table III Classical Simultaneous Test Unavesabmy 2

(per108) y A"17 8=730 0-43s0 T

Failures De9rees go

%.2 (106 hrs)

(per 10s hrs)

(hrs)

(hrs)

N (n = 2k + 2) 1, n 1

4 7.7779 6.467784

.001

.129 4.23 4

10 15.987 1.236

.543 19.4 5

12

.540 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' 3.264 3.831 137.9

'oeiermined from X,',,, = { ( t,o+ V2n I l' = l [1.28 + V2n 1 l' for n > 30.

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l TetWe IV Beyeelen Simunaneous Test UnevadetWey 2

x (perlos) so"2(p +T) e -730 e - 43eo FaNures Doorees a

N (n=ak+2a)'

.1, n

($+T)

(per10e hrs)

(W (hrs) l l

1 5

9.236 6.565578

.730

.178 8.327 4

11 17.275 1.318

.615 22.14 5

13 19.812 1.500

.400 29.11 l

9 21 29.615 2.256 1.807 86.05 t

14 31 41.316' 3.146 3,517 126.82 1

15 33 43.639 t 3.323 3.924 141.13 i

t

• reom selected prior matribution, a gamma estribution with a - 3t2, p - 97794.

r Determinedirem x. { [tn+ V2n 1 l' = i [1.2e + Van 1 l' er n > So, f

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T References

1. Mann, N.R., Schafer, R.E., and N.D. Singpurwalla, Methods for Statlatical Analyals of Reliability and ufe Data. John Wiley and Sons, Inc,1974.

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

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