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- 5 13 Mr. Vincent lettieri Brookhaven National Laboratory Upton, tew York 11973 C :-a r C ncent:
Enciesed please find a su=ary of our statistical analysis of the primer proMctive crating backfit ir.spection prograr at Cc inche feat, Unit 1.
The a alysis is t= red cn solely on the data te racei'.3d fr w Lisa Eielfeldt of T: as Jtilities c.1.areting C: pany in letters d3:ec 3.29/S4, z/;7'E4 and 4/23/84 The ts.c veriables ar.alyzed in this report are ac'hesion and dry fiin thickness (DFT).
For each variable, vie provide both the s_. pie proportion of failed sil as a C5" up;er car.fidence irtarval for it.e pcpulaticr ;rescrtion ac:a as of t:a defective area.
The interpre:ation of the sun :ary statistics should be nade in light of the cc=ents and assumptions i.e offer in the ett:c'" ant.
Should you have any nuestions, please give either one of us a call.
Sinecreiy, N,. -
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Dan Lurie, Mather:atical Statistician Cost and " r.9 a:nt Support Eranch Of fice cf F..< c.urce "anacen ent (301) 4E:-4959 l e ;. ' i
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STATL5r1 CAL A'iLYSIS OF PROTICT1cE C U A T l ??G (PF. 1ER O !iLY )
SACKFIT L ;SciC fl0N PROG RAM AT CC '! \\ Z H E PEAK -
L'. T 1 9
Failure Rate and 95% Upper Confidence Limit (UCL)
Adhesion Test DFT test I.
CONCRETE
\\
.022
.000 101/4623 Failure Rate 0/1691
=
=
.0018 (a)
.022+1.645(.0022)=.0254 (b) 95% UCL 3.00/1691
=
II. STEEL LI!?ER
.0703 Failure Rate 2/405 =.0049 105/1494
=
.0812 (b)
.0156 (a)
.0703+1.645(.0066) 95% UCL 6.30/405
=
=
III. Misc. Steel - PIPE SUPPORT
.0739 Failure Rate 5/230 =.0217 17/230
=
.1129 (a)
.'. 57 (a) 25.5' 230 95*
l' C L 10.51/230
=
=
LV.
Misc. Steel - CABLE TRAY SUPPORT
.1178
.0101 35/297 Failure Rate 3/297
=
=
.1562 (a)
.0261 (a) 46.;0/297 9 5 '; UCL 7.75/297
=
=
V.
Misc. Steel - CONDUIT SUPPORT
.0t44
04; l 1; 225 Failure nate 1/225
=
=
.0754 (a) 9 5 ". UCL 4.7 4/ 2 2 5 =.0211 (a) 10.4.'225
=
VI.
M i c; c. Steel - OTHER
.0876 Failure Rate 11/765 =.011.4 t,7 / 7 t> 5
=
95% UCL 18.21/765 =
.2 380( a )
.087f>+1.645(.0102)
.1044 (b)
=
(a) C :. ': s t r u c t e d fro: Poir, son,ruhabilit: :,Sie (b) Calculated fror S i. o r.1 11 prc: iSility d i,: r i $.u ' i i r.
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- 4 TAILSTIC\\L AldLYSIS.0F i'f.3TEC f1VE CO ATI NG ( P R t.tLR OSLY)
BACKFIT INSPSCTION PROGRAM AT COMANCHE PEAK - UNIT 1 1
COMMENTS AND ASSUMPTIONS 1.
The failure rate in a population is defined.to be the ra t io of the defective area to the total area in the population.
It is virtually impossible to obtain the exact.opulation failure rate witout teshing the entire population of interest.
Two estimators of the population failure rate are derived from the sample and are 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 called a " point estimator")'in and by itself may not be very i
caaningful, as no ceasure of assurance is associated with it.
The second estimator is a 95% upper confidence limit (UCL) on the j
population failure rate.
This estimator is constructed from the sample 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 similarly constructed.
2.
The 950 UCL's for the failure rates of the va rious itens in Unit I were calculated using two approaches.
Whenever the number ij of defective points was low (50 or'less) a table value for the j
confidence limit for a poisson variable was used.
(See Table 40, "Sie,etrika Tables for Statisticians", vol 2,
by Pearson and
- 'n i v e r s i t y F r e s s, 1970).
hen t :s t
.u-ber of "artley, Cambridge def-ctives exceeded 50, a nor,a1 approxination to the binc-i=1 distribution was used.
3.
The failure rate is not necessarily the best single i
statistical criterion for determining the adequacy of the coating.
Instead, one may wish to estimate the total area tbat would flake off in case of an accident.
This may be a cconpli s h ed
[
by multiplying the given estimators by their corresponding total areas.
The lat'ter quantities are found in Bielfeldt's letters of 3/29/84 and 4/14/ 8 4.
I 4
As stated in the cover letter, the analysis 13 Lsued s o l e '. y u r.
the data supplied by TUGC.
It does not reflect the resu: ts of subsequent tests conducted by BNL.
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