ML20045A951
| ML20045A951 | |
| Person / Time | |
|---|---|
| Issue date: | 04/08/1992 |
| From: | Fraley R Advisory Committee on Reactor Safeguards |
| To: | Advisory Committee on Reactor Safeguards |
| Shared Package | |
| ML20042D089 | List:
|
| References | |
| FRN-57FR14514, REF-GTECI-B-56, REF-GTECI-EL, RULE-PR-50, TASK-B-56, TASK-OR AE06-1-035, AE6-1-35, NUDOCS 9306150376 | |
| Download: ML20045A951 (7) | |
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UNITED STATES NUCLEAR REGULATORY COMMISSION e g.,
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<c ADVISORY COMMITTEE ON REACTOR SAFEGUARDS "1
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WASHINGTON, D. C. 20555 i
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April 8, 1992
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MEMORANDUM FOR:
ACRS Members FROM:
R.
raley, Executive Director l
l
SUBJECT:
DIESEL RELIABILITY r
{
Hal Lewis has requested that the attached be provided to you l
as another crack at the diesel data.
l
Attachment:
More Diesels, dated April 5, 1992 by H. Lewis l
cc w/Atch:
l A.
Serkiz, RES J. Johnson, OCM/IS j
- D. Trimble, OCM/JC W. Minners, RES R.
Savio, ACRS S. Duraiswamy, ACRS I
P. Boehnert, ACRS l
b e
i 9306150376 930422 PDR PR
.PDR
- 50 57FR14514 I R D'-
l More Diesels April 5,1992 Here's another crack at the dicsci data that have fallen into our hands, from another, some-what more (but not yet completely) Bayesian approach. I have no doubt that it has a name.
5 (The point of this series of notes is to illustrate by doing that there are a bunch of reputable E-l statistical approaches to analyzing the data, BEFORE deciding on a proposed cure for a conjectured problem. As a general rule, therapy works best if it follows the diagnosis.)
Again think first of attempts to start and failures to start. (Loads are treated the same wAy.) Again, there are data for 195 diesels, and for the i'h diesel we have N attempts and i
ni ailures. Assume, as everyone does, that this is a Bernoulli process, and the problem, as f
before, is that there are so few failures that the random fluctuations for an individual diesel E
preclude any straightforward statistical treatment of individuals.
This time we start with a Baye:ian opproach, assuming that the diesels form a population l
with a distribution of intrinsic unreliabilities og, and that these are drawn (for each dicscl) 3 i
randomly from an underlying distribution of unreliabilities, which we don't know. If this a
were a true Bayesian approach, we would collect all the information we have about this
. mother distribution," label it the " prior," multiply it by the
- likelihood function" for the observed failures, and use that as an update to the conjectured prior. We would then have an updated statement of the distribution of unreliabilities in the population, but still no information about individuals.
So what we can do (and this is common among Bayesians) is to assume that the mother y
distribution of reliabilities is of the form (1 - cr)0, which describes unreliabilities clustered
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near zero, but with a range determincd by the parameter 6, which we don't know. However, i
we can determine from the population data a value of b that best fits the facts, and with this many observations our prior information about b hecomes relatively unimportant. (This is a degenerate beta distribution-lifting the degeneracy doesn't help.) Sparing you the a
details,it turns out that the best value of 6 is around 230 for the starting data, and 115 for the loading data. This is, in effect, a different way of letting the population influence the analysis of the individual diesels.
Ono can now take the next step, and a.nalyze the data 9p each individual, using this distri-E bution, with the newly determined value of 6, as the family from which the individual was drawn. That will be a genuine Bayesian update for the individual, using the prior deter-i mined by the population. The answer turns out to be extremely simple: the estimated mean unreliability for the individual is given by (ng + 1)/(Ni + b + 1), and that is what we show in the table. Again, it is a mixture of data from the individual, and data from his family, but
=
a different mixture from the one we had from the Empirical Hayes treatment. And again, the last column is the net unreliability, assuming that the start and load unreliabilities are a unconclated.
i m
On this last point, if it were really true that there were some inept utilities out there, one would expect that those who show mote failures to start would also show more failures to load-ineptitude has a way of affecting everything you do. A very straightforward cle3ical calculation of the correlation coeflicient between start failures and load failures leads to a As value of 0.107, which gives some validation to the idea of treating them separately.
before, there is a tendency (as there should be) for the diesels with niost failures to be grouped toward the start of the list, but, aga'm as before, the best estimates are far from the numbers you would get from simplistically dividing failures by tries.
1 Given my ' druthers between the two methods I've dumped on you, I have a slight preference for this one,if only because it is more nearly Bayesian, so it has a better theoretical under-pinning. They don't differ a great dealin the results, and both highlight the fact that the number of failures for any given diesel is far too small to justify a calculation of its reliability front its own failure record alone.
As real statisticians get to work on these data, far better analyses will emerge. I'm just BUT, you can't get blood from a turnip, and it is impossible to trying to set the stage.
l distinguish between bad diesels and statistical fluctuations in these data, Tierefore, any effort to punish those with the worst records is ill-based. (It is of courso always possible that some bad actor will stand out from the crowd in a statistically significant way-it just hasn't happened, and hasn't even come close.)
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i starts fails startunrel loa'ds fails loadunrel net unrel 1
77 1
0.006 49 3
0.024 0.031 2
149 2
0.008 44 2
0.019 0.026 124 2
0.008 94 4
0.024 0.032 61 1
0.007 55 2
0.018 0.024 5
145 1
0.005 118 5
0.026 0.031 6
101 1
0.006 54 2
0.018 0.024 7
102 3
0.012 119 2
0.013 0.025 8
114 0
0.003 44 2
0.019 0.022 9
153 0
0.003 45 2
0.019 0.021 10 69 3
0.013 59 0
0.006 0.019 11 77 1
0.006 67 2
0.016 0.023 12 144 1
0.005 58 2
0.017 0.022 13 58 0
0.003 50 2
0.018 0.021 14 95 0
0.003 75 3
0.021 0.024 15 65 0
0.003 51 2
0.018 0.021 16 187 4
0.012 172 3
0.014 0.026 17 196 5
0.014 151 2
0.011 0.025 18 97 2
0.009 63 1
0.011 0.020 19 249 1
0.004 62 2
0.017 0.021 20 85 2
0.009 79 1
0.010 0.020 21 103 0
0.003 84 3
0.020 0.023 22 59 1
0.007 53 1
0.012 0.019 23 87 2
0.009 79 1
0.010 0.020 24 135 0
0.003 57 2
0.017 0.020 f 25 71 1
0.007 47 1
0.012 0.019 j 26 123 0
0.003 58 2
0.017 0.020 i 27 139 0
0.003 88 3
0.020 0.022 104 2
0.009 69 1
0.011' O.020 122 2
0.008 60 1
0.011 0.020 l 30 271 5
0.012 70 1
0.011 0.023 a
l 31 86 1
0.006 48 1
0.012 0.018
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0.007 57 1
0.012 0.018 33 95 2
0.009 90 1
0.010 0.019
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0.003 63 2
0.017 0.020
' 35 299 0
0.002 129 4
0.020 0.022 36 148 0
0.003 99 3
0.019 0.021 37 81 1
0.006 63 1
0.011 0.018
, 38 94 0
0.003 39 1
0.013 0.016 l 39 84 1
0.006 76 1
0.010 0.017 40 82 1
0.006 79 1
0.010 0.017 43 106 1
0.006 67 1
0.011 0.017 42 124 0
0.003 83 2
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( 43 122 0
0.003 42 1
0.013 0.015 i 44 88 1
0.006 83 1
0.010 0.016 l 45 87 2
0.009 74 0
0.005 0.015 46 144 2
0.008 110 1
0.009 0.017 47 110 1
0.006 72 1
0.011 0.016 48 283 0
0.002 132 3
0.016 0.018 49-149 1
0.005 128 2
0.012 0.017 50 45 1
0.007 43 0
0.006 0.013 51 182 4
0.012 51 0
0.006 0.018 l b2 156 1
0.005 64 1
0.011 0.016 ~
149 2
0.008 123 1
0.008 0.016 59 0
0.003 48 1
0.012 0.016 i do 106 1_
0.006 87 1
0.010 0.016 56 j 54 0
0.004 49 1
0.012 0.016 57-155 1
0.005 147 2
0.011 0.017 l 58 129 0
0.003 106 2
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0.011 0.014 61 1
0.007 43 0
0.006 0 013 138 1
0.005 110 1
0.009 0.014 127 2
0.008 102 0
0.005 0.013 8
109 0
0.003 64 1
0.011 0.014 212 1
0.005 190 2
0.010 0.014 p
66 1
0.007 65 0
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77 0
0.003 67 1
0.011 0.014 161 0
0.003 67 1
0.011 0.013 88 0
0.003 67 1
0.011 0.014 71 1
0.007 67 0
0.005 0.012 97 0
0.003 74 1
0.011 0.014
- 150 2
0.008 64 0
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0.003 75 1
0.010 0.013
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1 77 0
0.003 76 1
0.010 0.014 2
163 1
0.005 158 1
0.007 0.012
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3 95 0
0.003 81 1
0.010 0.013 l4 247 1
0.004 126 1
0.008 0.012 l5 223 0
0.002 87 1
0.010 0.012
'6 154 0
0.003 88 1
0.010 0.012 l7 90 1
0.006 59 0
0.006 0.012 l8 102 0
0.003 92 1
0.010 0.013 l9 126 0
0.003 100 1
0.009 0.012 EE l0 102 1
0.006 96 0
0.005 0.011 l1 144 0
0.003 110 1
0.009 0.011 l2 136 0
0.003 111 1
0.009 0.012 l3 119 0
0.003 112 1
0.009 0.012 l4 145 0
0.003 123 1
0.008 0.011 3
!5 124 1
0.006 112 0
0.004 0.010
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0.006 89 0
0.005 0.010 l7 126 1
0.006 96 0
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0.002 129 1
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0.004 0.009 42 156 1
0.005 127 0
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0.002 194 1
0.006 0.009 ja4 227 1
0.004 62 0
0.006 0.010 45 305 1
0.004 133 0
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0.003 100 0
0.005 0.007 ft8 74 0
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0.005 0.008 11 52 0
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0.006 0.009 12 69 0
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0.006 0.009 13 51 0
0.004 41 0
0.006 0.010 14 86 0
0.003 66 0
0.005 0.009 15 114 0
0.003 87 0
0.005 0.008 16 147 0
0.003 76 0
0.005 0.008 17 53 0
0.004 47 0
0.006 0.010 18 62 0
0.003 57 0
0.006 0.009 19 46 0
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0.006 0.010 10 67 0
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0.003 55 0
0.006 0.009 12 38 0
0.004 37 0
0.007 0.010 13 36 0
0.004 34 0
0.007 0.010 14 58 0
0.003 50 0
0.006 0.009 15 67 0
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0.006 0.009 16 166 0
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17 95 0
0.003 63 0
0.006 0.009 11 119 0
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0.006 0.010 il 76 0
0.003 69 0
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52 82 0
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0.005 0.008-53 62 0
0.003 32 0
0.007 0.010 14 71 0
0.003 60 0
0.006 0.009 35 63 0
0.003 34 0
0.007 0.010 56 53 0
0.004 35 0
0.007 0.010 57 63 0
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0.006 0.009 58 110 0
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@7 65 0
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0.003 55 0
0.006 0.009 91 95 0
0.003 70 0
0.005 0.008 92 115 0
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