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Mr.' Vincent lettieri Brookhaven l'ational Laboratory Upton, tew York 11973
Dear Vincent:
Enclosed please find a su :r.ary of our statistical andysis of the primer protective coating backfit inspection program at Coc.anche Peak, Unit 1.
The ardlysis is r? sed en solely on the data we received f rem Lisa Eielfeldt of
~
Texas Utilities Gic.erating Cc: pany in letters date*d 3/29/84, 4/17/84 and 4/23/84.
The two variables analyzed in this report are a nesion and dry film thickness (DFT). For each variable, we provide both the sanple proportion of failed arca as well as a 9P: u;'per confidence interval for the pr.pulatien proportion of the defective area. The interpretation of the su=iary statistics should be r.ede.in light of the to: cents and assumptions we offer in the attech.ent.
Should yeu have any cuestions, plene*give either one of us a call.
Sincarely,
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.be-- y Dan Lurie, Mathematical Statistician Cost and P...r.Scenent Support Branch Office of Rt. source Manacement (301) 49~'-49S9 t es F.. A.br.:r,i.n, Sec tior L c h oer F.e.et.or Pi s t F...nch Office of :.uclear icgulatory Ressrch (301) 452-76 C gkr*
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,h { 7 k siECTION P R O G R A P.
AT CM:ANCHE FEAR,- U NI T 1 j
Tas1ure Rate and 95: Upper confidence Limit (UCL)
Adhesion Test DTT test 1.
CONCRETE Failure Rate 0/1691
.000.
101/4623
.022
=
=
i 95: UCL 3.00/1691
.0018 (a)
.022+1.645(.0022)=.0254 (b)
=
II. STEEL LINER Failure Rate 2/405 =.0049
- l05/1494
.0703
=
v/
95 UCL 6.3 0/ 05 =.0156 (a)
.0703+1.645(.0066)
.0812 (b)
=
i III. Misc. Steel - PIPE SUPPORT Tailure la t e 5/230( =.024 7 -
, 17/230
.0739
=
95 UCL 10.51/230 =.0457 (a) 25.50/230
.1109 (a)
=
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IV.
Misc. Steel - CABLE TRAY SUPPORT
?Y' m
Failure Rate 3./297
.0101\\
35/297
.1178
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.1562 (a)
. ~~~j, 95: UCL 7.75/297 *.0261 (a) 46.40/297
=
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V.
Misc. Steel - CONDUIT SUPPORT
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Teilure nate 1/225
.0044 10/225
.0444
=
=
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950 UCL 4.7 4/ 225 =.0211 (a) 16.46/225
.0754 (a) -
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a VI.
Misc. Steel - OTHER Wy Y
s.-
Tailure Rate Il'/765 =.0144
,q7/765 =.0876
.1044 (b)
)
95 UCL' 18.21/765 = ?g2380(a)
.0876+1.645(.0102)
=
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(a) C t.n s t r u c t ed fru: } o i r,s o n probsbilftv' table
.E (b) Calculated fro = b i n o r:1 a l prc:.,5111ty (!stribiiion' d
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leTICAL 1515
/{$cnr1T I NSP ECTI O N FROGF.AM AT CCMANCHE PEAK - U NI T 1 bd c0MMENTS AND ASSUMPTIONS 3,
The.fai ure rate in a population is defined.to be the ratio of the defective area to the total area in the population.
It is virtually impossible to obtain the exact population failure rate witout t esbing the entire population of interest.
Two estimators of the population failure rate are derived from the sacple and ere given in this analysis.
The first estimator is the sample failure rate which is the ratio of the number of. defective tests to the number of tests in the sample.
This estimator (often
,eslied a " point esticator") in and by itself may not be very meaningful, as no ceasure of assurance is associated with it.
The second esti=ator is a 95* upper confidence' limit (UCL) on the population failure rate.
This esti=ator is constructed from the ce=ple such that one is '95 sure" that the,true failure rate does not exceed this UCL.
Other UCL's, such as 90% UCL or 99%
UCL, could be si=ilarly constructed.
2.
The 95% UCL's for the failure rates of the va rious ite=s in Unit I were calculated using two appropches.
Whenever the number of defective points was low (50 or*1es,s) a table value for the confidence limit for a poisson variable'was.used.
(See Table 40,
~Biometrika Tables for Statisticians", vol 2, by Pearson and Eartley, Cambridge University Press, 1970).
When the number of defectives exceeded 50, a normal approxination to the binomial distribution was used.
3.
The failure rate is not necessarily the best single ntatistical criterion for determining the adequacy of the coating.
Instead, one may wish te estimate the total area'that would flake off in case of an accident.
This may be a cc ompl i s h ed.
s-.
by mul tiplying the given estimators by their corresponding total areas.
The latter cuantities are found in Bielfeldt's letters of 3/29/84 and 4/14/84.
4 As stated in the c o v e'r letter, the analysis i r.
b a r. e d sole;y un the data supp1'idd b y' T,U G C.
It does not reflect the resuits of subsequent tests conducted by BNL.
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