~Alamos

BC 02154447

NATIONAL LABORATORY

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memorandum
Theoretical Design Division
XTD-5, Air Force Systems

D00033883 D00033740

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XTD-5:13-00738
March 5, 2013

CONFIRMED TO BE UNCLASSIFIED
Secondary Performance Implications of W78 SLT 34-1 (U)

DOE OFFICE OF CLASSIFICATION

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On December 11 , 2012, the CSA in unit W78 SLT 34-1 (build fabrication number 9407-24-0909) underwent
destructive evaluation at Y-12. This 32.7-year-old unit was chosen for disassembly (from eight units that were
randomly selected from the stockpile in Cycle 34) because nondestructive evaluation (NDE) 1 had indicated that it
possessed abnormal conditions of particular concern. During disassembly, significant abnormal conditions were
confirmed. However, these conditions are not expected to have a significant effect on W78 secondary nuclear
performance beyond that which has been previously determined. 2~
_ _ _ _ _ _ DATE

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\All SFI would be superfluous.
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An Equal Opportunity Employer I Operated by Los Alamos National Security LLC for DOE/NNSA

20140007901

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This report is intended to support the assertion that W78 SLT 34-1 was in an abnormal condition due to aging for
which its secondary performance is understood sufficiently to be able to make a qualified yield assessment, thereby
obviating the need for an SFI. \

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/This report is not a comprehensive update to the W78 CSA life expectancy,q-o though
the aforementioned items will constitute the foundational elements of such a study to be completed later this year.

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1. W78 Full-System Baseline Modeling

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fNonetheless, it is still

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informative and legitimate to depict the model predictions in the low-yield range.

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are given in Table 1.

c::---:--:-:--:-----:--.--D_e_le_te_d--:-::--::--::-:-:::- :-.-----:-:-----:---:--.--_J b(3)

he yield degradation assessed in 2010 and the corresponding results from the
W78 baseline mode are s own m Fig. 4.

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In 2013, the W78 b( )

yield is the system yield properly averaged over the currently assessed primary operating range.

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2. j

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r=:-:------:-:---:----:-------'

~~~~------~----~----~~~~--------~~----~--~--~~--=-~I Thispreructionisnot
the fmal answer, of course, because it is subject to appreciable uncertainty that is also affected by aging.

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The choice of a normal distribution is deliberate. If the only things one knows about a random variable are the first
two moments of its probability distribution (the mean and variance), with no knowledge of the other moments, then
the maximum-entropy principle 13 implies that a normal distribution best expresses one's belief about the value of
the variable. More precisely, the normal distribution is the one that possesses the greatest entropy (contains the
least information) for a given variance 14 and avoids, as much as possible, the introduction of subtle biases into the
distribution. In a sense, the normal distribution is "maximally noncommittal with regard to missing information." 13
Accordingly, the normal distribution is a sensible choice in order to "play it safe", minimizing inadvertent bias.

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~~~
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ITacit assumption of other information can lead to subtle, undesirable

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~onsequence~-for exam

Je a PDF that concentrates robabili

unrealisticall

aivine: more o timistic results t

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1s warranted.

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It is appropriate to express the prediction uncertainty in terms of our worst prediction failures for feature-degraded
nnclear

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1 J he amount o! aegraaauon 10 such a test must be 101errea rrom SliDUJatlons smce me yteia

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'---:-:-- - - - : - - - - - '

without the feature is not experimentally known. \

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Iff* were chosen precisely at the mean of the distribution, then

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o = 1 - e-\ or ln(l - o) == -1.

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In contrast, Eq. (14) is cogent and easy. The formulation with variable confidence
the analysis to be quantified and controlled.
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oenables the conservatism of

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\Figure 5 compares yield predictions and prediction uncertainties for
the 2010 CSA studyq and for the present 2013 assessment.

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In 2013, there is a dramatic reduction in the prediction uncertainty compared to the 2010 assessment.\

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Figure 5. Yield predictions and prediction uncertainties.

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\ One obtains the bounds of the 95% confidence interval by
finding the yield limits between which the area under the curve is 0.95. The most likely yield is that for which the
PDF attains its maximum value.

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It will be helpful to observe some numerical considerations in using these formulae.

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The error

turns out to be a minor one because the fmal distribution, Eq. (24), is relatively insensitive to this parameter.

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L---------------------------~ W e are not being surprised by W78

CSA surveillance findings.
17

has proposed a W78 CSA stud in which 15 units from the available CSAs at Y-12 have been randoml
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.-T-h-e-se- 30_ u_m-.ts- ar_e_t_o _b_e_ _~ b(3 )
L-.--.,..-.,-,-....,....-e-s"""'t-an-d'ar
-d-.--s_u,icte
:--o-f;;-:N
....,;::;
D:-:E;: :;-t:e-~st:-s,"""'i:-n--,cl;-u-;d-:-in-g-r-a-;-di:-.o_gr_a_p-;-h-y-, -w--:-:it7h-:-t;h-e---:in-:-te-n-:-t-o-;:f:-'
cycling through all units over
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a three-year cycle. Current data obtained on these 30 units has been assembled in a preliminary report. 18

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b( ) radiographed at least twice, and almost half of them were radiographed a third time.

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IEach CSA unit was

  
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Conclusions
Predictive capability advances and improvements in statistical formulation have enabled remarkable reductions in
yield prediction uncertainty.

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e W78 CSA life expectancy will be based on the-foundational elements discussed above.
References

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13. E. T. Jaynes, "Information Theory and Statistical Mechanics," Physical Review 106, 620-630 (1957).
14. C. E. Shannon, "A Mathematical Theory of Communication," Bell System Technical Journa/27, 379-423,
623--656 (1948); see pp. 628-632.
15.
Blenton (U), JOWOG-32S, LANL presentation LA-CP-12-0575 (May 15, 2012) (S/RD).
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16. F. S. Acton, Numerical Methods that Work, Harper and Row, New York (1970); p. 19.
17.
Y-12 andLANL 78 CSA Special Study (U), private communication (February 14, 2012) (S/RD).
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18.
W78 CSA Special Radiography Study (U), Y-12 report
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RP-YAREA-F-0200 000 00 (November2012) (S/RD).

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Distribution