Abstract

Homogenization heat treatment is performed to attain uniformity in microstructure which is helpful to achieve the desired workability and microstructure in final products and, eventually, to gain predictive and consistent performance. Fabrication of low-enriched uranium alloys with 10 wt% molybdenum (U-10Mo) fuel plates involves multiple thermomechanical processing steps. It is well known that the molybdenum homogeneity in the final formed product affects the performance in the nuclear reactor. To ensure uniform homogenization, a statistical method is proposed to quantify and characterize the molybdenum concentration variation in U-10Mo fuel plates by analyzing the molybdenum concentration measurement data from scanning electron microscopy energy dispersive spectroscopy line-scan. Statistical tolerance intervals (TI) are employed to determine the qualification of the U-10Mo fuel plate. We formulate an argument for the minimum number of independent samples to define fuel plate qualification if no molybdenum measurement data are available in advance and demonstrate that the given TI requirements can be equivalently reduced to a sample variance criterion in this application. The outcome of the statistical analysis can be used to optimize casting design and eventually increase productivity and reduce fabrication costs. The statistical strategy developed in this paper can be implemented for other applications especially in the field of material manufacturing to assess qualification requirements and monitor and improve the process design.

References

References
1.
Wachs
,
D. M.
,
Clark
,
C. R.
, and
Dunavant
,
R. J.
,
2008
,
Conceptual Process Description for the Manufacture of Low-Enriched Uranium-Molybdenum Fuel
,
Idaho National Laboratory (INL)
,
Idaho Falls
.
2.
Van Den Berghe
,
S.
, and
Lemoine
,
P.
,
2014
, “
Review of 15 Years of High-Density Low-Enriched UMo Dispersion Fuel Development for Research Reactors in Europe
,”
Nucl. Eng. Technol.
,
46
(
2
), pp.
125
146
. 10.5516/NET.07.2014.703
3.
Meyer
,
M. K.
,
Hofman
,
G. L.
,
Hayes
,
S. L.
,
Clark
,
C. R.
,
Wiencek
,
T. C.
,
Snelgrove
,
J. L.
,
Strain
,
R. V.
, and
Kim
,
K. H.
,
2002
, “
Low-Temperature Irradiation Behavior of Uranium–Molybdenum Alloy Dispersion Fuel
,”
J. Nucl. Mater.
,
304
(
2–3
), pp.
221
236
. 10.1016/S0022-3115(02)00850-4
4.
Snelgrove
,
J. L.
,
Hofman
,
G. L.
,
Meyer
,
M. K.
,
Trybus
,
C. L.
, and
Wiencek
,
T. C.
,
1997
, “
Development of Very-High-Density Low-Enriched-Uranium Fuels 1 Work Supported by the US Department of Energy, Office of Nonproliferation and National Security, Under Contract No. W-31-109-ENG-38.1
,”
Nucl. Eng. Des.
,
178
(
1
), pp.
119
126
. 10.1016/S0029-5493(97)00217-3
5.
Hu
,
X.
,
Wang
,
X.
,
Joshi
,
V. V.
, and
Lavender
,
C. A.
,
2018
, “
The Effect of Thermomechanical Processing on Second Phase Particle Redistribution in U-10 wt% Mo
,”
J. Nucl. Mater.
,
500
, pp.
270
279
. 10.1016/j.jnucmat.2017.12.042
6.
Xu
,
Z.
,
Joshi
,
V.
,
Hu
,
S.
,
Paxton
,
D.
,
Lavender
,
C.
, and
Burkes
,
D.
,
2016
, “
Modeling the Homogenization Kinetics of as-Cast U-10 wt% Mo Alloys
,”
J. Nucl. Mater.
,
471
, pp.
154
164
. 10.1016/j.jnucmat.2015.11.026
7.
Garrett
,
C. E.
, and
Prasad
,
K.
,
2004
, “
The Art of Meeting Palladium Specifications in Active Pharmaceutical Ingredients Produced by Pd-Catalyzed Reactions
,”
Adv. Synth. Catal.
,
346
(
8
), pp.
889
900
. 10.1002/adsc.200404071
8.
Ren
,
H.
,
Hou
,
Z.
,
Huang
,
M.
,
Bao
,
J.
,
Sun
,
Y.
,
Tesfa
,
T.
, and
Ruby Leung
,
L.
,
2016
, “
Classification of Hydrological Parameter Sensitivity and Evaluation of Parameter Transferability Across 431 US MOPEX Basins
,”
J. Hydrol.
,
536
, pp.
92
108
. 10.1016/j.jhydrol.2016.02.042
9.
Ulewicz
,
R.
,
2003
, “
Quality Control System in Production of the Castings From Spheroid Cast Iron
,”
Metalurgija
,
42
(
1
), pp.
61
63
.
10.
Reid
,
R. D.
, and
Sanders
,
N. R.
,
2007
,
Operations Management: an Integrated Approach
,
John Wiley
,
New York
.
11.
Wang
,
X.
,
Xu
,
Z.
,
Soulami
,
A.
,
Hu
,
X.
,
Lavender
,
C.
, and
Joshi
,
V.
,
2017
, “
Modeling Early-Stage Processes of U-10 Wt.%Mo Alloy Using Integrated Computational Materials Engineering Concepts
,”
JOM
,
69
(
12
), pp.
2532
2537
. 10.1007/s11837-017-2608-z
12.
Fedorov
,
A.
,
Wells
,
W. M.
,
Kikinis
,
R.
,
Tempany
,
C. M.
, and
Vangel
,
M. G.
,
2014
, “
Application of Tolerance Limits to the Characterization of Image Registration Performance
,”
IEEE Trans. Med. Imaging
,
33
(
7
), pp.
1541
1550
. 10.1109/TMI.2014.2317796
13.
Rebafka
,
T.
,
Clémençon
,
S.
, and
Feinberg
,
M.
,
2007
, “
Bootstrap-Based Tolerance Intervals for Application to Method Validation
,”
Chemom. Intell. Lab. Syst.
,
89
(
2
), pp.
69
81
. 10.1016/j.chemolab.2007.06.001
14.
Sharma
,
G.
, and
Mathew
,
T.
,
2012
, “
One-Sided and Two-Sided Tolerance Intervals in General Mixed and Random Effects Models Using Small-Sample Asymptotics
,”
J. Am. Stat. Assoc.
,
107
(
497
), pp.
258
267
. 10.1080/01621459.2011.640592
15.
INL
,
2017
, “
Fuel Specification for MP-1, MP-2, and FSP-1
,” SPC-1691, Idaho National Laboratory, Idaho Falls.
16.
Guenther
,
W. C.
,
1972
, “
Tolerance Intervals for Univariate Distributions
,”
Nav. Res. Logist.
,
19
(
2
), pp.
309
333
. 10.1002/nav.3800190208
17.
2012
, NIST/SEMATECH e-Handbook of Statistical Methods.
18.
Loucks
,
D. P.
, and
van Beek
,
E.
,
2017
, “An Introduction to Probability, Statistics, and Uncertainty,”
Water Resource Systems Planning and Management
,
Springer
,
Cham
. pp.
213
300
.
19.
Lieberman
,
G. J.
,
1957
,
Tables for One-Sided Statistical Tolerance Limits
,
Applied Mathematics and Statistics Labs Stanford Univ
,
CA
.
20.
Natrella
,
M. G.
,
2013
,
Experimental Statistics
,
Courier Corporation
,
Mineola, NY
.
21.
Janiga
,
I.
,
Garaj
,
I.
, and
Witkovský
,
V.
,
2009
, “
On Exact Two-Sided Statistical Tolerance Intervals for Normal Distributions With Unknown Means and Unknown Common Variability
,”
Quality and Productivity Research Conference
, Yorktown Heights, New York, IBM Thomas J. Watson Research Center.
22.
Young
,
D. S.
,
2016
, “
Normal Tolerance Interval Procedures in the Tolerance Package
,”
R J.
,
8
(
2
), pp.
200
212
. 10.32614/RJ-2016-041
23.
Howe
,
W. G.
,
1969
, “
Two-Sided Tolerance Limits for Normal Populations, Some Improvements
,”
J. Am. Stat. Assoc.
,
64
(
326
), pp.
610
620
. 10.1080/01621459.1969.10500999
24.
Kenney
,
J. F.
, and
Keeping
,
E. S.
,
1951
,
Mathematics of Statistics, Part One
,
2nd ed
.,
Van Nostrand
,
Princeton, NJ
.
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