Analysis of Mechanisms for Early Waste Package/Drip Shield Failure  REV 00C

CAL-EBS-MD-000030

August 2004 


1. PURPOSE 
The purpose of this analysis is to evaluate the types of defects or imperfections that could occur 
in a waste package or a drip shield and potentially lead to its early failure, and to estimate a 
probability of occurrence for each. An early failure is defined as the through-wall penetration of 
a waste package or drip shield due to manufacturing or handling-induced defects, at a time 
earlier than would be predicted by mechanistic degradation models for a defect-free waste 
package or drip shield. 
The scope of this analysis is limited to the manufacturing or handling-induced defects that might 
lead to the early failure of the waste package or drip shield. Also, for the waste package only the 
outer (Alloy 22) barrier is investigated. No credit is taken for the structural (stainless steel) shell 
of the waste package; therefore, it is not analyzed. 
As a preliminary remark, it is important to note that even if a waste package is affected by a type 
of defect that may lead to its early failure, it does not mean that this waste package is due to fail 
at emplacement in the repository. Failure of the waste package will only occur after degradation 
processes take place, which may happen hundreds of years after emplacement. Also, even if a 
waste package was to fail early because of a defect, its radionuclide inventory may not 
necessarily be available for transport. This is because most through-wall penetrations, especially 
cracks from stress corrosion cracking, are usually of limited length and tight. 
The intended use of this analysis is to provide information and inputs to performance assessment. 
These information and inputs will be used to evaluate the waste package and drip shield lifetime. 
This calculation receives no direct input from other analysis reports or model reports or their 
associated data tracking numbers (DTNs). It provides direct inputs to WAPDEG Analysis of 
Waste Package and Drip Shield Degradation (ANL-EBS-PA-000001), Engineered Barrier 
System Features, Events, and Processes (ANL-WIS-PA-000002), and Screening Analysis for 
Criticality Features, Events, and Processes for License Application (ANL-EBS-NU-000008). 
2. QUALITY ASSURANCE 
This analysis is developed in accordance with Technical Work Plan for: Regulatory Integration 
Modeling and Analysis of the Waste Form and Waste Package (BSC 2004a). Also, the analysis 
is subject to the requirement of Quality Assurance Requirements and Description (DOE 2004) as 
determined in Section 8 of Technical Work Plan for: Regulatory Integration Modeling and 
Analysis of the Waste Form and Waste Package (BSC 2004a). 
The development of this analysis is governed by AP-3.12Q, Design Calculations and Analyses. 
The control of the electronic management of information was evaluated in accordance with 
AP-SV.1Q, Control of the Electronic Management of Information, as specified in Technical 
Work Plan for: Regulatory Integration Modeling and Analysis of the Waste Form and Waste 
Package (BSC 2004a, Section 8). The resulting methods used are given in the same reference. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
3. USE OF SOFTWARE 
The computer code SAPHIRE Version 7.18 (SAPHIRE V7.18, STN: 10325-7.18-00) was used 
to develop and quantify several event trees in the analysis. SAPHIRE is a qualified software 
code that was obtained from Software Configuration Management. It is appropriate for use in 
the present analysis and is used only within its range of validation in accordance with AP-SI.1Q, 
Software Management. SAPHIRE was installed on a Dell Dimension XPS T800i running 
Microsoft Windows 2000 Professional (central processing unit 151674). The inputs and output 
files are given in Attachment II. 
Mathcad 2001i Professional, a commercial off-the-shelf software program, was also used in the 
preparation of this analysis. Mathcad was installed on a Dell Dimension XPS T800i running 
Microsoft Windows 2000 Professional (central processing unit 151674). The Mathcad 
calculations performed in the analysis are documented in Attachment I. This attachment lists all 
the inputs and formulas used as well as the corresponding outputs so that the work can be 
reproduced and checked independently without recourse to the originator of the analysis. Thus, 
the use of this software is considered exempt from the requirements of AP-SI.1Q, Software 
Management. 
Finally, the input and output files given in Attachment II were compressed using Winzip 8.1. 
Because Winzip 8.1 is an office automation system, it is exempt from the requirements of 
AP-SI.1Q, Software Management. 
4. INPUTS 
4.1 DATA AND PARAMETERS 
4.1.1 Waste Package and Drip Shield Design Parameters 
The following parameters are appropriate for use in this analysis because they are from 
controlled documents and reflect the current design of the waste package and the drip shield. 
The materials comprising the waste package and drip shield are summarized in Table 1. 
Table 1. Materials Used for the Waste Package and the Drip Shield 
Item Description Material Used 
Inner vessel of the waste package (structural support) Stainless steel (SA-240-S31600)a 
Outer barrier of the waste package (corrosion resistance) Alloy 22 (SB-575-N06022)a 
Shield plates of the drip shield Titanium Grade 7 (SB-265-R52400)b 
Structural support of the drip shield Titanium Grade 24 (SB-265-R56405)b 
a
Source:BSC 2003a, Table 2 
b 
BSC 2003b, Table 5 
Dimensions of components of the 21-PWR (pressurized water reactor) waste package with 
absorber plates were taken from Repository Design Project, RDP/PA IED Typical Waste 
Package Components Assembly 1 of 9 (BSC 2003c) and are summarized in Table 2. The 21PWR 
waste package with absorber plates is a type of waste package designed to receive the 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
spent nuclear fuel from pressurized water reactors. The parameters pertaining to this kind of 
waste package were selected because the most common waste packages used in the repository 
will be of this type (BSC 2003a, Table 11). 
A comparison of the parameters used in this calculation for the 21-PWR waste packages with 
those of the 44-PWR waste packages (the second most common waste package) and recent 
changes to both designs indicate that this calculation is adequate to address the current 21-PWR 
and 44-PWR waste packages. 
Table 2. Waste Package Design Parameters Used in the Analysis 
Parameter Description Parameter Value 
Thickness of outer barrier 20 mm a 
Inner diameter of outer barrier 1524 mm b 
Length of waste package 5165 mm a 
Thickness of outer lid weld 25 mm b 
Thickness of middle lid weld 10 mm b 
Thickness of outer barrier bottom lid weld 25 mm b 
Diameter of outer lid 1541 mm b 
Diameter of middle lid 1527 mm b 
Source: a BSC 2003c, Table 1 
b 
BSC 2003c, Directory (references BSC 2001a for this information) 
The parameters used in the analysis related to the drip shield are summarized in Table 3. 
Table 3. Drip Shield Design Parameters Used in the Analysis 
Parameter Description Parameter Value 
Thickness of drip shield (plates) 15 mm a 
Mass of drip shield 5000 kg b 
Total mass of Titanium Grade 7 welds 110 kg b 
Density of Titanium Grade 7 4.51 g/cm3 c 
Source: a BSC 2003b, Table 1 
b BSC 2003b, Table 5 
c ASM International 1990a, p. 620) 
4.1.2 Human Error Probabilities 
Estimates of human error probabilities (HEPs) provided by Swain and Guttmann (1983) were 
used in this analysis. These probability estimates are accepted data. This is based on the fact 
that these data are recommended for use by PRA Procedures Guide, A Guide to the Performance 
of Probabilistic Risk Assessments for Nuclear Power Plants (NRC 1983, Sections 4.1 and 4.5.7) 
in order to evaluate the probability of occurrence of human errors in the conduct of probabilistic 
risk assessments for nuclear power plants. 
The data used are summarized in Table 4. Based on information by Swain and Guttmann (1983, 
pp. 2-18 and 2-19), the estimated HEPs are considered to follow a lognormal distribution. The 
nominal probability represents the median, and the 5th (respectively 95th) percentile is calculated 
by dividing (respectively multiplying) the median by an error factor, also shown in Table 4. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Table 4. Estimates of Human Error Probabilities 
Item # Description 
Nominal 
Probability 
Error 
Factor 
Source: 
Swain & Guttmann 1983 
1 Failure to carry out a plant policy 0.01 5 Item 1 of Table 20-6 
2 Failure to use written operations procedure under 
normal operating conditions 0.01 3 Item 3 of Table 20-6 
3 Failure to use written test or calibration procedure 0.05 5 Item 6 of Table 20-6 
4 
Error of commission in reading and recording 
quantitative information from unannunciated digital 
readout (less than 4 digits) 
0.001 3 Item 2 of Table 20-10 
5 Error of commission in check-readinga analog meter 
with difficult-to-see limit marks, such as scribe lines 0.002 3 Item 3 of Table 20-11 
6 Selection of wrong control on a panel from an array of 
similar-appearing controls identified by labels only 0.003 3 Item 2 of Table 20-12 
7 
Improperly mate a connector (this includes failures to 
seat connectors completely and failure to test locking 
features of connectors for engagement) 
0.003 3 Item 13 of Table 20-12 
8 Checker failure to detect error made by others during 
routine tasks 0.1 5 Item 1 of Table 20-22 
9 Operator failure to respond to an annunciator 0.0001 10 Item 1 of Table 20-23 
Source: Swain and Guttmann 1983 
a
NOTE: Check-reading means reference to a display merely to see if the indication is within allowable limits; no 
quantitative reading is taken. 
The fact that the HEP values given in Table 4 correspond to nominal probabilities should be 
emphasized. No performance shaping factors are employed except in very particular cases for 
which their use is reasonable and realistic. In general, performance shaping factors are utilized 
to alter the nominal HEP in order to account for the effects of equipment design, operator skills, 
psychological and physiological stresses, etc. Because the procedures and equipment that will be 
employed to perform the fabrication and handling of the waste package and the drip shield have 
not yet been written or precisely identified, use of performance shaping factors would be 
premature at this stage. Only in very particular cases, for which the use of a nominal HEP would 
not adequately reflect the environmental conditions under which the operator is to operate, have 
the HEP been altered to represent more accurate operating conditions (see Sections 6.2.4 and 
6.2.5). 
In addition to the estimates given previously, Swain and Guttmann (1983) provide general 
guidelines to assigning error factors to nominal HEPs, depending on the value of the probability 
and other factors such as stress level. This guideline was used in this analysis when no specific 
error factor was already assigned to the estimated probability. The values used are given in 
Table 5. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Table 5. Estimates of Error Factors for Human Error Probabilities 
Source: 
Error Swain & Guttmann 
Item # Description Factor (1983) 
1 
Task consists of performance of step-by-step procedure conducted 
under routine circumstances; stress level is optimal. 
The estimated nominal probability is lower than 0.001. 
10 Item 1 of Table 20-20 
Task consists of relatively dynamic interplay between operator and 
2 system indications, under routine conditions; stress level is optimal. 5 Item 5 of Table 20-20 
The estimated nominal probability is greater than 0.001. 
Source: Swain and Guttmann 1983 
As mentioned by Swain and Guttmann (1983, pp. 1 and 2), the HEPs given previously are not 
only applicable to human reliability in nuclear power plants but also may be used for other large 
process plants such as chemical plants, oil refineries, etc. These types of industries can be 
characterized by highly controlled environment and are governed by strict quality standards and 
controls. This characterizes also the fabrication and handling operations of the waste package 
and the drip shield. Based on this information, the HEPs and error factors given previously 
appear to be appropriate for use in this analysis. 
A review and comparison of Handbook of Human Reliability Analysis with Emphasis on Nuclear 
Power Plant Applications Final Report (Swain and Guttmann 1983) and Technical Basis and 
Implementation Guidelines for a Technique for Human Event Analysis (ATHEANA) (NRC 2000) 
was performed. Technical Basis and Implementation Guidelines for a Technique for Human 
Event Analysis (ATHEANA) (NRC 2000) is a description of a specific step-by-step sequential 
application of the Human Reliability Analysis (HRA) methodology. Some background 
information and discussion of errors of commission and omission are included, but no new or 
updated HEPs are included. 
4.1.3 Alloy 22 Weld Flaw Characteristics 
Sixteen weld rings of Alloy 22 have recently been fabricated and examined using various 
nondestructive examination techniques, followed by a metallographic examination (BSC 2003d). 
Information gathered from these experiments has been used to develop a flaw density and size 
distribution applicable to the closure welds of the waste package. The parameters used are 
summarized in the following subsections. 
4.1.3.1 Weld Ring Dimensions 
Weld ring dimensions are summarized in Table 6 with visualization and reference points of the 
weld given in Figure 1. Dimensions are given in the unit provided in the corresponding source 
of information. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Table 6. Weld Dimensions 
Parameter Description (see Figure 1) Parameter Value Source: BSC (2003d) 
Radius of the half-circle A1OA2 0.125 in Figure 2 
Distance OC 0.97 ina Figure 2 
Distance BC 0.43 inb Figure 2 
Angle B3A1B1 3 degrees Figure 2 
Angle C5B3C3 25 degrees Figure 3 
Angle B2A2B4 6 degrees Figure 2 
Angle C4B4C6 29 degrees Figure 3 
Diameter of the ring from centerline of the weld 60.765 inc Figure 2 
NOTES: a Value calculated from dimensions given in BSC 2003d, Figure 2. Note that this value, which 
characterizes weld thickness, has been rounded to 25 mm in all further calculations. 
b 
Rounded average value from dimensions given in BSC 2003d, Figure 2.
c 
Average value from dimensions given in BSC 2003d, Figure 2. 
The parameters given previously are appropriate for use in this analysis because they conform to 
the current design of the Alloy 22 closure welds of the waste package. 
C5 C3 C1 C C6C4C2 
B3 B4B2B1 B 
A1 A2 
O 
A 
Z 
Y 
Figure 1. Schematic Representation of the Cross Section of the Alloy 22 Weld 
4.1.3.2 Parameters for Ultrasonic Inspection and Flaw Characteristics 
Several nondestructive examination techniques were used to detect weld flaws in the specimen 
rings. Surface examinations included liquid penetrant and eddy current inspections. Volumetric 
examinations included radiographic and ultrasonic testing (UT). The surface indications, which 
consisted of nonwelding related indications such as tooling marks, were irrelevant (BSC 2003d) 
and are discarded from further consideration in this analysis. As far as volumetric inspection is 
concerned, it should be noted that the radiographic testing was mainly used for a secondary 
check of the UT inspections. Therefore, only the volumetric indications of the UT are further 
considered. 
RDP/PA IED Typical Waste Package Components Assembly (6) (BSC 2003d) indicates that the 
UT inspection threshold employed in the examination of the 16 weld rings that were fabricated 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
was 1 mm, which calls for detection of all flaws of size larger than 1 mm. This was confirmed 
by the metallographic inspections performed on the specimen rings: the weld imperfections 
discovered through this process were the same weld imperfections discovered during the UT 
inspections for all weld imperfections greater than 1 mm (BSC 2003d). The other imperfections 
were gas pores and the majority of them were less than 0.003 inch (around 0.08 mm) in diameter. 
Based on the information provided in RDP/PA IED Typical Waste Package Components 
Assembly (6) (BSC 2003d, Table 27), UT inspections revealed seven flaws that were later 
confirmed by metallography. Two of the weld flaws listed in Table 27 of RDP/PA IED Typical 
Waste Package Components Assembly (6) (BSC 2003d) could not be verified by metallography 
(Rings K2 and S1F) and therefore were not included in this evaluation. The weld flaw 
dimensions in the X, Y, and Z directions, as evaluated by the UT inspections, are given in 
Table 7. Note that metallographic examinations confirmed the UT dimensions or showed that 
they slightly overestimated the actual flaw dimensions (BSC 2003d). The parameters given in 
Table 7 were determined from DTN: MO030214WPWF01.000. 
Table 7. Dimensions of the Ultrasonic Indications 
UT Flaw X Direction Y Direction Z Direction 
Number Flaw Onset Flaw End Flaw Onset Flaw End Flaw Onset Flaw End 
Ring K  UT-2 a 54 1/2 in 54 5/8 in 3/8 in 7/16 in 1/2 in 9/16 in 
Ring K  UT-3 a 55 3/4 in 56 3/8 in 3/8 in 7/16 in 1/2 in 9/16 in 
Ring R  UT-1 b 19 1/8 in 19 7/8 in 11/16 in 13/16 in 9/16 in 5/8 in 
Ring R  UT-2 b 47 1/4 in 48 5/8 in 7/16 in 9/16 in 1/2 in 9/16 in 
Ring R  UT-3 b 20 7/8 in 21 1/4 in 11/16 in 13/16 in 9/16 in 5/8 in 
Ring W - UT-1 c 3 1/8 in 3 5/8 in 3/8 in 9/16 in 9/16 in 11/16 in 
Ring X  UT-1 d 4 5/16 in 4 11/16 in 3/16 in 3/4 in 11/16 in 11/16 in 
a
Source: DTN: MO030214WPWF01.000, p. 133 
b 
DTN: MO030214WPWF01.000, p. 807 
c 
DTN: MO030214WPWF01.000, p. 1171 
d 
DTN: MO030214WPWF01.000, p. 1246 
Based on RDP/PA IED Typical Waste Package Components Assembly (6) (BSC 2003d), the X 
direction gives the azimuthal location of the flaws in the direction of the weld (starting from 
some fixed point on the ring); the Y direction shows the position of the flaw in the through-wall 
extent of the weld; and the Z direction shows the radial position of the flaw in the weld. The Y 
and Z directions are shown on Figure 1. The X direction is shown on Figure 5, given in Section 
6.2.1.1.4. 
The flaws in Ring K are the result of a poor weld preparation (BSC 2003d) that was performed 
under conditions that are not representative of the highly controlled environment in which future 
manufacturing of the waste packages will take place. Nevertheless, following a conservative 
approach these flaws have been kept in this analysis. The other flaws reported in Table 7 are 
lack-of-fusion type defects (BSC 2003d). 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The parameters given previously are appropriate for use in this analysis because they yield 
characteristics of flaws of Alloy 22 welds, whose design conforms to that of the closure weld of 
the waste package. 
4.1.4 Anomaly Distribution Curve for Hard-Alpha Inclusion in Titanium Alloy 
Information from the U.S. Federal Aviation Administration (FAA), published in an advisory 
circular related to the distribution of hard-alpha inclusions in titanium engine rotors, was used in 
this analysis. Damage Tolerance for High Energy Turbine Engine Rotors (FAA 2001) contains 
several anomaly distribution curves associated with hard-alpha inclusions (also called Type I 
defects) (i.e., the number of hard-alpha inclusions per million pounds of titanium as a function of 
their size). These anomaly distribution curves are accepted data. The rationale for this is that 
these curves are accepted by the FAA to show compliance with requirements of Federal Aviation 
Regulations (14 CFR 33.14). 14 CFR 33.14 contains requirements applicable to the design and 
life management of high energy rotating parts of aircraft gas turbine engines (FAA 2001, 
Section 1). 
Briefly stated, the distributions were developed by modeling a complex series of interrelated 
steps that simulated the entire component manufacturing process from billet conversion to final 
machining as rotor components of aircraft engines. The final distributions were validated based 
on field experience. They are applicable to titanium rotor components manufactured after 1995 
using the triple vacuum arc remelt process or the cold hearth melt plus vacuum arc remelt 
process (FAA 2001, p. S3-7). 
Different distributions were developed reflecting different levels of sensitivity for the UT 
inspections performed at the billet stage and at the forging stage (FAA 2001, Appendix 3). 
Following a conservative approach, the anomaly distribution with the less sensitive UT 
inspections was selected for use in the present analysis. It corresponds to a UT inspection 
calibrated with #5 flat bottom hole at the billet stage and a UT inspection calibrated with #3 flat 
bottom hole at the forging stage. The flat bottom hole calibration standard consists of a block of 
material containing holes of varying diameters. The diameters of the holes are specified in 
multiples of 1/64 inch. 
In the advisory circular, the anomaly distribution curve is provided on a log-log graph (FAA 
2001, p. A3-2). From the log-log graph, a set of data points large enough to capture the main 
features of the curve was selected for use in this analysis and is given in Table 8. 
According to Damage Tolerance for High Energy Turbine Engine Rotors (FAA 2001, p. A1-1), 
the anomalies are considered spherically shaped and uniformly distributed throughout the part. 
Also, the same reference states that when anomaly sizes are required outside the range of data 
provided, the curve shown on the log-log graph should be linearly extrapolated. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Table 8. Set of Data Points for Hard-Alpha Inclusion Anomaly Distribution Curve 
Defect Inspection Area 
(square mils) 
Exceedancea 
(per million pounds) 
Defect Inspection Area 
(square mils) 
Exceedancea 
(per million pounds) 
100 6.6 2000 0.21 
200 3.6 3000 0.084 
300 2.6 4000 0.051 
400 2.0 5000 0.037 
500 1.7 6000 0.028 
600 1.3 7000 0.022 
700 1.1 8000 0.020 
800 0.90 9000 0.017 
900 0.75 10,000 0.016 
1000 0.65 20,000 0.010 
NOTE: a Number of inclusions of this size or larger. 
Source: FAA 2001, p. A3-2 
The data shown in Table 8 are appropriate for use in this analysis for the following reasons: 
 Hard-alpha imperfections are a dominant source of internal defects for titanium metal base. 
Hua et al. (2002, p. 7) suggest that this kind of defect may have been responsible for an 
abnormally high corrosion rate that was observed on several annealed Titanium Grade 7 
specimens exposed to a corrosive environment in a set of experimental tests. Hard-alpha 
defects are formed from very high nitrogen or oxygen concentrations in the bulk alloy and 
cannot be readily eliminated by a homogenizing heat treatment of primary mill processing 
(Hua et al. 2002, p. 7). These defects tend to string out during forging and rolling. Because 
they are hard they tend to break up during hot rolling and may form very small internal voids 
(Graham 2002). That is why they are accounted for among the potential defects that could 
lead to the early failure of the drip shield. 
 It is recognized that the anomaly distribution curve used in this analysis was intended for 
machined titanium-alloy rotors used in aircraft engines. This is a different type of titanium 
than the commercially pure (Grade 7) titanium to be used for the drip shield. Also, drip 
shield plates are obviously not similar to engine rotors. Nevertheless, hard-alpha defects are 
inherited from material processing, and from this point of view, titanium-alloy and 
commercially pure titanium have a very similar process route (Graham 2002). Moreover, 
titanium plates have a less complex shape than engine rotors, which should make the UT 
inspection and consequently the detection of hard-alpha defects much easier. For these 
reasons, it is considered that use of the previous data is appropriate in this analysis as it will 
provide a conservative estimate of the number of hard-alpha defects expected in the base 
metal of the drip shield, as a function of their size. It should nevertheless be kept in mind 
that the data used are only applicable to triple vacuum arc remelt or cold hearth melt plus 
vacuum arc remelt processed titanium. Also, these data apply to titanium that gets two UTs 
(at the billet stage, with #5 flat bottom hole, and at the forging stage, with # 3 flat bottom 
hole). 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
4.2 CRITERIA 
NRC requirements that pertain to the conduct of performance assessments are applicable to this 
evaluation. Section 63.102(j) of 10 CFR Part 63 states that: 
The features, events and processes considered in the performance assessment 
should represent a wide range of both beneficial and potentially adverse effects on 
performance []. Those features, events, and processes expected to materially 
affect compliance with Sec. 113(b) or be potentially adverse to performance are 
included, while events (event classes or scenario classes) that are very unlikely 
(less than one chance in 10,000 over 10,000 years) can be excluded from the 
analysis. 
The current design basis waste package inventory anticipates 11,184 waste packages to be 
emplaced in the repository (number based on the sum of the nominal numbers of each type of 
waste package shown in Table 11 of Repository Design Project, RDP/PA IED Typical Waste 
Package Components Assembly (2) (BSC 2003a). Therefore, the previous requirement would 
indicate that any feature, event, or process that has a probability of occurrence of less than 
10-4/11,184 = 8.9  10-9 per waste package over 10,000 years can be excluded from the 
performance assessment. Since this analysis results in early failure of waste packages and drip 
shields with a mean value on the order of 3  10-5 per waste package, this FEP is included in the 
TSPA-LA analysis. 
Yucca Mountain Review Plan, Final Report (NRC 2003) contains Acceptance Criteria (AC) 
intended to establish the basis for the review of the material contained in the License 
Application. As this model report serves, in part, as the basis for the License Application, it is 
important that the information contained herein conform to those same Acceptance Criteria. This 
calculation addresses the degradation of two engineered barriers. Brief summary descriptions of 
these components are provided in Sections 1 and 4.1.1. Based on the engineered barrier role of 
the waste package and drip shield, the processes involved with its degradation, and the potential 
impact of its degradation, the Acceptance Criteria that are applicable to this calculation are 
delineated below. 
YMRP Acceptance Criteria 2.2.1.1.3System Description and Demonstration of Multiple 
Barriers 
AC 1  Identification of Barriers is Adequate 
Barriers relied upon to achieve compliance with 10 CFR 63.113(b), as 
demonstrated in the total system performance assessment, are adequately 
identified and clearly linked to their capability. 
AC 2  Description of Barrier Capability Is Acceptable 
The capability of the identified barriers to prevent or substantially reduce the 
movement of water or radionuclides from the Yucca Mountain repository to the 
accessible environment or prevent the release or substantially reduce the release 
rate of radionuclides from the waste is adequately identified and described: 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
(1) The information on the time period over which each barrier performs its 
intended function, including any changes during the compliance period, is 
provided; 
(2) The uncertainty associated with barrier capabilities is adequately described; 
(3) The described capabilities are consistent with the results from the total system 
performance assessment; 
(4) The described capabilities are consistent with the definition of a barrier at 10 
CFR 63.2 
AC 3  Technical Basis for Barrier Capability is Adequately Presented. 
The technical bases are consistent with the technical basis for the performance 
assessment. The technical basis for assertions of barrier capability is 
commensurate with the importance of each barriers capability and the 
associated uncertainties. 
YMRP Acceptance Criterion 2.2.1.3.1.3, AC 3 (4) (NRC 2003) expects that the DOE use 
appropriate methods for nondestructive examination of fabricated engineered barriers to assess 
the type, size, and location of fabrication defects that might lead to premature failure as a result 
of rapidly initiated engineered barriers degradation. The criterion further states that the DOE 
specify and justify the allowable distribution of fabrication defects in the engineered barriers 
and [assess] the effects that cannot be detected on the performance of the engineered barriers. 
The analyses contained in this report consider the potential existence of such defects, the 
probability of their occurrence, and their potential impact. 
5. ASSUMPTIONS 
Many of the following assumptions are related to operations, processes and procedures 
governing the fabrication, closure, inspection and transportation of the waste packages and drip 
shields. No uncertainty or confidence level can be assigned at this time for the validity of these 
assumptions. 
5.1 ASSUMPTIONS RELATED TO FLAWS IN ALLOY 22 WELDS 
5.1.1 Flaw Detection by Ultrasonic Testing 
Assumption: It is assumed that all flaws greater than 1 mm (UT detection threshold) have been 
detected during the UT inspection of the specimen rings: these are the indications reported in 
Section 4.1.3.2. It is also assumed that these indications are sufficient to characterize the 
significant flaws expected in the Alloy 22 outer closure welds of the waste package. By 
significant flaws it is meant those flaws that may jeopardize the performance (time to breach) of 
the waste package in the repository. 
Rationale: The rationale for the first part of the assumption is as follows: 
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Metallographic inspections were performed on the specimen rings and the weld 
imperfections discovered through this process were the same weld imperfections 
discovered during the UT inspections for all weld imperfections greater than 1 mm (see 
Section 4.1.3.2). Of course, it was not possible to perform metallographic examination 
on the entire specimen rings since it is a very time-consuming process; instead, 
metallographic inspections (up to six per ring) were performed at randomly selected 
locations in the areas where no flaw had been detected through UT inspection. None of 
these metallographic inspections revealed a flaw of size larger than the UT detection 
threshold of 1 mm. This strongly suggests that the majority, if not all, of the flaws 
greater than 1 mm were detected. 
The rationale for the second part of the assumption follows: 
The imperfections uncovered through metallographic examinations, that were not 
detected through UT inspections, were gas pores, and the majority of them were less than 
0.003 inch (around 0.08 mm) in diameter. Gas pores are spherical in shape and have no 
orientation. Therefore, they are not part of those flaws that are radially oriented. Gas 
pores are treated the same as spherical porosity in Stress Corrosion Cracking of the Drip 
Shield, the Waste Package Outer Barrier, and the Stainless Steel Structural Material 
(BSC 2003e, Section 6.2.2.1). In other words, they will not induce propagation of cracks 
via stress corrosion cracking. Thus, they are not likely to jeopardize the performance of 
the waste package and can be discarded from further consideration. 
Use in the Calculation: This assumption is used in Section 6.2.1.1. 
5.1.2 Representation of Ultasonic Test Probability of Nondetection Curve 
Assumption: It is assumed that the UT probability of nondetection (PND) curve of the flaws in 
the waste package closure weld (i.e., the curve that gives the PND of a flaw as a function of its 
size) can conservatively be represented by using Equation 21 with the following parameters: 
e = 0.005, . = 3, and s0 = 2.5 mm. 
Rationale: This assumption is needed because the UT PND curve related to the UT inspection of 
the specimen rings was not developed. This makes it necessary to assume the shape of the curve 
and the associated parameter values. The rationale for this assumption is as follows. Equation 
21 is based on results of previous UT reliability studies summarized by Bush (1983, pp. 13A.5.6 
and 13A.5.7). The suggested parameter values are e = 0.005, . = 3, and s0 = 5 mm. However, 
these studies were performed in the late 1970s, and do not reflect the UT inspection capability 
attainable with current technology. More recent studies, such as that reported by Heasler and 
Doctor (1996), show significantly improved reliability. Also, the UT inspections performed on 
the specimen rings showed that flaws as small as 1 mm in size could effectively be detected (see 
Section 4.1.3.2). This is an important result since the welds on the specimen rings are very 
similar to the closure welds of the waste package. Based on this information, the parameter 
values suggested by Bush (1983) appear to be very conservative. Nevertheless, they have been 
kept for this analysis, except for the value of s0, which has been reduced to 2.5 mm. This has 
been done to have a more realistic representation of the UT PND curve and, in light of previous 
information, is still deemed conservative. Also, note that this value is appropriate to account for 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
those small flaws that will be detected, but left in the weld, because these flaws will not 
jeopardize the waste package performance. 
Use in the Calculation: This assumption is used in Section 6.2.1.2. 
5.1.3 Extension of Outer Lid Weld Flaw Distribution Characteristics 
Assumption: The characteristics of the distributions of flaw size in the Y direction, flaw density, 
flaw depth, and flaw orientation investigated in Sections 6.2.1.1 and 6.2.1.2 were developed for 
the outer lid weld of the waste package. It is assumed that these characteristics also apply to the 
middle lid weld and seam welds of the waste package (see Section 6.2.1.3 for the definition of 
the seam welds). 
Rationale: This assumption is needed because no flaw information concerning welds other than 
the outer lid weld is available. The rationale for this assumption is as follows: 
 Flaw size in the Y direction: The evaluations performed in Section 6.2.1.1.1 show that 
Equation 6 is compatible with the size given by the UT indications in the Y direction. 
Equation 6 is based on an exponential distribution that was adjusted to fit the flaw sizes 
within the thickness t of the weld considered. There is no reason to believe that the 
flaws in the other welds of the outer barrier of the waste package would be of a different 
nature than those detected through UT indications. Based on this reasoning, it can be 
expected that the differences in size in the through-wall direction (Y direction) will be 
mainly governed by the cap imposed by the weld thickness. Equation 6 was devised to 
take into account this weld thickness effect. It is worth noting that a basic comparison 
with another possible form of the equation that could account for the weld thickness 
effect was also performed (see Section 6.2.1.1.1 and Attachment I). Equation 6 was 
shown to provide more conservative results. Based on this information, Equation 6 
appears to provide a reasonable way to adjust the flaw size distribution in the Y direction 
to different weld thicknesses of the waste package outer barrier. 
 Flaw density: The flaw density parameter (which corresponds to a mean number of 
flaws per meter of weld) evaluated in Section 6.2.1.1.2 pertains to a 25-mm thick weld. 
The middle lid weld and the seam welds are respectively 10 mm and 20 mm thick (see 
Section 6.2.1.3 for explanations). Since the density of flaws in the welds can be 
expected to be proportional to the mass of weld used, there should be fewer flaws per 
meter of weld in the middle lid weld and the seam welds than in the outer lid weld. 
Therefore, applying the flaw density pertaining to the outer lid weld to the other welds is 
conservative. 
 Flaw depth: The investigation performed in Section 6.2.1.1.3 shows that the depth of 
the flaws detected through UT indications is uniformly distributed throughout the weld 
thickness. There is no reason to believe that the flaws expected to occur in the welds of 
the outer barrier of the waste package will be of a different nature than those that were 
detected through UT indications. Therefore, it is reasonable to consider that these flaws 
will be uniformly distributed throughout the through-wall extent of the welds. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
 Flaw orientation: The investigation performed in Section 6.2.1.1.4 shows that the 
orientation of the majority of flaws follows the direction of the weld. This is due to the 
fact that the significant weld imperfections correspond for the most part to lack-of-
fusions flaws. The investigation performed in Section 6.2.1.1.4 also accounts for a flaw 
making a 27-degree angle with the direction of the weld. This flaw was kept in the 
analysis though it resulted from a poor weld preparation that is not representative of the 
highly controlled conditions under which operations will be performed on the waste 
package (see Section 6.2.1.1.4). This makes the evaluation of the orientation of the flaw 
conservative. There is no reason to believe that the significant flaws in the other welds 
of the outer barrier of the waste package would be of a different nature than those 
detected through UT indications. Therefore, considering that the results obtained for the 
outer lid weld also apply to the other welds of the outer barrier of the waste package is 
reasonable. 
Use in the Calculation: This assumption is used in Section 6.2.1.3. 
5.2 ASSUMPTIONS RELATED TO FLAWS IN ALLOY 22 BASE METAL 
5.2.1 Repair of Alloy 22 Base Metal 
Assumption: It is assumed that repair of Alloy 22 base metal will occur on each waste package 
and affect approximately 100 cm2 of base metal. It is also assumed that introduction of flaws in 
the base metal during repair will result from the failure of the welder to use the written procedure 
governing the repairs to base metal, followed by the failure of the checker to detect the errors 
made by the welder. 
Rationale: The first part of this assumption is needed because, in absence of data, it is 
impossible to estimate an upper value for the frequency of improper base metal repair in the 
waste package. The rationale for the assumption is that assuming a base metal repair for each 
waste package is very conservative. Note that the number chosen for the affected area, 100 cm2 
(equivalent to a square with a side of 10 cm), is somewhat arbitrary. The difficulty here is that it 
is necessary to know the extent to which base metal repairs will be performed, but there is no 
available data. Nevertheless, it is known that rejectable defects detected during the UT 
inspection of the waste package may be repaired by welding, provided prior approval is granted 
by U.S. Department of Energy, and that defective material that cannot be satisfactorily repaired 
will be rejected and replaced (Plinski 2001, Section 6.5). Based on this information, it makes 
sense to consider that only a small portion of the waste package material might be subjected to 
repair and that beyond a certain extent, the material will be rejected. In that light, a 100-cm2 area 
seems realistic. Notice that the arbitrariness of that number is tempered by the conservatism in 
considering that every single waste package will require base metal repair. 
The rationale for the second part of the assumption is that the fabrication of the waste package 
will be performed following a strict quality assurance (QA) program (Plinski 2001, Section 6). 
Consequently, the basic scenario by which flaws could be introduced in the base metal appears to 
be adequate. 
Use in the Calculation: This assumption is used in Section 6.2.2. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
5.2.2 Ratio of Weld Flaws to Base Metal Flaws 
Assumption: It is assumed that the ratio of weld flaws to base metal flaws resulting from repairs 
in the Alloy 22 barrier of the waste package is eight to one. 
Rationale: This assumption is needed because there is no data available on the density of flaws 
in Alloy 22 base metal. The rationale for this assumption is that it is a conservative ratio, based 
on findings by Schuster et al. (2000, p. 2.3), resulting from the UT examination of an unused 
reactor pressure vessel. Schuster et al. (2000, pp. 4.2 and 4.3) propose several possible 
explanations for the flaws detected in base metal: laminations, imperfections at the clad-to-base 
metal interface of the vessel, and repairs to base metal. Here, it is conservatively considered that 
all the base metal flaws are a consequence of repairs. The ratio (Schuster et al. 2000, p. 23) was 
determined for a stainless steel container, but because of its conservative application in this 
assumption, it is also considered acceptable for the Alloy 22 barrier of the waste package. 
Use in the Calculation: This assumption is used in Section 6.2.2. 
5.3 ASSUMPTIONS RELATED TO IMPROPER WELD MATERIAL OR BASE 
METAL 
The following assumptions were used in Section 6.2.3 to estimate the probability that improper 
weld or base metal material is inadvertently used in the manufacturing of the outer barrier of the 
waste package. Improper weld or base metal material, if not detected, may result in the 
emplacement of an out-of-specification waste package in the repository. Because the approach 
of Section 6.2.3 was also employed for evaluating the probability of using improper weld or base 
metal material in the drip shield, these assumptions also apply to Section 6.3.3. 
5.3.1 Approximation of Probability of Using Improper Weld Material 
5
Assumption: It is assumed that the probability of using improper weld material in the fabrication 
of the outer barrier of the waste package can be approximated by a lognormal distribution whose 
th and 95th percentile are respectively 1.5  10-5 and 8.2  10-5. 
Rationale: This assumption is needed because no data has yet been accrued on the use of 
improper weld material in the fabrication of a waste package. 
The rationale for this assumption is based on the only well-documented occurrence of weld 
populations that were affected by improper weld material. In the preparation of a response to 
NRC Bulletin 78-12 (NRC 1978), which was prompted by the discovery that the weld chemistry 
of a portion of the Crystal River 3 surveillance-block weld did not meet the specification 
requirements, Babcock & Wilcox investigated their records to determine the extent to which out-
of-specification weld wire may have been used in the fabrication of reactor vessels (Babcock and 
Wilcox 1979). Out of 1,706,556 pounds of weld wire (Babcock & Wilcox 1979, p. I-6) that was 
used to make 43 reactor vessels for the American market (Babcock & Wilcox 1979, Table 1 of 
Part II), it was estimated that 65 to 350 pounds of weld wire was out-of-specification (Babcock 
& Wilcox 1979, pp. 2 and I-4). No other instances of improper weld material were reported in 
other vendors responses to NRC Bulletin 78-12 (NRC 1978). There have been around 120 
reactors operated in the United States (rounded-down number, based on ANS 1999, pp. 52 to 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
55), so these 43 reactors account for less than 36 percent (43/120) of the vessels fabricated for 
use in the United States. Conservatively round up this number to 40 percent. Therefore, the total 
mass of weld material used to fabricate these vessels has been at least 4,266,390 pounds 
(1,706,556/0.4). Thus, the probability of using improper welding material ranges from 1.5  10-5 
(65/4,266,390) to 8.2  10-5 (350/4,266,390 ). 
The information provided in Records Investigation Report Related to Off-Chemistry Welds in 
Material Surveillance Specimens and Response to IE Bulletins 78-12 and 78-12A  Supplement 
(Babcock and Wilcox 1979) is not sufficient in itself to draw conclusions on the shape of the 
distribution for the probability of using improper welding material. Nevertheless, the lower and 
upper values estimated previously are assumed here to represent the 5th and 95th percentile of a 
lognormal distribution. The reason for choosing the 5th and the 95th percentiles is that it is 
common practice when evaluating lower and upper bounds: for example, this is the percentiles 
recommended by Swain and Guttmann (1983, p. 2-19) in evaluating uncertainty of HEPs. As for 
the lognormal distribution, it has mainly been chosen for tractability reasons in the calculation of 
uncertainty bounds: this is based on the fact that the product of independent lognormal 
distributions (extensively used in this analysis) is also lognormal (Swain and Guttmann 1983, pp. 
A-2 and A-4). 
Use in the Calculation: This assumption is used in Section 6.2.3. 
5.3.2 Field Measurements of Material Compositions 
Assumption: It is assumed that quick field measurements of material compositions, using 
equipment such as a portable X-ray spectroscopy device, will be performed by a technician 
before welding material is used on the waste package. 
Rationale: The rationale for this assumption is that the technology for these types of 
measurements is currently available (ASM International 1990b, pp. 1030 to 1032) and used in a 
variety of similar commercial applications. 
Use in the Calculation: This assumption is used in Section 6.2.3. 
5.3.3 Probability of Using Improper Base Metal 
Assumption: It is assumed that the probability of using improper base metal in the fabrication of 
the outer barrier of the waste package is the same as the probability of using improper weld 
material (calculated in Assumption 5.3.1). 
Rationale: The rationale for this assumption is that the processes that would lead to the use of 
improper base metal (e.g., procurement, selection, or shipment of the incorrect material) are of 
the same nature as those that would lead to the use of improper weld material. Therefore, it is 
reasonable to consider that these probabilities are equal. As discussed in Section 6.1.6, no 
instances of improper base material use have been identified. 
Use in the Calculation: This assumption is used in Section 6.2.3. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
5.4 ASSUMPTIONS RELATED TO IMPROPER WASTE PACKAGE HEAT 
TREATMENT 
The following assumptions were used in Section 6.2.4 to estimate the probability that a waste 
package is improperly heat treated and that this improper heat treatment remains undetected. 
Because the approach of Section 6.2.4 was also employed for evaluating the probability of 
improper heat treatment of the drip shield, these assumptions also apply to Section 6.3.4. 
5.4.1 Heat Treatment Process and Procedural Controls 
Because the procedures and equipment for heat treating the waste package have not yet been 
written, it is necessary to make a set of assumptions on the process to be implemented and on the 
controls that will be put in place to detect any potential improper heat treatment of the waste 
package. 
Rationale: The rationale for this set of assumptions is that, in absence of written procedures, 
they describe a realistic process for implementing and controlling the heat treatment of the waste 
package based on current industry heat treatment techniques. In particular, the main assumption 
is that the process will be computerized. This is based on information from Heat Treating 
Progress, 1 (ASM International 2001, p. 103), which describes computer control of heat treating 
operations as common practice. Compared to manually controlled heat treatment, 
computerization provides for higher precision of measurement and control, increased speed of 
measurement and response to process changes, and better accuracy in record keeping and 
reporting. The set of additional assumptions related to the implementation and control of the 
heat treatment process is as follows: 
 It is assumed that the operator will have to select between several predefined heat 
treatment programs, each corresponding to a different kind of waste package. Also, it is 
considered that the heat treatment program will cover the heating phase as well as the 
quenching phase. Considering that the heat treatment program is predefined means that 
the temperature to reach inside the furnace, for the ramp-up and hold phases as well as 
the time required for quenching the waste package, is already known and executed by 
the program. 
 It is assumed that the waste package temperature will be measured by thermocouples 
installed on the waste package before each heat treatment. 
 It is assumed that the proper installation of the waste package thermocouples will be 
verified through an over-the-shoulder inspection performed by a checker. 
 It is assumed that some fixed instrumentation will be used for measuring and controlling 
the parameters governing the heat treatment process such as temperature of the furnace, 
flow rate of the fluid used for quenching, time spent by the waste package in ramp-up, 
hold, and quench phase, etc. Because this type of instrumentation and control does not 
need to be reinstalled each time a waste package is processed, it is further assumed that 
it will be sufficiently redundant and diversified, such that any significant process 
malfunction would be detected and signaled to the operator by alarm. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
 It is assumed that the thermocouples installed on the waste package will not be used to 
control the heat treatment program but only to measure the temperature of the waste 
package at specific locations and trigger an alarm if the measured temperatures deviate 
from the allowable range. The reason for this restriction in the role of the waste package 
thermocouples is that they need to be reinstalled for each waste package. As a 
consequence, they are more prone to improper installation and subsequent malfunction, 
than the fixed instrumentation of the furnace and the quenching equipment, 
instrumentation, which is considered more reliable since it can be more easily made 
redundant and diversified. 
 It is assumed that a log of the control parameters and the events recorded during the heat 
treatment process will automatically be generated by the computerized heat treatment 
system. It is further assumed that this log will be reviewed through a QA check 
performed by an individual other than the operator. 
Use in the Calculation: This assumption is used in Section 6.2.4. 
5.4.2 Event Sequence Resulting in Improper Heat Treatment 
Rationale: Additional assumptions are required to develop the event sequences that would lead 
to an undetected improper heat treatment of the waste package. The rationale for these 
complementary assumptions is that they are based on a conservative approach. 
 It is assumed that for a waste package to be properly heat treated, it is necessary that the 
operator selects the correct heat treatment program. An incorrect heat treatment 
program selection will result in a waste package temperature drift outside of the 
allowable range for adequate heat treatment of the waste package. Notice that this drift 
in temperature will normally be captured by the thermocouples installed on the waste 
package and will prompt an alarm from the computerized heat treatment control system. 
 It is assumed that if an incorrect heat treatment program is selected, the waste package 
thermocouples will not capture the temperature drift outside of the allowable range if 
their installation was improperly performed (for instance, the thermocouples might be 
incorrectly affixed to the waste package or installed in incorrect locations leading to 
different temperature measurements than those that a proper installation would yield). 
Conversely, notice that a correct selection of the heat treatment program combined with 
an incorrect installation of the thermocouples will not lead to an improper heat treatment 
of the waste package. This is due to the fact that the waste package thermocouples are 
utilized to measure the temperature, not to control the process (see Assumption 5.4.1). 
Therefore, this scenario cannot lead to an undetected improper heat treatment of the 
waste package. 
 It is assumed that operator failure to respond to an alarm prompted by the computerized 
heat treatment control system, signaling a process malfunction, will result in an 
improper heat treatment of the waste package. If, during the review of the log generated 
by the computerized heat treatment system, the checker fails to detect that the operator 
did not respond to the alarm the improper heat treatment of the waste package will 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
remain unnoticed. Conversely, it is assumed that detection of the alarm by the operator 
or the checker cannot lead to an undetected improper heat treatment. 
Use in the Calculation: This assumption is used in Section 6.2.4. 
5.4.3 Probability of a Significant Process Malfunction 
Assumption: It is assumed that the probability that a significant process malfunction occurs 
during the heat treatment of a waste package can be approximated by a lognormal distribution 
with a median of 0.005 and an error factor of 2. 
Rationale: This assumption is needed because there is no operating experience on malfunctions 
that may affect the heat treatment of the waste package (i.e., no data is available). The rationale 
for the malfunction probability given previously is that it is conservative. More details are given 
in the following paragraphs. 
The lognormal distribution was chosen for tractability reasons in the calculation of uncertainty 
bounds: this is based on the fact that the product of lognormal distributions (extensively used in 
this analysis) is also lognormal (Swain and Guttmann 1983, pp. A-2 and A-4). A median of 
0.005 and an error factor of 2 were chosen as conservative estimates for the probability of a 
process malfunction. This information can equivalently be expressed in terms of probability 
range with the 95th percentile for the distribution at 0.005  2 = 0.01 and the 5th percentile at 
0.005/2 = 2.5  10-3. On average, with the 95th percentile a process malfunction can be expected 
to occur every 1/0.01 = 100 heat-treated waste packages and with the 5th percentile every 
1/2.5  10-3 = 400 heat-treated waste packages. This range reflects a high frequency of 
malfunction occurrence. In reality, the heat treatment process can be expected to be much more 
reliable and it is not desirable to have a process jeopardize a valuable piece of equipment such as 
the waste package as often as predicted by the previous estimates. 
The fact that these values are conservative is also confirmed by a very simple preliminary 
reliability assessment (since the designs of the furnace and the quenching system have not been 
decided yet, it is too early to make a precise evaluation of the system reliability). A critical 
parameter of the heat treatment process is the temperature in the furnace, which, for illustration 
purpose, is considered here to be regulated by heaters and the associated instrumentation for 
control. Based on information from Eide and Calley (1993, Table 2), the failure rate of an 
electrical heater is approximately 5.0  10-6/h. Also, the failure rate for an element of 
instrumentation is 1.0  10-6/h and that for a transmitter is 3.0  10-6/h. These components 
constitute a base unit for maintaining the furnace at its proper temperature. Assuming that the 
heater is expected to operate for 10 hours per each processed waste package (which is a 
reasonable to conservative number), a point estimate for the probability of failure of the heater 
with its associated instrumentation is 10  (5 + 1 + 3)  10-6 = 9  10-5. Thus, it can be expected 
that proper operation of several heaters will be required for the correct heat treatment of the 
waste package. Also, it is reasonable to consider that the critical components will be redundant 
and diversified to lower their dependency to failure by common cause. Based on that 
information and the previous estimate, it can be expected that the heat treatment process will 
have a probability of malfunction in the 10-4 order of magnitude per heat-treated waste package 
(i.e., below the probability range considered in this assumption). 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Use in the Calculation: This assumption is used in Section 6.2.4. 
5.5 ASSUMPTIONS RELATED TO IMPROPER LASER PEENING 
The following assumptions were used in Section 6.2.5 to estimate the probability that the closure 
welds of a given waste package is improperly laser-peened, preventing an adequate stress 
mitigation, and that this improper laser peening remains undetected. 
5.5.1 Laser Peening Process and Procedural Controls 
Assumption: It is assumed that the laser peening system will be fully computerized and that 
process malfunctions will be signaled to the operator via alarms. 
Rationale: The rationale for this assumption is based on information provided by Sano et al. 
(2000), which describes a laser peening system that was successfully used for an industrial 
application, namely the stress mitigation of the core shroud of a nuclear reactor. The system 
included automated beam alignment/tracking function, remote handling equipment, an online 
monitor, and a system control unit (Sano et al. 2000, p. 2). Also, the system was computerized to 
allow continuous monitoring of the laser irradiation (Sano et al. 2000, p. 6). This example shows 
that a fully computerized laser peening system can be used for an industrial application. It is 
expected that a computerized system will be used for the laser peening of the waste packages, 
since more than 10,000 waste packages are expected to be processed, which calls for automation. 
Use in the Calculation: This assumption is used in Section 6.2.5. 
5.5.2 Automatic Generation of an Event Log 
Assumption: It is assumed that a log of the control parameters and the events recorded during the 
laser peening process will automatically be generated by the computerized laser peening system. 
It is further assumed that this log will be reviewed through a QA check performed by an 
individual other than the operator. Lastly, it is conservatively assumed that the operator failure 
to respond to an alarm prompted by the computerized laser peening control system, signaling a 
process malfunction, will result in an improper laser peening. 
Rationale: The rationale for this set of assumptions is that a computerized control system 
enables better reporting of the control parameters and better tracking of deviation from these 
parameters than a manually controlled system. Also, QA checks performed by independent 
checkers are common practice in the nuclear industry. 
Use in the Calculation: This assumption is used in Section 6.2.5. 
5.5.3 Approximation of Probability of a Significant Process Malfunction 
Assumption: It is assumed that the probability that a significant process malfunction occurs 
during the laser peening of a waste package can be approximated by a lognormal distribution of 
median 0.005 and error factor of 2. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Rationale: This assumption is similar to Assumption 5.4.3 and its rationale is basically the same. 
Only the highlights are given here. This assumption is needed because no operating experience 
has been accrued on laser peening of the waste packages (i.e., no data exist). The lognormal 
distribution has been chosen for tractability reasons in the calculation of uncertainty bounds. 
The value of the parameters is such that the probability range is conservative: on average, a 
significant malfunction of the process is expected to occur for every 100 to 400 waste packages 
treated, which is a high frequency of occurrence for malfunctions jeopardizing a piece of 
equipment as valuable as the waste package. 
Use in the Calculation: This assumption is used in Section 6.2.5. 
5.6 ASSUMPTIONS RELATED TO WASTE PACKAGE CONTAMINATION 
The following assumptions were used in Section 6.2.6 to estimate the probability that a waste 
package gets its surface contaminated by some corrosion-enhancing material and that this 
contamination remains undetected. Note that radiological contamination is not considered here. 
5.6.1 Naked-Eye Inspection of Waste Package for Contamination 
Assumption: It is assumed that a naked-eye inspection of the waste package will take place at 
reception to the surface facilities of the repository and that this inspection will detect all visible 
traces of contamination on the waste package (i.e., presence of foreign material on the waste 
package). It is also assumed that a remote inspection of the waste package (via camera) will take 
place just before the waste package is emplaced on the pallet in order to detect any visible trace 
of contamination. Lastly, it is assumed that these two inspections will be independent from each 
other. 
This assumption is needed because the procedures governing the control of operations on the 
waste package have not been written yet. 
Rationale: The rationale for the assumption is that performing an inspection when receiving a 
highly controlled piece of equipment such as the waste package, and another one before the 
equipment is going to be put in service, is to be expected since it is common practice to perform 
similar tasks in the nuclear industry on sensitive material. Also, it should be noted that when 
received at the facility the waste package can be easily and thoroughly inspected since it has not 
yet been loaded with nuclear waste and therefore is not radioactive. The final inspection is 
supposed to be performed right before emplacement on the pallet because it enables a complete 
inspection of the waste package and at the same time ensures that this inspection performed late 
in the process will catch potential contaminations that might have occurred earlier. Also, the 
final inspection is supposed to be performed remotely via a camera in order to account for 
protection of the operator against radiation. Independence of the two inspections is warranted by 
the fact that these inspections will take place at different locations, at different time, and using 
different means (naked-eye inspection versus remote inspection). Furthermore, these inspections 
will most likely be performed by different individuals. 
Use in the Calculation: This assumption is used in Section 6.2.6. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
5.6.2 Postexamination Contamination of the Waste Package 
Assumption: It is assumed that after the final waste package inspection (just before it is 
emplaced on the pallet) the probability that the waste package is subjected to further 
contamination without that being detected is negligible. 
Rationale: The rationale for this assumption is as follows: After the final waste package 
inspection, the most likely activity that could leave a foreign material on the waste package (i.e., 
causing its contamination) is through its handling. However, the waste package is subject to 
only one direct handling, namely its tilting onto the pallet. After that, it is the pallet which is 
directly handled, not the waste package (which merely sits on the pallet). Therefore, only the 
tilting operation is of concern here. At this time, the waste package will be loaded with 
radioactive waste. Consequently, for radioprotection purposes, the waste package tilting 
operation can be expected to be subjected to more scrutiny than the handling operations 
preceding the loading of the waste package with waste. In that light, it is unlikely that a 
contamination of the waste package would go unnoticed. Also, during its transport to the 
underground repository the waste package will be protected from exposure to exterior sources of 
contamination by the shielding from the waste package transporter. Then, the gantry will protect 
the waste package until it is emplaced in the drift. 
Use in the Calculation: This assumption is used in Section 6.2.6. 
5.6.3 Possibility of Waste Package Contamination During Cleaning 
Rationale: Because contamination of the waste package could occur during one of its cleanings, 
and since no procedures governing the cleaning process have yet been written, it is necessary to 
make a set of assumptions on the circumstances that could cause such contamination. The 
rationale for these assumptions is that they describe realistic conditions for a contamination 
scenario. 
 It is assumed that the Alloy 22 barrier will be subjected to a total of eight cleanings, 
namely: after each of five welds (two longitudinal and one circumferential for welding 
the outer barrier, one for welding the support ring, one for welding the bottom lid), after 
heat treatment, before shipping, and at reception at the surface facility of the repository. 
 It is assumed that there are different operators for each cleaning occurrence and that 
each cleaning is independent of the other cleanings. 
 It is assumed that contamination of the waste package through its cleaning may result 
only from the use of an improper cleaning agent. In other words, an incorrect cleaning 
process such as forgetting or incorrectly performing a step with proper cleaning agents 
cannot leave a residue that can have adverse effects on the metal. 
 It is assumed that the maintenance policies governing the facilities where the waste 
package will be fabricated and handled will require that the cleaning agents used for the 
waste package be stored in a separate stockage area so as to avoid confusion with other 
cleaning products. A consequence of this assumption is that selection of an improper 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
cleaning agent by the technician in charge of waste package cleaning means that the 
maintenance policies are not properly carried out. 
 It is assumed that a QA check will review the cleaning process after the cleaning has 
occurred. This is a check of the process, not the actual surface of the metal as the 
presence of contaminants from cleaning is considered not to be visible to the naked eye. 
Use in the Calculation: This assumption is used in Section 6.2.6. 
5.7 ASSUMPTIONS RELATED TO IMPROPER WASTE PACKAGE HANDLING 
The following assumptions were used in Section 6.2.7 to estimate the probability that a waste 
package is damaged by mishandling and that the damage remains undetected. 
5.7.1 Naked-Eye Inspection of Waste Package for Damage 
Assumption: It is assumed that the inspections considered in Assumption 5.6.1 will also serve to 
detect traces of damage to the waste package. Recall that two inspections of the waste package 
are supposed to take place in the surface facilities of the repository: a naked-eye inspection 
when the waste package is received and a remote inspection (via camera) just before the waste 
package is emplaced on the pallet. Also, as in Assumption 5.6.1, it is assumed that the two 
inspections will be independent from each other and that the inspection at waste package 
reception will detect all visible traces of mishandling. 
Rationale: The rationale for this assumption is the same as that given in Assumption 5.6.1. 
Use in the Calculation: This assumption is used in Section 6.2.7. 
5.7.2 Waste Package Damage Due to Mishandling After Reception But Before Final 
Inspection 
Assumption: It is assumed that between the inspection at waste package reception and the final 
inspection, the waste package might be mishandled and damaged on four occasions: when 
installed on the turntable to receive its collars, when tilted in an upward position, when installed 
in the staging area, and when removed from the staging area and placed onto the waste package 
pallet. 
Rationale: The rationale for this assumption is that these operations are the only ones during 
which the waste package is not expected to be protected from external shocks by some shielding 
equipment. When stored in the storage area or transported to the loading cell or the welding cell 
the waste package will be surrounded by protective equipment. Mishandlings that could occur 
when loading the fuel assemblies in the waste package are not considered because they will 
affect the waste package basket or at most the inner surface of the stainless steel cylinder, which 
is not of concern for the performance of the Alloy 22 barrier. 
Use in the Calculation: This assumption is used in Section 6.2.7. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
5.7.3 Waste Package Damage Due to Mishandling During Final Inspection 
Assumption: It is assumed that after the final waste package inspection (just before it is 
emplaced on the pallet), the probability that the waste package is subjected to further damage by 
mishandling, without that being detected, is negligible. 
Rationale: The rationale for this assumption is as follows. After the final waste package 
inspection, the most likely mishandling that could affect the waste package is its tilting onto the 
pallet. After that it is the pallet which is directly handled, not the waste package (which merely 
sits on the pallet). Therefore, only the tilting operation is of concern here. At this time the waste 
package will be loaded with radioactive waste. Consequently, for radioprotection purposes, the 
waste package tilting operation can be expected to be subjected to more scrutiny than the 
handling operations preceding the loading of the waste package with waste. In that light, it is 
very unlikely that damage of the waste package would go unnoticed. Also, during its transport to 
the underground repository the waste package will be protected from external shocks by the 
shielding from the waste package transporter. Then, the gantry will protect the waste package 
until it is emplaced in the drift. It is not expected that micro-shocks induced by vibrations during 
transportation will be significant enough to cause denting or gouging of the Alloy 22 barrier. 
Use in the Calculation: This assumption is used in Section 6.2.7. 
5.7.4 Approximation of Damage Due to Mishandling 
Assumption: It is assumed that the probability of damaging a waste package, due to an improper 
handling, can be approximated by a lognormal distribution with a mean of 4.8  10-5 (per waste 
package handling) and an error factor of 10. 
Rationale: The rationale for this assumption is as follows. No operating experience has been 
accrued on the handling of the waste packages, therefore no data exist that would enable a direct 
evaluation of the probability of damaging a waste package by mishandling. Instead, information 
on reported instances of damages to nuclear fuel assemblies during their handling was used to 
estimate that probability. This was done because a significant amount of operating experience 
has been accrued in that area. Also, fuel assembly handling activities are performed in a nuclear 
environment representative of the highly controlled conditions under which handling of the 
waste package is expected to occur. Therefore, it is deemed appropriate to use this information 
for estimating the probability of damaging a waste package by mishandling. 
Waste Package Misload Probability (BSC 2001b, Table 5) evaluates the probability of fuel 
assembly damage at 4.8  10-5 per moved fuel assembly. This point estimate is assigned to the 
mean of the distribution for the probability of damaging a waste package when handled. Also, 
Table 4 of Waste Package Misload Probability (BSC 2001b) states that the majority of fuel 
assembly damage events are due to human errors. Thus, based on the information given on 
HEPs in Section 4.1.2, it is appropriate to consider that the probability of mishandling a waste 
package has a lognormal distribution. Additionally, based on Table 5, an error factor of 10 is 
assigned to this probability. This value has accordingly been assigned to the probability of waste 
package mishandling. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Notice that in Section 6.1.2, a corroborative estimate of the probability of damaging a fuel 
assembly by mishandling is performed based on information found by Yang (1997, p. 10). A 
probability of 4.6  10-4 per discharged fuel assembly is found (see Section 6.1.2). This number 
is not directly comparable to the results of Waste Package Misload Probability (BSC 2001b), 
which provides a probability per moved fuel assembly that accounts for additional fuel assembly 
handlings such as those occasioned by shuffles in the core of the reactor. In addition, the study 
by BSC (BSC 2001b) uses a larger operating experience than the study by Yang (1997). With 
these caveats in mind, the two numbers do not appear to be incompatible. 
Use in the Calculation: This assumption is used in Section 6.2.7. 
5.8 ASSUMPTIONS RELATED TO FLAWS IN TITANIUM WELDS 
The following assumptions were used in Section 6.3.1 to estimate the probability of having weld 
flaws that remain undetected in the drip shield. 
5.8.1 Flaw Density and Size Distributions in Titanium Welds 
Assumption: It is assumed that the flaw density and size distributions of flaws in titanium welds 
are the same as those of Alloy 22 weld flaws. 
This assumption is needed because no detailed information about the distributions of these flaws 
in titanium welds was found in the literature. 
Rationale: The rationale for this assumption is based on the fact that welding of titanium is no 
more difficult than for many stainless steels (Ikeda and Shoesmith 1997, p. i). Based on 
Welding, Brazing, and Soldering (ASM International 1993, p. 740), weldability of Alloy 22 and 
stainless steel are similar. Therefore, it can be expected that the density and size distributions of 
flaws in titanium welds will be comparable to those of Alloy 22 welds. Moreover, the same 
reference mentions that molten nickel alloy weld metal does not flow as easily as steel weld 
metal. This might introduce more flaws in Alloy 22 welds. Consequently, applying the flaw 
density and size distribution of Alloy 22 weld flaws to flaws in titanium welds is likely to be 
conservative. 
Use in the Calculation: This assumption is used in Section 6.3.1. 
5.8.2 Ultrasonic Testing of Titanium Welds 
Assumption: It is assumed that the titanium welds of the drip shield will be inspected by UT. 
Rationale: The rationale for this assumption is that the welds will be inspected in order to verify 
that no significant defect is present. Several inspection methods are possible (Plinski 2001, 
Section 6). A UT inspection is assumed here because it is an effective method to detect 
significant flaws. 
Use in the Calculation: This assumption is used in Section 6.3.1. 
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5.9 ASSUMPTIONS RELATED TO FLAWS IN BASE METAL TITANIUM 
The following assumptions were used in Section 6.3.2 to estimate the probability of having base 
metal flaws that remain undetected in the drip shield. 
5.9.1 Hard-Alpha Inclusions in Titanium Used for the Drip Shield 
Assumption: It is assumed that the titanium that will be used for fabricating the drip shield will 
have hard-alpha inclusion levels corresponding at most to the levels found in triple vacuum arc 
remelt processed titanium that has had two UTs, once at the billet stage, with #5 flat bottom 
hole, and once at the forging stage, with #3 flat bottom hole. 
This assumption is required to ensure that the data of Section 4.1.4 are adequate for evaluating 
the flaw density and size distribution in the titanium base metal used for the manufacture of the 
drip shield. 
Rationale: The rationale for this assumption is that the triple vacuum arc remelt fabrication 
process and UT inspection sensitivity mentioned previously were used in the 1980s to produce 
alloy titanium rotors used for aircraft engines (Shamblen and Woodfield 2002). It is reasonable 
to expect that when the drip shield is fabricated the technology employed to produce the base 
metal titanium will be more performant or at least equivalent. Therefore, the frequency of 
occurrence for hard-alpha inclusions given in Section 4.1.4 can be expected to represent 
conservative levels of hard-alpha defects in the base metal titanium that will be used for the drip 
shield. 
Use in the Calculation: This assumption is used in Section 6.3.2. 
5.9.2 Frequency of Occurrence of High-Density Inclusions in Base Metal Titanium 
Assumption: It is assumed that the frequency of occurrence of high-density inclusions in base 
metal titanium used for the drip shield is the same as the frequency of occurrence of hard-alpha 
defects. 
Rationale: The rationale for this assumption is provided by Shamblen and Woodfield (2002, 
p. 3), who provide a figure showing the evolution in flaw frequencies for hard-alpha defects and 
high-density inclusions in premium-quality titanium alloys during the 1990s. It appears that the 
frequency of high-density inclusions is less than that of hard-alpha defects. Because the scale in 
the y-axis on the figure is not precisely defined, it is not possible to make a more detailed 
comparison. Nevertheless, it is conservative to state that both frequencies of occurrence are 
equal. It should be noted that the study performed by Shamblen and Woodfield (2002) pertains 
to titanium alloys used in the aircraft industry. Nevertheless, it is also considered applicable to 
Titanium Grade 7 and 24 that will be used for the drip shield. The reason for this is that high-
density inclusions correspond to tungsten carbides that are introduced in the base metal by 
melting recycled scrap (Graham 2002); therefore, these inclusions occur in titanium alloys in the 
same manner as in commercially pure titanium. 
Use in the Calculation: This assumption is used in Section 6.3.2. 
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5.10 ASSUMPTIONS RELATED TO DRIP SHIELD CONTAMINATION 
The following assumptions were used in Section 6.3.5 to estimate the probability that a drip 
shield surface becomes contaminated by some corrosion-enhancing material and that this 
contamination remains undetected. 
5.10.1 Drip Shield Inspection 
Assumption: It is assumed that an inspection of the drip shield will take place at reception to the 
surface facilities of the repository and that this inspection will detect all visible traces of 
contamination on the drip shield (i.e., presence of foreign material on the drip shield). It is also 
assumed that an inspection of the drip shield will take place just before it is transported to the 
underground repository. 
This assumption is needed because the procedures governing the control of operations on the 
drip shield have not yet been written. 
Rationale: The rationale for this assumption is the same as that given in Assumption 5.6.1 and 
will not be repeated here. The only notable difference is that because the drip shield is not 
radioactive, the second inspection does not need to be performed remotely. 
Use in the Calculation: This assumption is used in Section 6.3.5. 
5.10.2 Drip Shield Secondary Inspection 
Assumption: It is assumed that after the second inspection of the drip shield, the probability that 
the drip shield is subjected to further contamination is negligible. 
Rationale: The rationale for this assumption is as follows. After the second inspection, the drip 
shield leaves the surface facilities and is transported to the subsurface areas. Contrary to the 
waste package, which will be protected from exterior contamination by the shielding 
compartment of the transporter, the drip shield is more likely to be exposed to contamination, 
like dirt for example. Nevertheless, these exterior sources of contamination will probably not be 
adverse to the long-term performance of the drip shield. Contamination that may have more 
severe consequences can be expected to occur during the handling of the drip shield, which occur 
mainly in the surface facilities. Once the transporter has docked in the subsurface facilities, the 
drip shield will be subjected to one more handling only: namely, its emplacement in the drift. It 
can be expected that extra precautions will be taken to ensure that the drip shield is not 
contaminated during this final handling because such contamination could also affect the waste 
packages located in the drift. 
Use in the Calculation: This assumption is used in Section 6.3.5. 
5.10.3 Decontamination Process of Drip Shield 
Assumption: Assumption 5.6.3 is considered applicable for evaluating the contamination of the 
drip shield through its cleanings. It should be noted that in that assumption eight cleanings were 
considered for the waste package. The same number is kept for the drip shield. This is done for 
the sake of simplicity. As the procedures governing the fabrication of the waste package or the 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
drip shield have not yet been written, there is some subjectivity in determining how many 
cleanings should be considered. 
Rationale: It can be expected that the technician in charge of the cleanings for weld preparation 
will group welds with a similar function together. For example, the cleaning of the drip shield 
welds could be gathered as follows: welding of the upper plate with both side plates: two 
cleanings; welding of the support beams to the side plates: two cleanings; welding of the internal 
support plates and the bulkheads: two cleanings; welding of the drip shield connectors: two 
cleanings. This yields a total of eight cleanings. Other breakdowns are possible, but it is 
reasonable to consider that they would all fall around eight cleanings, which is used for the waste 
package. 
Use in the Calculation: This assumption is used in Section 6.3.5. 
5.11 ASSUMPTIONS RELATED TO IMPROPER DRIP SHIELD HANDLING 
The following assumptions were used in Section 6.3.6 to estimate the probability that a drip 
shield is damaged by mishandling and that the damage remains undetected. 
5.11.1 Drip Shield Damage Inspections 
Assumption: It is assumed that the inspections considered in Assumption 5.10.1 would also 
serve to detect traces of damage to the drip shield due to improper handling. Recall that two 
inspections of the drip shield are supposed to take place: one when the drip shield is received in 
the surface facilities of the repository and one just before it is transported to the underground 
repository. Also, as in Assumption 5.10.1, it is assumed that the inspection at drip shield 
reception will detect all visible traces of mishandling of the drip shield. 
Rationale: The rationale for this assumption is the same as that given in Assumption 5.10.1. 
Use in the Calculation: This assumption is used in Section 6.3.6. 
5.11.2 Drip Shield Mishandling Opportunities 
Assumption: It is assumed that between the inspection at drip shield reception and the second 
inspection just before departing for the underground repository, the drip shield might be 
mishandled and damaged on four occasions. 
This assumption is needed because the details on how the drip shield will be handled from its 
reception to its emplacement are not yet known. In fact, there are only two easily identifiable 
opportunities for mishandling the drip shield in the surface facilities: when installing the drip 
shield in the staging area, and when moving it from the staging area to the transporter. 
Rationale: The rationale for assuming four mishandling occasions is that it is the same number 
as the mishandling opportunities for the waste package, estimated in Section 5.7.2. This results 
in simplified estimates in Section 6.3.5. Moreover, assuming four mishandling opportunities, 
instead of the two identified, is clearly conservative. 
Use in the Calculation: This assumption is used in Section 6.3.6. 
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5.11.3 Additional Drip Shield Mishandling Opportunities 
Assumption: It is assumed that after the second drip shield inspection (just before the drip shield 
leaves for the underground repository), the probability that the drip shield is subjected to further 
damage by mishandling without being detected is negligible. 
Rationale: The rationale for this assumption is similar to the rationale of Assumption 5.10.2. In 
contrast to the waste package, the drip shield will not be protected by the shielding compartment 
of the transporter; therefore, the chances for damage to the drip shield are greater. As a side 
remark, note that these damages would most likely not result from mishandling, but rather from 
events such as rockfalls. However, it is very unlikely that these events could significantly 
damage the drip shield and remain unnoticed. Another opportunity for damage to the drip shield 
would be during its last handling, namely: its emplacement in the drift. It can be expected that 
extra precautions will be taken to ensure that the drip shield is not damaged during this final 
handling because mishandling could also affect the waste packages located in the drift. 
Therefore, even if a mishandling were to occur it is very unlikely that it would remained 
undetected. 
Use in the Calculation: This assumption is used in Section 6.3.6. 
5.11.4 Drip Shield Improper Handling Damage Probability 
Assumption: It is assumed that the probability of damaging a drip shield, due to an improper 
handling, can be approximated by a lognormal distribution with a mean of 4.8  10-5 (per drip 
shield handling) and an error factor of 10. 
Rationale: This assumption is the same as Assumption 5.7.4. It is needed because there is no 
operating experience on the handling of the drip shields, so no direct evaluation of the 
probability of damaging a drip shield by mishandling is possible. Information pertaining to the 
handling of fuel assemblies was used instead because it is representative of the probability of 
mishandling sensitive material in the nuclear industry. The other justifications for this 
assumption are the same as those given in Assumption 5.7.4. 
Use in the Calculation: This assumption is used in Section 6.3.6. 
5.12 ASSUMPTIONS RELATED TO DRIP SHIELD EMPLACEMENT ERROR 
The following assumption about verification of correct drip shield emplacement is used in 
Section 6.3.7. 
5.12.1 Drip Shield Emplacement Error Detection 
Assumption: It is assumed that once a drip shield is emplaced a remote inspection is performed 
to detect if the newly emplaced drip shield is properly interlocked with the adjacent drip shield. 
This assumption is needed because the procedures governing the installation of the drip shield in 
the repository have not yet been written. 
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Rationale: The rationale for this assumption is that it describes a verification step that conforms 
to work practices in the nuclear industry. 
Use in the Calculation: This assumption is used in Section 6.3.7. 
6. ANALYSIS 
6.1 REVIEW OF DEFECT-RELATED FAILURES OF CONTAINERS IN VARIOUS 
INDUSTRIES 
This section presents the results of a literature review performed to determine rates of 
manufacturing defect-related failure for various types of containers. In addition to providing 
examples of the rates at which defective containers occur, this information provides insight into 
the various types of defects that can occur and the mechanisms that cause defects to propagate to 
failure. 
6.1.1 Boilers and Pressure Vessels 
Waste packages are similar to pressure vessels in the sense that they are welded, metallic 
components of similar thickness that are typically fabricated in accordance with accepted 
standards and inspected prior to entering service. In addition, there are several sources of 
statistics on the numbers and types of failures that have occurred in large populations. 
One study (Doubt 1984, p. 7) examined data on 229 failures of pressure vessels constructed to 
Class I requirements of design codes recognized in the United Kingdom. The failures had 
occurred in a population of 20,000 vessels (Smith and Warwick 1978). The vessels were all 
welded or forged unfired pressure vessels with wall thicknesses greater than 9.5 mm and 
working pressures in excess of 725 kPa. The vessels included in the study were less than 
40 years old as of 1976 (Smith and Warwick 1978, p. 22). Doubt (1984, p. 7) identified 
17 instances of external leakage or in-service rupture that were caused by preexisting defects in 
weld or base metal or by incorrect material. Failures that were due to thermal or mechanical 
fatigue, corrosion, internal leaks, and part-through cracks found by visual examination or 
nondestructive examination were excluded. This yielded an estimated failure rate due to 
manufacturing defects of 8.5  10-4 per vessel. Further examination of the data (Smith and 
Warwick 1978, pp. 37 to 52) indicated that four of the failures were attributed to use of incorrect 
material in the weld, one to improper heat treatment, one to improper joint design, and the 
remaining failures were due to weld flaws. In all of the cases involving weld flaws, the vessels 
were in service for several years prior to failure, which suggests that fatigue also contributed to 
the propagation of the flaws through the walls of the vessels. In some cases, failures that were 
attributed to fatigue, and thus not included in the calculation of the previous failure rate, involved 
propagation of preexisting defects. Overall, approximately 29 percent of the failures appear to 
have involved a preexisting defect of some kind. Finally, it should be noted that the original 
source of the failure data (Smith and Warwick 1978, p. 24) indicates that many of the defects 
occurred in areas where it was not the practice at the time of construction, even with Class I 
Standard vessels, for nondestructive examination to be performed. Because waste packages are 
not subject to cyclic stresses (which is necessary for fatigue) and will be nondestructively 
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examined, application of the historical failure data for pressure vessels to estimate an early 
failure rate for waste packages would be extremely conservative. 
Another source of information on failures is available from the National Board of Boiler and 
Pressure Vessel Inspectors (NBBPVI 1999). The National Board of Boiler and Pressure Vessel 
Inspectors maintains records on all boilers and pressure vessels that carry a National Board-
registered stamping. For the period of 1919 through 1997, a total of 27,618,733 registrations 
have been filed (NBBPVI 1999). For the period of 1992 to 1997, incident reports indicate the 
number of failures that have occurred as a result of various causes. For the category of Faulty 
Design or Fabrication, the average incident rate is 83 per year. Assuming that this rate is 
constant over the 79 years in which vessels were registered, a point estimate probability of 2.4  
10-4 per vessel for failure due to fabrication or design defects can be calculated. Unfortunately, 
the National Board of Boiler and Pressure Vessel Inspectors information does not contain 
information on the cause of failure, and thus, its utility for this analysis is limited. 
Data from the previous sources, and from similar databases in Germany, have been used in 
various studies to calculate the annual probability of vessel failure for use in risk assessments. 
The expected value for disruptive failure rates ranges from 2  10-6 to 4  10-5 per vessel-year, 
and the upper limit of the 99 percent confidence interval ranges from 5  10-6 to 8  10-5 per 
vessel-year (Tschoepe et al. 1994, pp. 2-9 to 2-11). In general, these rates were not based on 
actual failures that had occurred but on reports on the size of the weld defects observed during 
inspection and the perceived consequences had the vessel been returned to service without repair 
of the defect. Because these rates involve significant interpretation as to the effect of weld flaws 
on component life under specific operating conditions, they cannot be directly used to determine 
a waste package early failure rate. 
Finally, two instances were also found in the literature where cracking of stainless steel cladding 
on the interior surface of reactor coolant system components occurred as a result of defects that 
occurred during fabrication or transport. In one case, during a visual examination following a 
hot functional test that was conducted in March 1975, Indian Point-3 personnel noted 
rust-colored deposits in the primary-water boxes of all four steam generators (S.M. Stoller and 
Company 1976, p. 44). A detailed chemical and metallurgical analysis of cladding samples was 
performed and three distinct types of cracking were identified: (1) longitudinal interbead cracks 
in the upper parts of the heads that propagated along grain boundaries, (2) transverse cracks 
adjacent to repair welds, and (3) extensive cracking in the lower half of the heads. Studies of the 
cladding samples identified stress corrosion and dilution of the clad deposit with base metal as 
possible causes for the imperfections. The supposition of stress corrosion was supported by the 
fact that the channel heads were accidentally exposed to seawater during shipment. 
In a second instance, microfissures were found in the cladding of two straight and two elbow 
sections of reactor coolant system piping during construction of Oconee 1 (Babcock & Wilcox 
1970a; Babcock & Wilcox 1970b). The fissures were found during a routine dye-penetrant exam 
while they were being reworked to accommodate the installation of Westinghouse reactor 
coolant pumps. They would likely not have been found before operation if the original Bingham 
pumps were installed. The cracks in the straight sections were caused by use of an improperly 
manufactured batch of flux in welding these sections. The cracking that occurred on the two 
elbow sections was attributed to the improper use of acidic cleaning agents. The Indian Point-3 
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and Oconee-1 cases were the only examples of contamination-related failures found in the 
nuclear-industry literature, and no efforts to determine their frequency of occurrence have been 
made. 
While this review has provided general information on the reliability of large, welded, pressure 
retaining components, the failure rate data cannot be directly applied to waste packages due to 
significant differences in operational conditions and degree of inspection performed prior to 
service. However, this review has identified several types of manufacturing defects that may be 
applicable to waste packages: 
 Weld flaws 
 Base metal flaws 
 Use of improper material in welds 
 Improper heat treatment of welded or cold-worked areas 
 Improper weld flux material 
 Poor joint design 
 Contaminants. 
The applicability of these types of defects to waste packages and their potential consequences to 
postclosure performance are discussed in Section 6.2. 
6.1.2 Nuclear Fuel Rods 
Nuclear fuel rods are conceptually similar to waste packages in the sense that they are 
manufactured in large numbers, are subjected to rigorous quality controls and inspections, and 
have radionuclide containment as one of their primary functions. As such, it is useful to review 
the reliability of these components and the rate at which manufacturing-induced defects occur. 
However, they are also simple, single-barrier components with a very small wall thickness 
compared to waste packages and are subjected to significantly different operating conditions 
over a much shorter period of operation. Thus, the failure rate information presented here cannot 
be directly used to estimate a waste package early failure rate. 
Because a significant amount of scrutiny by utilities, vendors, and the NRC follows any report of 
failure in nuclear fuel, there is a large database on the number and causes of fuel-rod failures. 
The fuel-rod failure rate for both PWR and boiling water reactor (BWR) fuel through 1985 
ranged from 2  10-4 to 7  10-4 per rod (EPRI 1997, p. 4-1). As a result of vendor efforts to 
develop improved fuel designs to address some of the causes of failure, the current range of 
failure rates is from 6  10-5 to 3  10-4 per rod (EPRI 1997, p. 4-2). The failures of fuel rods 
have been caused by a variety of mechanisms (Yang 1997, p. 10; Framatome Cogema Fuels 
1996, pp. 4-2 to 4-7), among which two are applicable to waste packages. These are handling 
damage and manufacturing defects. Handling damage represents a small amount of the fuel 
failures. It can occur during fabrication if loaded fuel rods are subjected to excessive flexing that 
causes defects, which lead to in-core failure or as a result of drops or other handling accidents 
which could occur at the utility. During the period from 1989 through 1995, there were a total of 
10 handling-damage failures in a population of 21,810 PWR discharged assemblies (Yang 1997, 
p. 10), yielding a rate of 4.6  10-4 per discharged assembly. In each case, only a few rods in 
each assembly were actually damaged. 
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Manufacturing defects also represent a small fraction of fuel failures. Types of manufacturing 
defects associated with the cladding include contamination by solvents; oils or filings; flawed or 
missing seal welds; flawed, missing or mislocated endcap welds; base metal flaws (stringers, 
inclusions); and out-of-specification weld material (Framatome Cogema Fuels 1996, Section 5). 
General Electric reports only 47 manufacturing-defect-related failures in 4,734,412 rods 
fabricated between 1974 and 1993 (Potts and Proebstle 1994, p. 92), which yields a rate of 
9.9  10-6 per rod. As of October 1990, Advanced Nuclear Fuels had experienced seven BWR 
fuel rod failures and nine PWR fuel rod failures related to manufacturing defects out of 570,200 
BWR fuel rods and 1,391,740 PWR fuel rods placed into service (Tschoepe et al. 1994, p. 2-4). 
The resulting rates are 1.2  10-5, 6.5  10-6, 8.2  10-6 for BWRs, PWRs, and combined failures, 
respectively. In addition to the previously mentioned defects, one occurrence of a rod that failed 
in service due to a missing seal weld was reported in Fuel Integrity (Framatome Cogema Fuels 
1996, p. 5-1). The rod had not passed the inspection process but had been inadvertently left with 
the accepted rods. Because this was an isolated event, it can be expected that the corresponding 
occurrence rate would be much lower than the reported global failure rate, excluding debris and 
fretting, of 1/200,000 = 5  10-6 per rod (Framatome Cogema Fuels 1996, p. 3-1). 
While this review has provided general information on the reliability of fuel rods, the failure rate 
data cannot be directly applied to waste packages due to significant differences in construction 
and operational conditions. However, general types of manufacturing defects were identified in 
the review that may be applicable to waste packages: 
 Weld flaws 
 Base metal flaws 
 Mislocated welds 
 Contamination 
 Missing welds 
 Improper weld material 
 Handling damage. 
The applicability of these types of defects to waste packages, and their potential consequences to 
postclosure performance, are discussed in Section 6.2. 
6.1.3 Underground Storage Tanks 
A substantial amount of information is available on causes of early failure for underground-
storage-tank systems. The most extensive data source, which was compiled by the U.S. 
Environmental Protection Agency, provides data on a large population of bare-steel, clad- or 
coated-steel, and fiberglass-reinforced-plastic tank systems through 1987 (EPA 1987a; EPA 
1987b). While overfilling and leakage of attached piping are dominant contributors to leakage 
from underground storage tank systems, failure of the tank itself is also a significant contributor. 
The majority of the tanks in service during the period covered by the study were bare-steel tanks, 
and 95 percent of those failures were caused by corrosion (EPA 1987a, p. 7). One interesting 
observation was that many bare-steel tanks that have been unearthed were found to have 
corrosion holes that were plugged with corrosion product and showed no signs of leakage (EPA 
1987a, p. 6). 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The study also indicates that 5 to 7 percent of bare-steel tanks leaked when they were tested for 
the first time due to manufacturing or installation defects (EPA 1987a, p. 6). However, failures 
found during such a leak test would generally be repaired and the fraction of the total population 
failed by unidentified defects would be much lower. The study indicates that 4 percent of a 
population of 980 in situ tanks were found to be leaking and 0.9 percent of 24,452 leaking tanks 
were found to be leaking in within 0 to 5 years (early life of the underground storage tank) of 
being placed into service (EPA 1987a, p. 8). This suggests an upper bound of approximately 
0.04 percent (4%  0.9%) of the fraction of the total population initially failed by an unidentified 
defect. Additional information provided by the Steel Tank Institute indicates that the fraction of 
the population failed by unidentified manufacturing defects is closer to 0.0003 percent (Grainawi 
1999). Types of noncorrosion defects identified as causing failure include installation damage 
(EPA 1987a, p. 10) and failure of weld seams (EPA 1987b, p. 82). 
While this review has provided general information on the fraction of the total population of 
underground storage tanks that fail due to any cause, rates of early failure by defects are 
generally obscured by the high rate of early corrosion failures. The information obtained is not 
directly applicable to waste packages because an underground storage tank made of bare steel is 
basically a single, less robust, noncorrosion-resistant barrier. However, it still indicates that even 
commercial-grade quality controls can produce components that have a relatively low rate of 
unidentified failures entering service. In addition, general types of manufacturing defects were 
identified in the review that may be applicable to waste packages: 
 Weld flaws 
 Handling or installation damage. 
The applicability of these types of defects to waste packages, and their potential consequences to 
postclosure performance, are discussed in Section 6.2. 
6.1.4 Radioactive Cesium Capsules 
During the period between 1974 and 1983, 1,600 radioactive cesium capsules were fabricated at 
the U.S. Department of Energys Hanford facility. These capsules were double-walled cylinders 
initially designed and tested to be stored in storage pools at Hanford that were later used by 
commercial companies as radiation sources (Tschoepe et al. 1994, p. 2-7). One of these capsules 
failed during 1988 as a result of its use in environmental conditions that were drastically 
different from those for which the capsules were designed and from the development test 
conditions. An investigation into this failure concluded that, despite other deficiencies that were 
found, the capsule would not have failed if it had operated in the environment for which it was 
designed. The remaining capsules were recalled to Hanford after this incident and there have 
been no other failures to date. Thus, the failure rate to date is 6.3  10-4 per capsule. 
While this type of administrative or operational error does not represent an actual defect in the 
fabrication of the component, it, nonetheless, caused an early failure. The applicability of this 
type of defect to waste packages, and its potential consequences to postclosure performance, are 
discussed in Section 6.2. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
6.1.5 Dry Storage Casks for Spent Nuclear Fuel 
Dry storage casks that are sealed with a closure weld (as opposed to bolting) represent a close 
analog to waste packages. Examples include the Dry Shielded Canister that is part of 
TransNuclears NUHOMS system and the VSC-24 dry storage cask fabricated by Sierra Nuclear 
Corporation (Hodges 1998). While there have been no recorded cases of closure welds failing 
after casks were placed into service, there have been four cases where cracks in closure welds 
have been identified during postweld inspection of the cask (Hodges 1998). All of these cases 
have been associated with the VSC-24 of which there were 19 in service through July 1998. 
Table 9 summarizes relevant information on each of the cracking events. Figure 2 provides an 
illustration of the VSC-24 closure welds. A VSC-24 Owners Group weld review team, 
composed of industry experts in metallurgy, welding, and nondestructive examination, evaluated 
each of the four weld-cracking events to identify the root causes. 
The team concluded that the Palisades weld crack was caused by an existing condition in the 
rolling plane of the shell material that was opened up by the process of making the shield lid 
weld (Hodges 1998). Metallographic analysis revealed a crack that propagated along prior 
austenitic grain boundaries of a preexisting weld of unknown origin (the weld had not been 
documented during fabrication). This base metal defect may have resulted from improper repair 
or incomplete removal of temporary low quality welds used to facilitate the fabrication process 
(i.e., attachment of strong backs to assist in the rolling of plate material). 
Table 9. Summary of VSC-24 Weld Cracking Events 
Facility Date Detection Location Crack Description 
Palisades 3/95 Helium leak test Shield lid-to-shell 
weld 
About 6 inches long by 1/8 inch deep that 
extended from about 1/8 inch above the 
shield lid-to-shell weld fusion line into the 
shell base metal 
Point Beach 5/96 Dye-penetrant 
test 
Structural lid-to-
shell weld 
Three cracks, each less than 1 inch long, 
located along the center of the root pass at 
Structural lid-to-
shield lid weld 
locations where the fit-up gap between the lid 
and the backing ring was widest. In addition, 
cracking and weld porosity were found in the 
structural lid-to-shield lid seal weld (fillet weld 
associated with the vent port covers) 
Arkansas 12/96 Helium leak test Shield lid-to-shell About 4 inches long located along the weld 
Nuclear One weld fusion line 
Arkansas 3/97 Dye-penetrant Shield lid-to-shell About 18 inches long located along the weld 
Nuclear One test weld fusion line of the root pass 
The causes of the weld cracks at Point Beach were found to be associated with weld flaws 
caused by poor welding technique and moisture contamination (Hodges 1998). The cracks on 
the root pass of the structural lid-to-shell weld were caused by wide fit-up gaps that were not 
properly filled by the welding technique. The cracking and weld porosity found in the structural 
lid-to-shield lid seal weld were found to be caused by moisture contamination of the weld. The 
moisture came from water forced out of the drain line during cask loading. The team concluded 
that none of the cracks at Point Beach were caused by the mechanism that produced the Palisades 
cracks. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The crack in the shield lid-to-shell weld for the first cask loaded at Arkansas Nuclear One was 
initially attributed to lamellar tearing based on visual observations of the crack by the welders 
before it was repaired (Hodges 1998). However, it was later shown that this crack was similar in 
appearance to the second crack that was discovered, which was attributed to hydrogen-induced 
cracking. The hydrogen-induced cracking was attributed to (1) high hydrogen content of the 
weld wire, (2) susceptible microstructure of the steel welded, and (3) a highly restrained weld 
joint configuration leading to residual stresses at or near the yield level. 
Welds 
Figure 2. Illustration of Closure Welds for the VSC-24 Dry Storage Cask 
General types of manufacturing defects were identified in the review that may be applicable to 
waste packages. These types of defects are: 
 Weld flaws 
 Base metal flaws 
 Contamination. 
The applicability of these types of defects to waste packages, and their potential consequences to 
postclosure performance, are discussed in Section 6.2. 
6.1.6 Summary 
Table 10 briefly summarizes the information obtained from the literature search on the rate and 
causes of manufacturing defects in welded metallic containers. Eleven generic types of defects 
were identified: 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
 Weld flaws 
 Base metal flaws 
 Improper weld material 
 Improper heat treatment 
 Improper weld-flux material 
 Poor weld-joint design 
 Contaminants 
 Mislocated welds 
 Missing welds 
 Handling or installation damage 
 Administrative or operational error. 
Table 10. Summary of Defect-Related Failures in Various Welded Metallic Containers 
Container Type Information on Failure 
Types of Defects Leading to 
Early Failure 
Boilers and 
Pressure Vessels 
17 out of 20,000 pressure vessels fabricated less than 40 
years old as of 1976 failed due to manufacturing defects 
(dominant cause was fatigue growth of weld flaws). 
Stainless steel cladding on some reactor coolant system 
components for two nuclear units (different fabricators) 
cracked due to surface contamination remaining from 
transport or fabrication. 
- Weld flaws 
- Base metal flaws 
- Improper weld material 
- Improper heat treatment 
- Improper weld flux 
- Poor weld-joint design 
- Contaminants 
Nuclear Fuel Rods 
(PWR and BWR) 
Undetected manufacturing defect-related failure rate 
approximately one rod per 100,000. 
Overall failure rates in the range of 2 to 7 rods per 10,000 
before 1985, 0.6 to 3 rods per 10,000 from 1985 to 1997. 
- Weld flaws 
- Base metal flaws 
- Mislocated welds 
- Contamination 
- Missing welds 
- Improper weld material 
- Handling damage 
Underground 
Storage Tanks 
Fraction of population initially failed due to manufacturing 
or handling defects in the range of 0.04% to 0.0003%. 
- Handling or installation 
damage 
- Weld flaws 
Radioactive One failure out of 1,600 capsules. - Administrative error resulting 
Cesium Capsules in unanticipated operating 
environment 
Dry Storage 4 out of 19 Sierra Nuclear VSC-24 casks found to have - Weld flaws 
Casks for Spent cracked closure welds during postweld inspection (dye- 
Base metal flaws 
Nuclear Fuel penetrant and helium leak test only). - Contamination 
A complementary type of defect is added to the previous list: out-of-specification (improper) 
base metal. This type of defect was not identified in the literature search: only instances of 
improper weld material were found. Nevertheless, for the sake of completeness, it is reasonable 
to consider the possibility that base metal, as well as weld material, might be out of specification. 
Weld flaws (e.g., slag inclusions, porosity, lack of fusion, hydrogen-induced cracking) were a 
dominant contributor to early failure but usually required an external stimulus (e.g., cyclic 
fatigue) or environmental condition to cause the flaw to propagate to failure. In many cases, 
components with unidentified defects entered service not because the defect was missed by an 
inspection, but because no inspection for that type of defect was required at the time they were 
fabricated. For dry-storage casks, all of the defects were identified by postweld inspection prior 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
to commencement of the storage phase and thus do not represent early failure as it is defined for 
this analysis. The 12 types of defects (11 from the literature search, plus improper base metal) 
are reviewed for their applicability to waste packages in Section 6.2. Section 6.2.5 also discusses 
the probability of improper laser peening that could result in early stress corrosion cracking. The 
probability of occurrence and consequences for postclosure performance of the package are 
assessed for the applicable defects. 
As indicated previously, many of the defects require an external stimulus or the component was 
not subjected to inspections that would have identified the defect. Furthermore, there is 
insufficient information available to defensibly relate the cumulative effect of the environment or 
stresses to which the component was subjected to that of the waste package (e.g., are the 
cumulative effects of the stresses and environmental conditions experienced by a pressure vessel 
in a 40 to 60 year life equivalent to 100, 1,000, or 10,000 years of waste package lifetime?). 
Accordingly, the information on the fraction of components that experienced defect-related 
failure during their intended lifetime is not directly applicable to waste packages. In addition, 
these population-based failure rates do not provide any insight into the time distribution of early 
failures. However, in some cases information on the occurrence rate of particular types of 
defects was obtained from the literature search. This information proved useful in the waste 
package defect probability and consequence portion of the analysis. 
6.2 MECHANISMS FOR EARLY WASTE PACKAGE FAILURE 
A list of 12 generic types of defects were identified in Section 6.1 as potential causes for early 
failure of metallic containers. Many of these types of defects could also be introduced to a waste 
package during fabrication, transport to the repository, storage, loading, or emplacement. 
However, the following generic defect types are not considered further (for the waste package or 
the drip shield): 
 Improper weld-flux material: Waste package welds will employ a welding method 
(such as tungsten inert gas or metal inert gas) that does not use weld-flux material. 
 Poor joint design: A significant development and testing effort will have gone into the 
design of the final closure joint. Lessons learned from the types of closure weld 
problems that have been experienced in the dry-storage cask systems (see Section 6.1.5) 
are expected to be incorporated in the design of closure welds for waste packages. 
Therefore, problems with the design of the weld joint for the waste packages are not 
expected. This does not exclude weld flaws or other types of weld related defects that 
could occur during the closure process. 
 Missing welds: Data on the occurrence of this type of defect in fuel rods (presented in 
Section 6.1.2) indicated that it would occur at a rate much lower than 5  10-6 per rod. A 
missing weld on a waste package would be easier to identify than on a fuel rod and 
would have a noticeable effect on the configuration of the waste package (e.g., a missing 
closure weld could cause the lid to fall off when the waste package is tilted to a 
horizontal position). Therefore, it is expected that the occurrence rate of this defect for a 
waste package would be significantly less than the dominant failure mechanism of 
improper heat treatment. 
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 Mislocated welds: This defect is mainly applicable to very small, single pass welds 
(e.g., fuel rod end caps). For larger multipass welds, such as those on the waste 
package, any significant mislocation of the electrode would cause the weld arc not to 
strike. This would be immediately obvious to both the operator and the control system 
for the automated welder. This is much less likely than the dominant failure mechanism 
of improper heat treatment. 
The remaining defects are evaluated in the following subsections. 
6.2.1 Weld Flaws 
Weld flaws are among the most extensively studied types of defects that can affect the 
performance of metallic components used in the nuclear industry. For example, results from 
Khaleel et al. (1999), which report flaw density and size distributions in nuclear piping welds, 
were extensively used to determine the main characteristics of the flaws to be expected in the 
closure welds of the waste package (CRWMS M&O 2000). The major drawback of this 
approach is that the inputs utilized from Khaleel et al. (1999) were primarily developed for 
stainless steel and not Alloy 22. 
Work has been performed involving the welding of Alloy 22 specimen rings that duplicate as 
closely as possible the actual outer lid weld of a waste package (BSC 2003d). Although the 
design of the outer lid has since been modified since this work was performed, the modifications 
do not impact the validity of the results. Only the closure weld configuration was modeled in the 
test. The changes in design only effect the reinforcement around the weld configuration and the 
actual weld groove has not changed. Sixteen specimen rings were welded employing 
procedures, processes, and equipment similar to that expected to be used for the closure of the 
waste package. Nondestructive examination followed by metallographic examination made it 
possible to accumulate significant information on the weld flaws. Based on this information, 
summarized in Section 4.1.3, several distributions are developed in Section 6.2.1.1 to 
characterize the size of the flaws in the through-wall extent of the weld (Y direction on Figure 1), 
their density (mean number of flaws per meter of weld) and their depth (distance between the 
outer surface of the weld and the onset of the flaw in the Y direction). In addition, the 
orientation of the flaws in the plane of the specimen rings, with respect to the direction of the 
weld, is used to make an estimate on the probability that a flaw has an angle greater than 
45 degrees. 
UT inspections will be performed on the welds of the waste package in order to identify those 
flaws that may jeopardize its performance so that these flaws can be removed. The 
characteristics of the flaws that will remain in the welds, especially their size and density, are 
investigated in Section 6.2.1.2. 
Section 6.2.1.3 gives a summary guideline for calculating the main characteristics of the flaws 
expected in the welds of the waste package. The main results for the outer lid weld, the middle 
lid weld, and the other welds of the outer barrier are given. Also, a comparison of the developed 
distributions is made with the results from Khaleel et al. (1999), which pertain to nuclear piping 
weld flaws and on which estimates performed for the Site Recommendation and the 
Supplemental Science and Performance Analysis were based. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The calculations in the following subsections were carried out using Mathcad. A paper copy is 
given in Attachment I. Note that the results of the calculations performed are shown with 
rounded values. A reader wanting to re-do the calculations should carry them out from the input 
values given in Section 4, and not use the intermediate values, unless otherwise stated. 
6.2.1.1 Flaw Characteristics in Welds Before Inspection and Repair 
6.2.1.1.1 Flaw Size Distribution in the Y Direction 
The flaw size distribution in the Y direction (see Figure 1 for conventions on orientation) is 
estimated using the Bayesian approach with a noninformative prior. Information on the 
Bayesian approach in the evaluation of parameters is given in NUREG/CR-2300 (NRC 1983, 
Section 5.5.2). Briefly stated, the Bayesian estimation consists of updating the analysts belief 
about the parameter (embodied in a prior distribution) with evidence from observation 
(quantified in a likelihood function) to obtain a posterior distribution. 
The reason for using the Bayesian approach, rather than the classical (also named frequentist) 
approach, is that it utilizes a probability distribution on the parameter to be estimated in order to 
express confidence. As mentioned in NUREG/CR-2300 (NRC 1983, p. 12-16), this has been a 
common way of representing uncertainty since WASH-1400 (NRC 1975). Expressing 
uncertainty around a parameter in terms of a probability distribution is also adequate for 
subsequent performance assessments of the waste package. 
The reason for using a noninformative prior distribution is that in generating the posterior 
estimate, this minimizes the relative importance of the prior distribution compared to the data 
(NRC 1983, p. 5-34). This is appropriate here because there is very little generic information on 
flaws in Alloy 22 welds. 
An exponential distribution has been chosen to represent the size distribution of the weld flaws 
in the Y direction. The reason for this choice is that it is a widely used distribution, determined 
by a single parameter, which makes it very tractable. Notice that the exponential distribution is a 
particular case of the more general Weibull distribution, which has been employed to 
characterize flaw size distributions (Schuster et al. 1998, p. 8.2). Weibull distributions are 
determined with two parameters, one more than the exponential, which allows for more 
flexibility in the shape of the distribution. However, it will be shown in the following that an 
exponential distribution is sufficient to fit the UT indication dimensions in the Y direction 
accrued on the specimen ring welds. Therefore, for tractability reasons, it has been decided to 
use the exponential distribution to characterize the flaw size in the Y direction. 
The cumulative exponential distribution for the flaw size s (in mm) in the Y direction of the weld 
has the form (Martz and Waller 1991, p. 330): 
P ()=1-e-.s s (Eq. 1) 
s
s 
where .s is the parameter (in mm-1) that is to be determined. It will be referred to as the flaw size 
parameter in the following. Note that s is always positive. 
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Based on Assumption 5.1.1, the information presented in Section 4.1.3.2 is appropriate to 
characterize the size distribution of the significant flaws in the welds. 
In order to calculate the probability density function (PDF) related to the flaw size parameter, it 
is first necessary to determine which sampling scheme was employed to get the flaw size 
information. The information presented in Section 4.1.3.2 can be viewed as a fixed number of 
flaws nf (nf = 7) to which correspond random flaw sizes. A sampling scheme characterized by a 
fixed number of items (namely, the number of flaws) to which is associated a random variable 
(namely, the size of the flaws) is referred to as gamma sampling (Martz and Waller 1991, 
pp. 330 and 331). Based on the same reference, for this kind of sampling, a sufficient statistic 
for estimating .s is st, the sum of all flaw sizes, which has been evaluated at 31.75 mm. 
According to Martz and Waller (1991, p. 336) the noninformative prior distribution for .s based 
on gamma sampling is proportional to 1/.s. The resulting posterior PDF p.s of the flaw size 
parameter .s is given as: 
s
. 
p ()= stn f 
. nf - 1  e-. st (Eq. 2) 
. ss s
G (n )
f 
where G is the gamma function. 
The posterior mean, .sm, the 5th percentile, .s0.05, and the 95th percentile, .s0.95, are respectively 
given by (Martz and Waller 1991, pp. 336 and 337): 
.= 
nf (Eq. 3) 
sm 
st 
2 
= 
.. /2 ( 2  nf ) (Eq. 4) 
.
s05.0 
2  st 
2
. 
1-. /2 ( 2  nf ) (Eq. 5) 
=
.
s 95.0 
2  st 
22
where, given . = 0.1, .. /2 ( 2  nf ) and .1-. /2 ( 2  nf ) respectively represent the 5th and 95th 
percentiles of the chi-square distribution with 2  nf = 14 degrees of freedom. This yields the 
following values: .sm = 0.22/mm, .s0.05 = 0.10/mm, and .s0.95 = 0.37/mm. 
It is interesting to compare these results to the values that would be found using the classical 
(frequentist) approach. According to this approach, no probability distribution is attached to .s, 
the parameter of the exponential distribution defined in Equation 1. Instead, .s has a fixed but 
unknown value, which can be approximated by calculating the maximum likelihood estimator. 
Also, the classical approach makes it possible to determine the lower and the upper value of the 
90 percent two-sided confidence interval for .s. Based on work by Martz and Waller (1991, pp. 
336 and 337), these estimators are respectively equal to .sm, .s0.05, and .s0.95 calculated in 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Equations 3 to 5. Therefore, the Bayesian approach concurs with the classical (frequentist) 
approach. 
Based on previous parameters, the size distribution of the weld flaws in the Y direction follows 
an exponential distribution of parameter .s, with .s having a PDF given by Equation 2. Notice 
that Equation 2 is only applicable to the outer lid weld of the waste package and not to welds 
with other thicknesses such as the middle lid weld, which has a smaller thickness (10 mm instead 
of 25 mm, see Section 4.1.1). Because it is desirable to have a flaw size distribution that could 
be applicable for different weld thicknesses, it has been decided to use a modified version of the 
exponential distribution which includes an additional parameter, namely the thickness t of the 
weld. The cumulative flaw size distribution Psg(s,.s,t) for a flaw of s mm in the Y direction of a 
weld of thickness t mm with the flaw size parameter .s (in mm-1) is taken to be: 
P (s,., t )= 1 - e-.s s 
with 0= s = t (Eq. 6) 
sg s 1 - e-.s t 
As a reminder, in Equation 6 the variable of interest is the flaw size s, while .s and t are 
parameters. In order to be consistent with Mathcad notations used in Attachment I, .s and t are 
shown on the left side of the equation along with s. 
It should be noted that the form of the equation proposed previously is not the only one possible. 
For example, an alternative choice would be to discard the denominator and introduce t inside 
the exponential term of the numerator. This case is examined in Attachment I and shown to be 
less conservative than Equation 6. Based on this comparison, only the modified exponential 
distribution given in Equation 6 is considered in the following. 
It is worth noting that in the case of the specimen rings, most of the UT indications report flaws 
that are much smaller than the weld thickness. Therefore, Equation 6 is a modified flaw size 
distribution that is, numerically, only slightly different from the original exponential distribution. 
To verify that it is not unreasonable that Psg(s,.s,t) adequately fits the data from the UT 
indications, a chi-square test is performed using .sm as the flaw size parameter and t = 25 mm. 
Several other types of goodness-of-fit tests exist such as the Kolmogorov-Smirnov test or the 
Anderson-Darling test. The chi-square test is often less powerful than those tests but is 
nevertheless chosen because it is a widely used statistic that applies to any distribution and is the 
most generally applicable test of fit (DAgostino and Stephens 1986, p. 63). 
The chi-square test requires the empirical data to be partitioned into several cells. The following 
statistic is then calculated (DAgostino and Stephens 1986, p. 64): 
2
M (N - n  p ) (Eq. 7) 
ii
X 2= . 
i=1 n  p
i 
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where 
X 2 = chi-square statistic (also called Pearson statistic) 
M = number of cells into which the empirical data are partitioned 
pi = probability that a random observation falls into cell i (i varies from 1 to M) 
n = total number of empirical data (for the flaw size data, n = nf) 
Ni = number of empirical data that fall into cell i 
Based on the recommendations of DAgostino and Stephens (1986, pp. 70 and 71), the cells are 
chosen to be approximately equiprobable. Also, DAgostino and Stephens (1986, p. 71) mention 
the following guidelines for choosing the value of M: M should be greater than or equal to 3, 
n greater than or equal to 10, and the ratio n2/M greater than or equal to 10. Of course, because 
n = nf = 7, it is not possible to respect one of the previous rules, but with choosing M = 3, the 
other rules (i.e., M greater than or equal to 3, and n2/M = 16.3 greater than or equal to 10) are 
met. Therefore, the cells will be divided into M = 3 equiprobable cells. 
To determine whether or not the flaw size data fit the distribution, the Pearson statistic X2 is 
2
compared to .(M - - 1), which represents the 95th percentile of the chi-square distribution
1
95.0 
with M-1-1 = 1 degree of freedom. The 95th percentile is chosen because it corresponds to a 
level of significance of the test of 1  0.95 = 0.05, which is often used (DAgostino and Stephens 
1986, p. 70). The number of degrees of freedom is determined based on the fact that one 
parameter of the distribution, namely .sm, has been estimated using the empirical data. Because 
.sm is also the maximum likelihood estimator, it is appropriate to consider M-1-1 degrees of 
freedom (DAgostino and Stephens 1986, pp. 67 and 68). 
The cells are found to be approximately equiprobable by selecting the following ranges: 0 to 
1.8 mm, 1.8 mm to 4.9 mm, and 4.9 mm to 25 mm. Calculation of the Pearson statistic yields 
2 
1around 2.0, which is lower than . ()=8.3 . In other words, using Psg(s,.sm,t) to represent the 
95.0 
weld flaw sizes in the Y direction is not contradicted by the data at the 0.05 significance level. 
Attachment I provides the detail of the calculation performed to obtain the previous results. 
The PDF psg for the flaw size distribution based on Equation 6 is given by: 
-.s s 
s
p
sg (s,., t )=
.e 
with 0=s =t (Eq. 8) 
s 1 -e-.s t 
As a reminder, in Equation 8 the variable of interest is the flaw size s, while .s and t are 
parameters. 
As complementary information, the PDF pmsg accounting for all possible values of .s, weighted 
by their probability, is calculated. The PDF pmsg is a function of s, with parameter t, and is 
evaluated using the following equation: 
-.s s 
()=. 8.e
s 
,
p
msg t s 
1 -e-.s t p.s (.s ) d. (Eq. 9) 
0 s 
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The associated cumulative distribution function (CDF), Pmsg, on the flaw size s (t being a 
parameter) is determined by: 
s
P ()=. pmsg (du t u (Eq. 10) 
t s 
msg ,0,) 
CDF 
Figure 3 shows Pmsg for the outer lid weld (t = 25 mm). 
1 
0.8 
0.6 
0.4 
0.2 
0 
0 5 10152025 
Flaw Size (m m) 
Figure 3. Cumulative Distribution Function for Flaw Size Before Ultrasonic Inspection in Outer Lid Weld 
In conclusion, the size s (in mm) of the flaws in the Y direction of a weld of thickness t (in mm) 
can be evaluated using the cumulative distribution Psg(s,.s,t) given in Equation 6. The flaw size 
parameter .s has the PDF defined in Equation 2. It is worth noting here that the use of Psg(s,.s,t) 
has been justified only for the outer lid weld (i.e., for t = 25 mm). Applicability to other weld 
thicknesses will be addressed in Section 6.2.1.3. 
6.2.1.1.2 Flaw Density 
The flaw density is the mean number of flaws per meter of weld. The flaw density is 
investigated because it will help predict the number of flaws expected in the waste package. In 
searching for a distribution that can adequately describe the number of flaws (which takes 
discrete values), the Poisson distribution was chosen because it is a discrete distribution that is 
used for characterizing many processes. Given a length of weld L (in m) and a flaw density 
parameter .d, the Poisson distribution characterizing the probability on the number of flaws n has 
the form (Martz and Waller 1991, pp. 254 and 255): 
n 
.dd
P (n,., L)=e - L (.L) (Eq. 11) 
nd 
n! 
Note that the mean of this distribution is .d L (Martz and Waller 1991, p. 17). 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The length of weld in a waste package is known; therefore, the number of flaws to be expected 
will be governed by .d whose PDF is determined in the following. The Bayesian approach with 
a noninformative prior is used for the PDF determination for the same reasons as those presented 
in Section 6.2.1.1.1. 
Based on Assumption 5.1.1, the information on UT indications presented in Section 4.1.3.2 is 
appropriate to characterize the flaw density of the significant flaws in the closure welds. In the 
total weld length of the 16 specimen rings, nf = 7 flaws were detected. Here, nf is random while 
the length of weld is fixed. This corresponds to Poisson sampling (Martz and Waller 1991, 
pp. 254 and 255). According to Martz and Waller (1991, p. 286), the noninformative prior 
-1/ 2
distribution for .d based on Poisson sampling is proportional to . . The resulting posterior 
dPDF p.d of the flaw density parameter .d is given in the same reference as: 
.d 
.d .d 
Lnt 
f +5.0 
.dnf -5.0 e - Lt (Eq. 12)p ()=
G(n +5.0 )
f 
where Lt is the total weld length examined. Sixteen specimen rings have been welded and each 
of them has a diameter approximately equal to the diameter of the outer lid weld (the diameter of 
a specimen ring is 60.765 inches [see Section 4.1.3.1], or equivalently 1.543 m, while the 
diameter of the outer lid is 1.541 m [see Section 4.1.1]). This yields a weld length of around 
4.85 m for a specimen ring, which is the value used in the rest of this analysis. The 16 rings 
account for a total weld length, Lt = 77.60 m. 
The associated CDF P.d is given in Equation 13 and is shown on Figure 4. 
()=..dp (du u (Eq. 13)
P.d .d .d )
0 
The posterior mean, .dm, the 5th percentile, .d0.05, and the 95th percentile, .d0.95, are respectively 
given by (Martz and Waller 1991, pp. 286 and 287): 
.
2 nf +1 
dm = (Eq. 14) 
2 Lt 
2 
.
d 05.0 
../2 (2 nf +1) (Eq. 15) 
= 
2 Lt 
2 
.
d 95.0 
.1-./2 (2 nf +1) (Eq. 16) 
= 
2 Lt 
where . = 0.1. This yields the following values: .dm = 0.097 flaw per meter of weld, 
.d0.05 = 0.047 flaw per meter of weld, and .d0.95 = 0.16 flaw per meter of weld. As mentioned in 
Martz and Waller (1991, pp. 286 and 287), these estimates are close to the classical maximum 
likelihood estimator, the lower, and the upper value of the 90 percent confidence interval for .d. 
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This shows that the Bayesian approach used to estimate the flaw density parameter is in 
agreement with the classical (frequentist) approach. 
1 
0.8 
CDF 
0.6 
0.4 
0.2 
0 
0 0.05 0.1 0.15 0.2 0.25 
0 
Flaw Density Parameter (Flaws / Meter of Weld) 0.25 
Figure 4. Cumulative Distribution Function for Flaw Density Parameter before Ultrasonic Inspection 
Based on previous parameters, the distribution on the number of flaws in the weld follows a 
Poisson distribution Pn(n,.d,L) (Equation 11) with .d having the PDF given in Equation 12. 
To verify that Pn(n,.d,L) adequately fits the data from the UT indications a chi-square test is 
performed using .dm as the flaw size parameter and L = Lwp, the length of weld in a specimen ring 
(4.85 m). The chi-square test is selected because it can be applied to test the goodness-of-fit of 
discrete distributions (DAgostino and Stephens 1986, p. 63). 
The symbols of Equation 7 are utilized to perform the goodness-of-fit test. The test is carried out 
using the number of flaws reported in each of the specimen rings, yielding a total of n = 16 
observations. The test is done at the 0.05 significance level using M = 4 cells. The cells are 
determined by the number of flaws observed in the specimen rings as follows: 0 flaw, 1 flaw, 
2 flaws, and 3 or more flaws. It should be noted that contrary to what was done in 
Section 6.2.1.1.1 for the flaw size in the Y direction, it is not possible to choose equiprobable 
cells (this is because the distribution tested is discrete). Nevertheless, the recommendations of 
DAgostino and Stephens (1986, p. 71) on the selection of the cells are respected. These 
recommendations are to choose M greater than or equal to 3, n greater than or equal to 10, and 
n2/M greater than or equal to 10. Additionally, it is recommended that when cells are not 
equiprobable, n should be greater than 2 M at the 0.05 significance level. Attachment I 
provides information used to calculate the Pearson statistic, which is found equal to 5.3. 
The number of degrees of freedom to consider in the test is determined based on the fact that one 
parameter of the distribution, namely .dm, has been estimated using the empirical data. Because 
.dm is fairly close to the maximum likelihood estimator, it is appropriate to consider 
M-1-1 = 2 degrees of freedom (DAgostino and Stephens 1986, pp. 67 and 68). This yields 
2 
2
.
95.0 ()=0.6 , which is greater than the Pearson statistic. Therefore, using the Poisson 
distribution to predict the number of flaws in the specimen rings (and thus the waste package 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
outer lid weld since they have approximately the same length of weld) is not in contradiction 
with the data at the 0.05 significance level. 
In conclusion, the probability on the number of flaws n in a length of weld L can be evaluated 
using the Poisson distribution Pn(n,.d,L) given in Equation 11. The flaw density parameter .d has 
the PDF defined in Equation 12. It is worth noting that this probability distribution was 
evaluated for use on the outer lid weld of the waste package only. Applicability to other welds 
will be addressed in Section 6.2.1.3. 
6.2.1.1.3 Flaw Depth 
The flaw depth is the distance between the outer surface of the weld and the onset of the flaw in 
the Y direction (see Figure 1 for orientation of the Y direction). 
A uniform distribution has been chosen to represent the flaw depth. The reason for this choice is 
that the UT indications shown in Table 7 seem to indicate that flaws are scattered over the entire 
extent of the Y direction. 
To verify that the use of a uniform distribution is not unreasonable to represent flaw depths, a 
chi-square test is performed at the 0.05 significance level. 
The symbols of Equation 7 are utilized to perform the goodness-of-fit test. The evaluation 
performed is based on Assumption 5.1.1. The onsets of the n = 7 UT indications in the 
Y direction are partitioned into M = 3 equiprobable cells: one ranging from 0 to 8.33 mm, one 
ranging from 8.33 mm to 16.67 mm, and the last ranging from 16.67 mm to 25 mm. Three cells 
have been chosen for the same reason as that given in Section 6.2.1.1.1. The resulting Pearson 
statistic is 2.0 (see Attachment I for the detail of the calculations). 
The number of degrees of freedom is M  1 = 2, based on DAgostino and Stephens (1986, 
p. 64). Notice that no parameter needs to be estimated with the uniform distribution. That is 
why, contrary to what was done in the previous sections, there is no need to remove an extra 
2 
2degree of freedom. This yields .95.0 ()= 0.6 , which is greater than the Pearson statistic. 
Therefore, using a uniform distribution to estimate the flaw depth distribution is not in 
contradiction with the data 
In conclusion, the depth of the flaws in the outer lid weld of the waste package is considered to 
follow a uniform distribution. Applicability to other welds will be addressed in Section 6.2.1.3. 
6.2.1.1.4 Flaw Orientation 
The orientation of the flaws is investigated in the plane of the specimen rings. The objective is 
to investigate the angle . that the flaws make with the direction of the weld (see Figure 5 for 
schematic representation). This is important in trying to determine an estimate of the flaws 
which are radially oriented (a broad definition of radially orientated flaws is those flaws that 
have an angle . greater than 45 degrees). 
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ild 
(X dii)l.ion 
Directon of the werectonflaw 
Direction of the faw 
Z direct
Figure 5. Schematic Representation of Flaw Orientation on Specimen Ring 
The calculations which follow are based on Assumption 5.1.1. The extent of the UT indications 
in the radial direction (Z direction) and their length in the direction of the weld (X direction) are 
given in Section 4.1.3.2. Because the largest flaw in the X direction does not exceed 3.5 cm, 
which is very small compared to the radius of the specimen ring (around 77 cm, see 
Section 4.1.3.1), the effect of the curvature in the direction of the weld is negligible. Therefore, 
the angle . of a flaw can be calculated by taking the arctangent of the ratio of its extent in the 
Z direction over its extent in the X direction. Notice that the inputs given in Section 4.1.3.2 
make it possible to evaluate the absolute value of . only, not its sign. 
Orientation of defects in welds has been investigated by Shcherbinskii and Myakishev (1970). 
They report that the angle between a defect and the direction of the weld can be fit to a centered 
normal distribution with a standard deviation of around 5 degrees. Based on this information, 
the present analysis considers a centered normal distribution in trying to fit the data. 
The fact that the distribution is chosen to be centered (i.e., with a mean of 0 degree) is natural 
since most of the defects observed are lack-of-fusion flaws, which typically are in the direction 
of the weld. The standard deviation of 5 degrees is discarded from further consideration since 
the available data report a flaw with an angle around 27 degrees, which suggests a larger 
standard deviation. It should be noted that the flaw with an angle around 27 degrees is not a 
lack-of-fusion defect but results from a poor weld preparation (flaw found on ring K: see 
Section 4.1.3.2 and angle values calculated in Attachment I). In a conservative approach, this 
flaw was kept in the analysis though it is not representative of the highly controlled conditions 
under which operations will be conducted on the waste package. The standard deviation s of the 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
normal distribution is evaluated using the Bayesian approach with a noninformative prior. A 
noninformative prior is selected so as to put maximum emphasis on the information provided by 
the data. 
Only the absolute values for . are available, not their signs. Therefore, the distribution for . is 
not normal by definition, since it is defined only by positive values. In fact, there are two 
possible initial angle values (one positive, one negative) that correspond to a single value of .. 
Therefore, the actual PDF p. for . is equal to twice the PDF of the centered normal distribution, 
with standard deviation s. The PDF of a normal distribution is found in Martz and Waller (1991, 
p. 49), and the resulting PDF for . is as follows. 
2
.
.
. 
...
..
.
 2 
1 exp2 sps 
 - 
1
..
.
p
. 
(s. )
, 
.=
 = 
2 
for 
0 (Eq. 17) 
..
.
 
The corresponding CDF P. is: 
2
.
.
...
..
.
 sps 2 
1 exp2 
 - 
1
..
.
. 
u
P(s. )
,
. 
 = 
2
.
du 
(Eq. 18) 
..
.
 
0 
Based on Martz and Waller (1991, pp. 225 and 226), a noninformative prior for s when 
considering the quasi-normal PDF p.(.,s) is 1/s. 
Applying Bayes theorem leads to the following expression for the posterior PDF ps of s (Martz 
and Waller 1991, pp. 174 and 175): 
L. (s ) 
p()= 
8
s (Eq. 19) 
s 
s 
L. (s ) 
ds 
.
0 s 
nf 
where L. (s ) =. p (s . ) is the likelihood function related to the nf = 7 observed angles .i.
. i ,
i= 1
5
Based on the posterior PDF, the mean value of sm is calculated to be around 13.9 degrees. The 
th and 95th percentiles are around 8.7 and 21.6 degrees, respectively. The maximum likelihood 
estimator, based on the formula given in Martz and Waller (1991, p. 225) is around 12.3 degrees, 
which is relatively close to sm. 
To verify that it is not unreasonable that the flaw orientation information fits P., a chi-square test 
is performed at the 0.05 significance level, using sm as the standard deviation. 
The variables of Equation 7 are utilized to perform the goodness-of-fit test. There are n = 7 data 
points, and the fitted distribution has one of its parameters evaluated from the data. The same 
approach as that outlined in Section 6.2.1.1.1 (i.e., partition the flaw orientation dataset into 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
M = 3 approximately equiprobable cells and compare the Pearson statistic to the 95th percentile 
of the chi-square with 1 degree of freedom is performed). 
The cells are found to be approximately equiprobable by selecting the following ranges: 0 to 
5.6 degrees, 5.6 to 12.7 degrees, and more than 12.7 degrees. The Pearson statistic is located 
2 
1around 0.44, which is lower than .95.0 ()=8.3 (see Attachment I for the detail of the 
calculations). In other words, fitting the flaw orientation information to P.(.,sm) is not 
contradicted at the 0.05 significance level. 
Based on previous developments, the expected fraction of flaws, F., that have an angle . greater 
than 45 degrees is calculated using the following formula: 
8
F.=. [1 -P (,45 s)]p (s s (Eq. 20) 
) d
.s
0 
This yields F. = 8 10-3. Therefore, around 0.8 percent of the flaws will have an angle greater 
than 45 degrees. 
In conclusion, investigation of flaw orientation has shown that almost all of the flaws are in the 
direction of the weld. The fraction of flaws that are radially oriented (i.e., making an angle of 45 
degrees or more with respect to the direction of the weld) is 0.8 percent of the flaws. This result 
was obtained for the flaws in the outer lid weld of the waste package. Applicability to other 
welds will be addressed in Section 6.2.1.3. 
6.2.1.2 Flaw Characteristics in Welds after Inspection and Repair 
The flaw characteristics that were developed in Section 6.2.1.1 are representative of those to be 
expected in the noninspected outer lid weld of a waste package. A UT inspection will be 
performed to detect and repair the flaws that may adversely affect the waste package 
performance. The objective of this section is to assess the characteristics of the flaws remaining 
in the waste package. 
6.2.1.2.1 Ultrasonic Inspection Characterization 
This section investigates the UT PND of a flaw of size s in the Y direction. The corresponding 
PND curve was not developed during the UT inspection of the specimen rings. Nevertheless, 
information from the literature, available results from UT inspection capability on the specimen 
rings, and anticipation that not every detected flaw will need to be removed from the weld were 
combined to elaborate a conservative UT PND curve. 
Bush (1983, pp. 13A.5.6 and 13A.5.7) summarizes the results of previous studies on UT 
reliability and provides parameter values for a PND curve defined as follows: 
1 .. s ..
P
ND1(s,e, s ,.) =e+ (1-e) erfc. 
.ln.. ..
. (Eq. 21) 
0 
2 .. s 0 .. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
where 
s = size of the flaw (in mm)
e = lower limit of PND1 (from assumption 5.1.2 = 0.005) 
v
s
= shape factor (from assumption 5.1.2 = 3) 
0 = characteristic flaw size, in mm, for which around 50 percent of the flaws are 
detected (from assumption 5.1.2 = 2.5 mm) 
erfc = complementary error function 
It should be noted that in Equation 21, s is the variable while e, ., and s0 are parameters. 
Focusing on detection of intergranular stress corrosion cracking in austenitic piping, Bush (1983, 
p. 13A.5.7) suggests using the following parameter values: e = 0.005, . = 3, and s0 = 5 mm. 
Notice that these results are based on experiments performed in the late 1970s, so they reflect 
detection capabilities that have been significantly surpassed. A way to account for finer 
detection capabilities is to reduce the value of s0, for example take s0 at 2.5 mm (Bush 1983, 
p. 13A.5.7). This value is not reduced further in order to account for those small flaws that are 
detected but are left in the weld because the welds will not jeopardize the waste package 
performance. 
A more recent study on UT detection of intergranular stress corrosion cracking in stainless steel, 
reported in Heasler and Doctor (1996), shows significantly improved reliability. This reference 
provides the parameters for a logistic function giving the probability of detection as a function of 
flaw size s for near-side access (i.e., the defect is located on the accessible side of the weld 
centerline). The PND curve based on Heasler and Doctor (1996, p. 5.1) has the form: 
1 
)exp(1 
1)( 
21 
2 s 
sPND --+ 
-= 
 
(Eq. 22) 
where: 
s = flaw size in mm 
1 = -2.67, based on Heasler and Doctor (1996, p. 5.9) 
2 = 1.6709 /mm, based on Heasler and Doctor (1996, p. 5.9) 
The resulting UT PND curves identified previously are summarized in Figure 6. 
It should be noted that the references reviewed previously indicate that the PND for flaws of 
various sizes is dependent on a number of variables such as the type of material, operator skill, 
access to the weld, and type of defect. In that context, the UT inspections performed on the 
specimen rings provide useful information, since they were carried out on welds very similar to 
the closure weld of the waste package. 
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0 1 2 3 4 5 6 7 8 90 
0.2 
0.4 
0.6 
0.8 
1 
PND 
PND1 (s0) 
PND1 (s0 ) 
   PND2 
10 
= 5 mm = 2.5 mm
Flaw Size (mm) 
Figure 6. Comparison of Several Ultrasonic Probability-of-Nondetection Curves Identified in the Literature 
As mentioned in Section 4.1.3.2, the UT inspection threshold employed in the examination of the 
specimen rings had a sensitivity of 1 mm, which calls for detection of flaws of this size or larger. 
This was confirmed by metallographic examination of the specimen rings: all the uncovered 
flaws that were larger than 1 mm had been detected through the previous UT inspections. 
Therefore, the UT PND curves shown in Figure 6 appear to display less detection capability than 
what is attainable on waste package closure welds using current industry equipment. 
Lastly, the fact that a flaw is detected through UT inspection does not mean that it will be 
removed. The reason for this is that weld repairs are time- and resource-consuming and will 
therefore be implemented only when deemed necessary to ensure waste package performance. It 
can be expected that small flaws and flaws located deep in the weld will be left if it is shown that 
they will not cause early waste package breach. Also, gas porosities will not be removed since 
they have no orientation and therefore do not promote stress corrosion cracking. 
Based on the elements of information given previously, a conservative assumption 
(Assumption 5.1.2) has been developed. It is assumed that an acceptable UT PND curve, 
applicable to the waste package closure weld, is given in Equation 21 with the following 
parameter values: e = 0.005, . = 3, and s0 = 2.5 mm. This UT PND curve is used in the 
following to develop the flaw density and size distributions of the flaws remaining in the weld 
after inspection and repair. Notice that this curve is shown on Figure 6 (it is the curve plotted 
with dots, designated by PND1 with s0 = 2.5 mm). With this curve the flaws smaller than 1 mm 
are not detected. Around 50 percent of the 2.5 mm flaws are detected. 
A weld flaw detection criteria equal to or greater than 1.6 mm (1/16th of an inch) has been 
established for the fabrication of a prototype waste package (BSC 2003f, Requirements 7.1.B 
and 7.1.C). This detection criteria specifies that the UT inspection method employed must be 
able to detect all weld flaws equal to or greater than 1.6 mm (PND=0.0). This will result in 
smaller weld flaws being detected than is being modeled in this calculation since, as shown in 
Figure 6, the PND of a 1.6 mm flaw is approximately 1.0 (i.e., the model predicts that no weld 
flaws 1.6 mm or smaller would be detected). 
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6.2.1.2.2 Flaw Size Distribution in the Y direction 
Equation 8 in Section 6.2.1.1.1 gives the PDF for the flaw size distribution of flaws of size s in 
the Y direction based on welds of thickness t, before UT inspection. It is a function of the 
random parameter .s whose PDF is given by Equation 2. 
The UT inspection and subsequent weld repair are characterized by the UT PND PND1 curve 
given in Equation 21 with the parameter values: e = 0.005, . = 3, and s0 = 2.5 mm. 
Using the calculated value of .s, the fraction of flaws that remain in the closure weld after UT 
inspection and weld repair is calculated with the following equation: 
F
ND ( t,e ., s ,.)= tpsg (s,. , t)  P (s,e , s ,. ) ds (Eq. 23) 
,
s 0 s ND10
.0 
The corresponding CDF for the flaw size of those flaws remaining in the closure weld after UT 
inspection and weld repair, Psgut, is given by the following equation: 
s 
P
sgut ( t s , 
.0 
psg (u,. , t)  P (u,e , s ,. ) du
s ND1 
(Eq. 24) 
s 0 
, 
, , e . , s ,.)=
FND ( t,e . , s ,.) 
0 
s 0 
It should be noted that in Equation 24, s is the variable while t, .s, e, s0, and . are parameters. 
As complementary information, pmsgut, the PDF for the size of the remaining flaws accounting for 
all possible values of .s, weighted by their probability, can be calculated using the following 
equation: 
, , e , s ,.)= .0 
8psg (s,. , t)  P (s,e , s ,. )
s ND10 
p ( t s 
FND (t,e . , s ,. ) 
 p. s (. s ) d. s (Eq. 25) 
msgut 0 
,
s 0 
The corresponding CDF is: 
s 
, , e, s ,.)= pmsgut (t u 
P
msgut ( t s , , e , s ,. ) du (Eq. 26) 
00
.0 
Figure 7 shows Pmsgut(s,t,e,s0,.) for t = 25 mm, which corresponds to the size distribution of the 
flaws remaining in the outer lid weld of the waste package after UT inspection and repair. Recall 
that this CDF accounts for all possible values of .s, weighted by their probability. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
0 
0.2 
0.4 
0.6 
0.8 
1 
CDF 
01 2 3 4 5 6 7 8 
Flaw Size (mm) 
Figure 7. Cumulative Distribution Function for Flaw Size After Ultrasonic 
Inspection and Repair in Outer Lid Weld 
The corresponding mean size, for the flaws remaining in the 25-mm thick closure weld, is given 
by: 
s
mgut (t,e, s ,.)= t pmsgut (t u 
, , e, s ,.)  du u (Eq. 27) 
0 0
.0 
This yields a value of 1.3 mm. As for the 5th and 95th percentiles, they are calculated by solving 
Equation 26 for values of Pmsgut equal to 0.05 and 0.95, respectively. This yields 9.9  10-2 and 
2.8 mm. 
6.2.1.2.3 Flaw Density 
Recall that before UT inspection, the mean number of flaws per meter of weld is given by the 
flaw density parameter .d, whose PDF is shown in Equation 12 of Section 6.2.1.1.2. After UT 
inspection and repair, the mean number of remaining flaws per meter of weld, .dut, will be equal 
to .d, adjusted by the fraction FND of flaws that will not be detected. This corresponds to the 
following equation: 
.
dut (. , . , , e, s ,.)=.  FND (t, . ,e, s ,.) (Eq. 28) 
d st 0 ds 0 
where FND is evaluated with Equation 23. 
It should be noted that in Equation 28, .dut is a function of two independent random parameters 
(.d and .s), and four fixed parameters (t, e, s0, and .). 
As complementary information, the CDF of .dut, accounting for all possible values of .s and .d, 
weighted by their probability, is calculated using Latin Hypercube Sampling. 
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The principle of Latin Hypercube Sampling is provided in Modarres (1993, p. 244). For this 
case there are two random parameters: .d and .s. To start the process the range [0,1] is divided 
into ns equal intervals. Within each of these intervals a random value ui is chosen. Considering 
the CDF associated with .d, each ui can be interpreted as the probability that .d will not exceed a 
certain value .di. Each .di is evaluated at each ui, so that ns values of .di are obtained. This same 
procedure is repeated with .s so as to obtain a sample of ns values associated with .s. The two
CDF 
samples are then randomly combined according to Equation 28, in order to have a set of ns 
random values, .dut i, associated with .dut. This set is sorted out to obtain a sample CDF of .dut. 
Figure 8 shows the result obtained from the Latin Hypercube Sampling performed on 
Equation 28 with ns = 2000. A large value was chosen for ns in order to ensure that the results of 
the sample CDF is close to the true CDF of .dut. 
1 
0.8 
0.6 
0.4 
0.2 
0 
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 
Flaw Density Parameter (Flaws / Meter of Weld) 
Figure 8. Cumulative Distribution Function for Flaw Density Parameter After Ultrasonic Inspection and 
Repair in Outer Lid Weld 
The mean density parameter of the flaws remaining in the 25-mm thick closure weld after UT 
inspection and repair is evaluated based on the sample CDF using the following equation: 
ns
1 
n 
.
mdut = ..i dut (Eq. 29) 
si=1 
where .dut i is the ith Latin Hypercube Sample value of .dut. This yields .mdut = 4.1  10-2 flaw /m 
of weld. The 5th and 95th percentiles are estimated by linear interpolation on the sorted set of 
sample values of .dut, around the 5th and 95th percentiles. This helps delimit a range for the flaw 
density parameter that encompasses 90 percent of the probability. The large value ns = 2000 
selected for Latin Hypercube Sampling ensures that the estimates for the 5th and 95th percentiles 
are close to the true value, but is too small to reach complete certainty on the first two significant 
figures. Therefore, only a range that encompasses the true 5th and 95th percentile is presented 
here. It is evaluated by rounding down the 5th percentile estimate, and rounding up the 95th 
percentile estimate. The resulting values are 1.6  10-2 flaws /m of weld and 7.6  10-2 flaws /m 
of weld, respectively. Note that because of the long time required for computation, it was not 
judged useful to make the calculation with a larger value of ns. Besides, the value that was 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
selected proved sufficient to make an estimate of the mean with two significant figures. This is 
due to the fact that, by nature, Latin Hypercube Sampling provides estimates of the mean which 
are more stable than those related to lower and upper percentiles. 
In conclusion, the probability on the number of flaws n remaining in a weld of length L (in m) 
after UT inspection and repair is calculated using the following Poisson distribution: 
n 
-.dut L  dut
P
nut (n,. , L)= e (.  L) (Eq. 30) 
dut 
n! 
where .dut is estimated based on Equation 28. 
6.2.1.2.4 Flaw Depth and Flaw Orientation 
The flaws that are detected during UT inspection will be evaluated in accordance with the ASME 
Code. It is planned that this inspection be performed in-situ as the weld is made. In the event 
that a flaw is identified, the flaw will be evaluated to determine if it fails to meet code 
requirements. If any flaw not meeting requirements is identified, the welding process will be 
interrupted and the flaw removed and that flaw site repair welded. The flaws that do not meet 
code requirements are most likely to jeopardize the long-term performance of the waste package 
and, therefore, is additional justification for their removal. 
As a consequence, it is expected that any flaws that remain in the closure weld will be smaller 
than Code allowable. This and the test data indicating that none of the expected flaws are 
perpendicular (or greater than 5 degrees from the hoop stress) means that flaws remaining in any 
closure weld will be very small and unlikely to grow due to applied stresses. 
The repair of weld flaws may affect the flaw depth distribution and flaw orientation results of 
Sections 6.2.1.1.3 and 6.2.1.1.4. This means that the flaw depth distribution will no longer be 
uniform. Nevertheless, following a conservative approach, the results of Sections 6.2.1.1.3 and 
6.2.1.1.4 are still considered adequate to characterize the flaw depth distribution and the flaw 
orientation in the closure welds that have been inspected and repaired. 
6.2.1.3 Summary of Results and Comparison with Results from Literature 
In this section, the information needed to calculate the characteristics of the flaws expected in the 
waste package welds is summarized in Tables 11 and 12. The overall results are summarized in 
Table 13 (see Attachment I for the details of the calculations performed to obtain the results). 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Table 11. Parameters Needed for Calculating Weld Flaw Characteristics 
Type of Numerical Value or 
Parameter Symbol Description Related Equation 
Random s Flaw size in the Y direction (in mm) See Table 12 
variable n Number of flaws in the weld See Table 12 
10 mm for middle lid weld 
t Thickness of the weld (in mm) 20 mm for seam welds 
25 mm for outer lid weld 
4.80 m for middle lid weld 
L Length of the weld (rounded-up values, in m) 4.85 m for outer lid weld 
15 m for seam welds 
nf Number of UT indications in specimen rings 7 
Fixed parameter st Sum of UT indications sizes in the Y direction (in mm) 31.75 mm 
Lt Total length of weld examined in specimen rings (in m) 77.60 m 
e Lower limit for UT PND 0.005 
s0 Characteristic flaw size for UT PND (in mm) 2.5 mm 
. Shape factor for UT PND 3 
A Cross sectional area of specimen ring welda 239.88 mm2 
Random .s Flaw size parameter in the Y direction (in mm-1) PDF: see Equation 2 
parameter .d Flaw density parameter (flaws per meter of weld) PDF: see Equation 12 
NOTES: a Value given for convenience (not used in the equations referred to in Table 12). Value calculated in 
Attachment I. 
Table 12. Summary Table for Evaluating Flaw Characteristics 
Flaw 
Characteristic Before UT Inspection After UT Inspection and Weld Repair 
Flaw size 
(s, in mm) 
CDF Psg given in Equation 6 
Secondary equation: 2 
Parameters : .s, t, nf, st 
CDF Psgut given in Equation 24 
Secondary equations: 2, 8, 21, 23 
Parameters: .s, t, nf, st , e, s0, . 
Flaw number 
(n) 
Poisson distribution: Equation 11 
Secondary equation: 12 
Parameters: .d, L, nf, Lt 
Poisson distribution: Equation 30 
Secondary equations: 2, 8, 12, 21, 23, 28 
Parameters: .d, L, nf, Lt, .s, t, e, s0, ., st 
Flaw orientation 0.8% of the flaws are radially oriented 0.8% of the flaws are radially oriented 
Flaw depth Uniform distribution on weld thickness Uniform distribution on weld thickness 
In addition to the outer lid weld of the waste package, which has been extensively studied 
previously, the parameters and the results pertaining to the middle lid weld and the seam welds 
of the waste package are provided. This was done based on Assumption 5.1.3. It should be 
noted that the seam welds are those welds that are required to fabricate the outer cylinder of the 
waste package with its associated bottom lid. The outer cylinder is composed of two plates 
rolled to form two half-cylinders (longitudinal welds), which are then welded to each other 
(circumferential weld). An additional weld is made to attach the bottom lid to the cylinder 
(Plinski 2001, pp. 14 and 15). The dimensions taken for the seam welds are as follows. The 
diameter of the bottom lid is taken to be the same as the outer lid diameter, and the length of the 
longitudinal welds is that of the waste package. This yields a total length of 15 m (see 
Attachment I for details of the calculation). The weld thickness is taken to be 20 mm, which is 
CAL-EBS-MD-000030 REV 00C 65 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
the thickness of the outer cylinder wall (it should be noted that for the bottom lid weld, the 
thickness of the weld in reality is 25 mm; considering that it is only 20-mm thick is 
conservative). In Table 12, note that the expression radially oriented flaws for the flaws 
located in the seam welds should be interpreted as those flaws that deviate from an angle of more 
than 45 degrees from the direction of the weld. 
Table 13 shows the mean, the 5th, and the 95th percentiles of the predicted flaw sizes, before UT 
inspection and after UT inspection and weld repair. These values are calculated based on the 
distribution of the flaw size, weighted with the probability values assumed by .s (see 
Equations 10 and 26). 
Table 13 also shows the probability of having zero, one, and two or more flaws in the welds of 
the waste package before UT inspection and after UT inspection and weld repair. In each case, 
these probabilities have been calculated using the mean flaw density parameter. Notice that in 
contrast to what has been done for the flaw size, this calculation does not take into account the 
uncertainty of the flaw density parameter. This is because after UT inspection and weld repair, 
the calculation of the flaw density parameter is based on two random parameters, namely .d and 
.s, which makes the evaluations more complex. In this case, it is simpler to use the mean value 
of the flaw density parameter than trying to incorporate the uncertainty of this parameter in the 
calculation. 
Table 13. Main Characteristics of Flaws in Welds of Waste Package 
Before UT Inspection After UT Inspection and Weld Repair 
Flaw Sizea (mm) mean 
5th 
percentile 
95th 
percentile mean 
5th 
percentile 
95th 
percentile 
Outer lid weld 4.8 0.23 15.2 1.3 0.099 2.8 
Middle lid weld 3.3 0.20 8.6 1.2 0.098 2.7 
Seam weldsb 4.6 0.23 13.8 1.2 0.099 2.8 
Number of Flawsc 0 1 2 or more 0 1 2 or more 
Probability per outer lid weld 0.63 0.29 0.08 0.82 0.16 0.02 
Probability per middle lid 
weld 0.63 0.29 0.08 0.80 0.18 0.02 
Probability per seam weldc 0.23 0.34 0.43 0.54 0.33 0.13 
NOTES: a Flaw sizes are given with two significant figures. 
b 
For information only  Do not use in calculations (see previous explanations). 
c 
Probability values on number of flaws are rounded so as to add up to 1. 
It is important to note that the numbers reported in Table 13 for seam welds account only for UT 
inspection. This is extremely conservative since the fabrication welds of the waste package will 
undergo several types of inspections, including radiographic and liquid-penetrant testing (Plinski 
2001, pp. 14 and 15), and therefore it is expected that any significant flaw will be detected and 
removed. Thus the seam weld flaw characteristics in Table 13 are given for information only 
and should not be used in further calculations. 
Notice that the UT inspection followed by weld repair is an effective filter regarding the flaw 
size. This is because the UT inspection detects the larger flaws, which are then removed through 
weld repair. In other words, the UT inspection puts a cap on the maximum size of the flaws, 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
regardless of the thickness of the weld. It is worth noting that this cap is dependent on the shape 
of the UT PND curve. For example, using a different value than s0 = 2.5 mm would yield a 
different cap. As previously mentioned in Section 6.2.1.2.1, the UT PND considered in this 
analysis is considered conservative. 
Khaleel et al. (1999, Figure 7), reported results from simulations of flaws in welds that pertained 
to nuclear piping. The report modeled the flaw sizes in stainless steel welds (manufactured using 
the tungsten inert gas method) with a lognormal distribution, for which they give the median 
flaw size (in inches) and the shape parameter (no dimension) as a function of the weld thickness 
(in inches). Converting to the metric system, their equations become: 
s 
t 2 
50k =4.25 1169.0 - 0445.0  t + 00797.0  (Eq. 31) 
 
4.25 
2 
sk= 09733.0 + 3425.0 

t 
4.25
- 07268.0

..
.
t 
4.25
..
. 
(Eq. 32) 
where s50k, sk, and t are respectively the median flaw size (in mm), the shape parameter (no 
dimension), and the thickness of the weld (in mm). The PDF of the associated lognormal 
distribution is (Khaleel et al. 1999, p. 131): 
2
[ln(/ )]
50
.
.
1 
s 
s 
k
p (s) = 
sk 
- 
(Eq. 33) 
..
. 
..
. 
 exp 
 2k s ps
2
2 sk 
where s is the size of the flaw in mm. 
Also, based on Khaleel et al. (1999, p. 131), the mean flaw size smk (in mm) can be calculated as: 
2
s
k
..
.
..
. 
(Eq. 34) 
= exp
s
mk s50k 
2
.
.
The previous equations are used to calculate the mean, the 5th, and the 95th percentiles of the flaw 
size for a 25-mm thick weld. This yields 2.2 mm, 1.1 mm, and 3.8 mm, respectively (see 
Attachment I for details of the calculation). 
It should be noted that these flaw sizes were developed with simulations that included the effects 
of inspection (Khaleel et al. 1999, p. 132). Therefore, they are to be compared to the post-UT 
inspection and weld repair results shown in Table 13. However, because the parameters used for 
modeling the inspections in the paper by Khaleel et al. (1999) are not known, it is difficult to 
make a meaningful comparison, especially regarding the 95th percentile since it reflects the size 
of the larger flaws (i.e., those flaws which are the most sensitive to the inspection parameters). 
That is why, for a sensitivity case, it has been decided to investigate the effects that a UT 
inspection of the type used in this analysis would have on the flaws reported by Khaleel et al. 
(1999). The calculation, detailed in Attachment I, is similar to that shown in Section 6.2.1.2.2, 
CAL-EBS-MD-000030 REV 00C 67 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
the only difference being the use of a lognormal distribution in lieu of an exponential. The new 
mean, 5th, and 95th percentiles are now: 1.8 mm, 1.1 mm, and 2.7 mm. 
Notice that the 95th percentile of the flaw size is nearly identical to that shown in Table 13, which 
confirms the filtering effect of the UT inspection on the larger flaws. This also shows that the 
cap put by the UT inspection on the maximum flaw size is not dependent on the shape of the 
distribution used to characterize the flaw size but is rather governed by the UT PND curve (a 
different UT PND curve would provide a different cap). 
The major difference between the flaw sizes reported by Khaleel et al. (1999) and the results 
shown in Table 13 is the size of the small flaws. The 5th percentile flaw size for the former is 
1.1 mm, while it is 0.099 mm for the latter (see Table 13). The difference is due to the shapes of 
the lognormal and exponential distributions. 
The flaw density is the other possible element of comparison between the literature and the 
results of this analysis. Khaleel et al. (1999, Table 6) report 0.0448 flaw per inch for a 
noninspected 1-inch thick weld. This corresponds to 1.8 flaws per meter of weld. This can be 
directly compared to the mean flaw density parameter of a 25-mm thick weld before UT 
inspection, calculated in Section 6.2.1.1.2, which is 0.097 flaw per meter of weld. The flaw 
density reported by Khaleel et al. (1999) is therefore about 18 times larger than the flaw density 
calculated in this analysis. This difference can be explained in part by the fact that the software 
code (RR-PRODIGAL), which was used to perform the weld flaw simulations of Khaleel et al. 
(1999), makes conservative estimates. This is mentioned by Simonen and Chapman (1999, 
p. 105) which report that the flaw frequencies predicted by RR-PRODIGAL were consistent with 
measured flaws found in actual piping and vessel welds, or were conservative by a factor as large 
as ten. Another reason to explain the large difference in flaw frequencies is that the welds 
compared are different: those simulated by Khaleel et al. (1999) were meant to model nuclear 
piping welds made of stainless steel, while the specimen rings studied in this analysis are made 
of Alloy 22 and meant for sealing waste packages. Thus, keeping in mind the conservatism of 
the RR-PRODIGAL simulation code and the inherent differences of the welds examined, the 
difference in the flaw frequencies is explicable and within reasonable limits. 
6.2.2 Base Metal Flaws 
In contrast to the wealth of information on the occurrence of weld flaws, information on the 
occurrence of flaws in base metal material is sparse. The occurrence frequency of base metal 
flaws has been estimated using results from various nondestructive examination techniques, 
including detailed UT examination of an unused reactor pressure vessel, validated by 
metallography (Schuster et al. 2000). While the primary emphasis of the study was on the 
density and depth distribution of weld flaws, flaw densities in the base metal regions outside of 
the heat-affected zone were also examined. 
UT inspection showed that the density ratio of weld flaws to base metal flaws was 8 to 1 
(Schuster et al. 2000, p. 2.3). The validation efforts (metallography) were unfortunately very 
limited, which led Schuster et al. (2000, pp. 4.2 and 4.3) to propose a list of potential 
explanations for the unvalidated base metal UT indications. Among those, only laminations and 
repairs to base metal may apply to the waste package (the other listed flaws were related to the 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
clad-to-base metal interface of the reactor vessel and are consequently not of interest here). 
Laminations are not a concern since they are in a plane parallel to the surface of the component 
and are therefore not expected to significantly jeopardize its integrity. This leaves repairs to base 
metal, which appeared to be associated with the larger flaws (Schuster et al. 2000, p. 5.2). It 
turned out later that these flaws were only clusters of small indications with little or no potential 
significance to structural integrity (Schuster et al. 2000, p. xiii). Nevertheless, based on previous 
information, repairs to base metal emerge as the dominant mechanism by which flaws with a 
significant through-wall extent could be introduced in the base metal. It is important to note that 
such flaws would result from an improper implementation of the procedure related to base metal 
repairs. 
Several assumptions are required to evaluate the probability of the number of base metal flaws 
expected in the Alloy 22 barrier of the waste package. Because these assumptions are 
conservative, only a point estimate is calculated. 
The frequency of occurrence for introducing base metal flaws is based on Assumption 5.2.1. 
This frequency of occurrence is considered to be initiated by an error of the welder performing a 
base metal repair (a base metal repair is conservatively assumed to be performed for each waste 
package). The failure of the welder to use the written procedure governing the repairs to base 
metal can be represented by the HEP for failing to follow a written procedure under normal 
operating conditions, and is estimated at 0.01 (median) with an error factor of 3 (Item 2 of 
Table 4). The failure of the checker to detect the errors made by the welder is estimated at 0.1 
(median) with an error factor of 5, based on Item 8 of Table 4. 
As mentioned in Section 4.1.2, the HEPs follow lognormal distributions. The relationship 
between the error factor EF and the shape parameter sk of a lognormal distribution (see 
Equation 33) is given by (Modarres 1993, p. 266): 
s
k 
ln(EF )
= (Eq. 35) 
645.1 
Therefore, using this result with Equation 34 makes it possible to express the mean m of a 
lognormal distribution as a function of its median m50 and its error factor EF as follows: 
2
.
.
1

..
.
ln(EF ) 
645.1
..
. 
(Eq. 36) 
..
.
..
.
m= m50  exp 
2 
The product of independent lognormal distributions yields a lognormal distribution (Swain and 
Guttmann 1983, pp. A-2 and A-4). The resulting median mr and error factor EFr can be 
calculated using the following equations (NRC 1983, pp. 12 to 33): 
m=. m (Eq. 37) 
ri 
i 
EF
r 
= exp
.
.
.
.
. 
i 
2
( ln(EF ) 
i 
) 
(Eq. 38) 
.
.
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
where mi and EFi are the individual medians and the error factors of the lognormal distributions. 
Based on Equations 36 to 38, applied to the means and error factors of the HEPs given 
previously, the mean, Fbm, for the frequency of occurrence of base metal flaws due to repairs can 
be calculated as Fbm = 2.0  10-3 per waste package. Note that this concerns an area of 100 cm2, 
or equivalently, a volume Vrbm of repaired base metal equal to 2  10-4 m3, since the thickness of 
the Alloy 22 barrier is 20 mm (see Table 2). 
The ratio of weld flaws to base metal flaws resulting from repairs in the Alloy 22 barrier of the 
waste package is 8 to 1, based on Assumption 5.2.2. It should be noted that this number is based 
on results of Schuster et al. (2000), which compared the densities of flaws in the welds and base 
metal of an unused reactor pressure vessel. Because this reactor vessel had been fabricated under 
standard quality procedures used for the manufacturing of nuclear equipment, it had been 
subjected to regular nondestructive examination tests for detecting and removing unacceptable 
flaws. As a consequence, the flaw densities found by Schuster et al. (2000) pertained to 
inspected material. Thus, the weld flaw density to consider here is the weld density after UT 
inspection. 
Based on Section 6.2.1.2.3, the mean weld flaw density of an inspected 25-mm thick weld is 
4.1  10-2 flaws/m of weld. In order to evaluate a flaw density applicable to base metal flaws, 
this number needs to be expressed in terms of a volumetric density. Based on the calculations 
performed in Attachment I and after applying the 1/8 correction factor mentioned previously, the 
flaw density pertaining to base metal, .bm, was obtained. .bm is found to be approximately 
21 base metal flaws per cubic meter. 
The previous information is used to obtain the CDF Pnbm on the numbers n of base metal flaws in 
the Alloy 22 barrier of a waste package. It is the sum of the probability that the base metal repair 
is correctly performed, evaluated at 1  Fbm (yielding a waste package with zero base metal 
flaws), and the probability that n flaws are present, given that the base metal repair is defective. 
As in Section 6.2.1.2.3, a Poisson distribution is used to calculate the probability of the number 
of base metal flaws, given that the base metal repair is faulty. With a volume Vrbm = 2  10-4 mof base metal, the expression for the CDF is: 
i 
-.bm Vrbm bm
P
nbm (n,. ,V ) =(1 - F )+ F  e  . 
n (. Vrbm ) (Eq. 39) 
bmrbm bm bm 
i=0 i! 
The expected number of base metal flaws is Fbm  .bm  Vrbm = 8.6  10-6 per waste package. 
Because the parameter of the Poisson distribution is very small (.bm  Vrbm is around 0.004), the 
probability that a randomly selected waste package has at least one base metal flaw is also 
approximated by Fbm  .bm  Vrbm = 8.6  10-6. 
After investigating the probability of the number of previous flaws, the size distribution of these 
potential flaws is examined. It is likely that the flaws present in improperly repaired base metal 
will not be detected through the UT inspections performed during the faulty repair. Also, a base 
metal repair consists of a patch of weld material aimed at replacing the initial defective base 
metal. Therefore, the size distribution of the flaws present in improperly repaired base metal can 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
be represented by the flaw size distribution developed in Section 6.2.1.1.1 (i.e., the weld flaw 
size distribution in noninspected weld). Note that the thickness t to consider is 20 mm, which is 
the thickness of the Alloy 22 barrier. The flaw sizes will be the same as those found in the seam 
welds of the waste package before UT inspection (see Table 13 for main flaw size 
characteristics). 
6.2.3 Improper Weld Material or Base Metal 
While the use of improper weld materials was responsible for early failures in several of the 
container types examined in Section 6.1, there is little information to support the development of 
its probability for a waste package. As for the use of improper base metal material, no instance 
was found in the literature search reported in Section 6.1. 
The only well documented occurrence of the extent to which a weld population was affected by 
improper weld material is described in Records Investigation Report Related to Off-Chemistry 
Welds in Material Surveillance Specimens and Response to IE Bulletins 78-12 and 78-12A  
Supplement (Babcock and Wilcox 1979). This inspection of all vendors welding records was 
prompted by the discovery that the weld chemistry of a portion of the Crystal River 3 
surveillance-block weld did not meet the specification requirements. Based on this information, 
Assumption 5.3.1 was developed and the frequency for use of improper welding material was 
evaluated as a lognormal distribution whose 5th and 95th percentiles are 1.5  10-5 and 8.2  10-5, 
respectively. 
Using the fact that the 5th percentile (respectively the 95th percentile) can be obtained by 
multiplying (respectively dividing) the median m50 by the error factor EF, the following formulas 
are written: 
m50 =th5 percentile th95 percentile (Eq. 40) 
EF =
percentile 
percentile 
th 
th 
5 
95 (Eq. 41) 
This yields a median of 3.5  10-5 and an error factor of 2.3. 
Records Investigation Report Related to Off-Chemistry Welds in Material Surveillance 
Specimens and Response to IE Bulletins 78-12 and 78-12A  Supplement (Babcock and Wilcox 
1979) concluded that the evolution of shop practices as of 1979 had virtually eliminated the 
possibility that improper weld material would be used in the fabrication of a reactor vessel. New 
instrumentation, such as portable X-ray spectroscopy equipment, makes it possible to perform 
quick field measurements of material compositions (ASM International 1990b, pp. 1030 to 
1032). It is assumed (Assumption 5.3.2) that such a verification will be performed. However, 
there is still the possibility that the technician in charge of this work fails to perform the 
operation correctly. This HEP can be approximated by the (lognormal) probability of improperly 
checking a digital display, which has a median of 0.001 and an error factor of 3 (Item 4 of 
Table 4). 
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The probability that an improper welding material is inadvertently used in the manufacturing of 
the Alloy 22 barrier of the waste package, and that this mistake is not detected, is the 
combination of the previous probability distributions. Using Equations 37 and 38, the resulting 
median and error factor are 3.5  10-8 per waste package and 4.0, respectively. The mean is 
5.0  10-8 per waste package based on Equation 36. 
Based on Assumption 5.3.3, the frequency for use of improper base metal in the fabrication of 
the outer barrier of the waste package is the same as the frequency of use of improper weld 
material. In other words, it follows a lognormal distribution whose 5th and 95th percentiles are 
1.5  10-5 and 8.2  10-5, respectively. 
In addition, only certified material will be used for the fabrication of the waste package (Plinski 
2001, Section 6.2.3). Therefore, it is expected that a check of base metal composition similar to 
that done for the weld will be performed. The failure to perform this operation correctly is 
quantified with the same HEP as that considered for the weld. 
Consequently, the probability that an improper base metal is inadvertently used in the 
manufacturing of the Alloy 22 barrier of the waste package, and that this mistake is not detected, 
is the same as the probability of using an improper welding material. It follows a lognormal 
distribution with a median of 3.5  10-8 per waste package and an error factor of 4.0. The mean 
is 5.0  10-8 per waste package. 
6.2.4 Improper Heat Treatment 
The procedures and equipment that will be employed to perform the heat treatment during the 
fabrication of the waste package components have not yet been decided. Therefore, in order to 
evaluate the probability that the waste package components will be subjected to an improper heat 
treatment, without being detected prior to emplacement in the repository, it is necessary to make 
a set of assumptions on the general elements of the heat treatment process. These are 
Assumptions 5.4.1 and 5.4.2. 
Based on Assumptions 5.4.1 and 5.4.2, events involved in the improper heat treatment of the 
waste package components are developed. These events are then combined into event sequences 
identifying the scenarios that could lead to waste package components improper heat treatment. 
This is done by developing an event tree. This event tree is then used to quantify the 
corresponding probability. 
The elementary probabilities of the events involved in the improper heat treatment event tree are 
as follows: 
 The operator failure to choose the correct heat treatment/quenching program is 
approximated by the selection of a wrong control on a panel from an array of similar-
appearing controls identified by labels only (Item 6 of Table 4). The median of the 
corresponding HEP is 0.003 and the error factor is 3. Notice that this HEP is an error of 
commission, not an error of decision (i.e., the operator mistakenly pushes a wrong 
button that launches an improper heat treatment program). Since similar types of waste 
packages will most likely receive the same heat treatment, there will be a very limited 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
number of possible heat treatment programs to choose from. It is therefore not credible 
that the operator gets confused on the program to select for the type of waste package to 
be heat treated. In other words, the most plausible cause for mistake is an error of 
commission. 
 The technician failure to properly install the waste package thermocouples is considered 
to be caused by the failure to use a written test or calibration procedure. The 
corresponding HEP is 0.05 (median) with an error factor of 5 (Item 3 of Table 4). 
Notice that installation of the thermocouples at correct locations is necessary to obtain 
meaningful temperature measurements. The most probable reason for failing to perform 
this task correctly is to overlook the corresponding written procedure. The HEP related 
to the failure to use a written test or calibration procedure was chosen in lieu of the HEP 
related to the failure to use written operations procedure under normal operating 
conditions (Item 2 of Table 4). This is because the former is more appropriate than the 
latter to account for the repetitive aspect of the task, which might lead the technician in 
charge of the thermocouple installation to ignore the procedure. Note that the 
corresponding HEP is greater (0.05 versus 0.01 for Item 2 in Table 4). 
 The failure of the checker to detect an improper installation of the waste package 
thermocouples by the technician is approximated by an HEP of 0.1 (median) with an 
error factor of 5. This is based on Item 8 of Table 4, which evaluates the probability of 
failing to detect error made by others during routine tasks. 
 During the QA check of the log generated by the computerized heat treatment system, 
the failure of the checker to detect that the operator chose a wrong heat treatment 
program is approximated by an HEP of 0.1 (median) with an error factor of 5, based on 
Item 8 of Table 4. 
 The probability that a process malfunction will occur during the heat treatment of a 
waste package is approximated by a lognormal distribution with a median of 0.005 and 
an error factor of 2. This is based on Assumption 5.4.3. 
 The probability that the operator fails to respond to an alarm (annunciator) signaling a 
process malfunction during the heat treatment of a waste package is approximated by an 
HEP of 0.0001 (median) and an error factor of 10. This is based on Item 9 of Table 4. 
Note that the main reason for such an error would be inattention. 
 During the QA check of the log generated by the computerized heat treatment system, 
the failure of the checker to detect that the operator did not respond to an alarm 
generated by a process malfunction is approximated by an HEP of 0.02 (median) and an 
error factor of 5. The fact that an alarm was triggered during the heat treatment of the 
waste package will be written in the report generated by the computerized heat treatment 
system. It is expected that this alarm will catch the attention of the checker and prompt 
him/her to be more attentive of the operator response than he/she would be in the case of 
unannunciated anomalies such as improper thermocouple calibration, for instance. The 
corresponding HEP is based on Item 8 of Table 4, but because of the alarming factors, 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
the lower bound of the HEP is chosen instead of the point estimate value (which is 0.1). 
As for the error factor, it is based on Item 2 of Table 5. 
The previous information is used to develop an event tree for the improper heat treatment during 
the fabrication of the waste package components. Although there are three components that are 
to be heat treated separately, namely the waste package outer lid, middle lid and outer barrier 
(including the outer barrier bottom lid), only two of these components are considered in this 
analysis (the waste package outer lid and the outer barrier). The waste package middle lid is not 
considered because it is not heat treated subsequent to the performance of its closure weld. Two 
separate event trees representing the heat treatment processes of these components have been 
developed. Although there is no significant difference between the two processes and the event 
trees are identical, they have different names to maintain independence between the two heat 
treatment processes. 
The SAPHIRE software code is used to perform this task, and the resulting event trees are shown 
on Figures 9 and 10. The electronic files of the SAPHIRE project are contained in Attachment 
II. Table 14 shows the events, along with their mean probability. The means are calculated 
based on the median and the error factor, using Equation 36. 
Table 14. Description of Events for Improper Heat Treatment of the Waste Package 
Event Name Event Description (Failure-Oriented) Mean Probability Correlation Class 
INIT Placeholder initiating event 1 a N/A 
HT_PRCDR_S 
HT_PRCDR_L 
Operator fails to select correct heat 
treatment/quenching program 3.75  10-3 HTSL 
INSTLN_S 
INSTLN_L 
Technician fails to properly install the waste 
package thermocouples 8.07  10-2 INST 
HT_CCR_S 
HT_CCR_L 
Checker fails to detect that waste package 
thermocouples were impropely installed 1.61  10-1 HTCK 
HT_PCR_S 
HT_PCR_L 
Checker fails to detect that operator chose 
incorrect heat treatment/quenching program 1.61  10-1 HTCK 
HT_PRCSS_S 
HT_PRCSS_L 
Process malfunction occurs during the heat 
treatment of the waste package 5.46  10-3 HTPC 
HT_ANN_S 
HT_ANN_L 
Operator fails to respond to alarm (annunciator) 
triggered by process malfunction 2.66  10-4 HTAN 
HT_ACR_S 
HT_ACR_L 
Checker fails to detect that operator did not 
respond to alarm triggered by process malfunction 3.23  10-2 HTAC 
NOTE: aThis is a placeholder with a value of unity. It has no uncertainty. 
It should be noted that the probabilities of nominally identical events have been correlated 
together. By nominally identical events, it is meant those events that are distinct but for which 
the states of knowledge that determine their distributions are identical. When performing the 
quantification of the event tree, and especially an uncertainty analysis, these events should be 
treated as completely dependent events (Apostolakis and Kaplan 1981, pp. 136 to 139). Table 14 
indicates the correlation classes that were assigned in SAPHIRE to each event. Nominally 
dependent events share the same correlation class. 
CAL-EBS-MD-000030 REV 00C 74 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The sequences that lead to an improper heat treatment end state on Figures 9 and 10 are labeled 
IPHT. 
A Monte Carlo sampling was performed with 90,000 realizations on the resultant events. The 
principle of the Monte Carlo sampling method is explained in Modarres (1993, pp. 243 and 244) 
and is not repeated here. Monte Carlo sampling is performed to propagate the variability of the 
events to obtain the characteristics of the resulting distribution. The seed value for the sampling 
(which is randomly chosen) was 59,027. The sample size was chosen large enough to get a good 
approximation on the main characteristics of the distribution. 
The resulting mean, median, 5th percentile, and 95th percentile are 2.7  10-5, 3.0  10-6, 
1.2  10-7, and 1.1  10-4 per waste package, respectively. 
It should be noted that the probability of improper heat treatment estimated here is independently 
corroborated by the pressure vessel failure statistics reported in Section 6.1.1. Those statistics 
indicated that one vessel in 20,000 experienced failure due to improper heat treatment. This 
yields a probability of 5  10-5 per vessel for this type of defect. 
In the discussion that follows, which will be used in Section 6.4.8, it is shown that the probability 
that a waste package is improperly heat treated is independent of the fact that another waste 
package has already been improperly heat treated. In other words, the fact that a waste package 
receives an improper heat treatment does not increase the probability that the subsequent waste 
package to be processed also receives an improper heat treatment. 
As shown on Figures 9 and 10, an improper heat treatment of a waste package may result from 
two types of failure scenarios. 
The first type of scenario is the occurrence of a significant process malfunction. This will in turn 
trigger an alarm. Improper heat treatment will ensue if both the operator and the checker fail to 
respond to the alarm. There is no reason other than coincidence for the subsequent waste 
package to receive an improper heat treatment, unless the operator and the checker consider that 
the alarm triggered by the process malfunction is a false indication. This situation can be 
discarded from further consideration because it is incompatible with the highly controlled 
operating conditions under which heat treatment of the waste package will be performed. 
Indeed, the operator and the checker would have to justify why they considered the alarm to be a 
false indication, and subsequent verifications would prove them wrong. The fact that the 
corresponding waste packages were subjected to an improper heat treatment would thus be 
detected. 
The second type of scenario is the failure of the operator to select the correct heat treatment 
program. As previously mentioned at the beginning of Section 6.2.4, this corresponds to an error 
of commission, rather than an error of selection (i.e., the operator knows which type of waste 
package is to be heat treated but mistakenly pushes the wrong button that launches an incorrect 
heat treatment program). By nature, this type of mistake is unlikely to be made again, except 
through coincidence, when the program for the subsequent waste package to be heat treated is 
launched. 
CAL-EBS-MD-000030 REV 00C 75 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Therefore, based on the previous information, occurrences of waste package improper heat 
treatment can be considered independent from each other. 
6.2.5 Improper Laser Peening 
No final decision has been reached on the stress mitigation technique to be used for the outer lid 
weld of the waste package. The laser peening method is considered in the following because it is 
deemed representative of the advanced technical process that will be employed. 
The procedures and equipment that will be employed if the laser peening method is chosen for 
stress mitigation of the outer lid weld of the waste package have not yet been decided. 
Therefore, in order to evaluate the probability that the outer lid weld of a given waste package 
will be subjected to an improper laser peening, without being detected prior to emplacement in 
the repository, it is necessary to make a set of assumptions on the general elements of the laser 
peening process. These are Assumptions 5.5.1 and 5.5.2. 
CAL-EBS-MD-000030 REV 00C 76 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
ilure 
iily ?technician's 
ly 
ling 
Plii# 
1 OK 
2 OK 
3 OK 
4 
5 OK 
6 OK 
7 
8 OK 
9 OK 
11 OKYES 
NO 
l) /
HT_ACR_S 
Checker detects 
operator's fato respond to 
annuncator ? 
HT_ANN_S 
Operator responds 
to annuncator ? 
HT_PRCSS_S 
Heat treatment 
process works 
properHT_PCR_S 
Checker 
recovers 
operator's 
mistake ? 
HT_CCR_S 
Checker 
recovers 
mistake ? 
INSTLN_S 
WP thermocouples 
properinstaled ? 
HT_PRCDR_S 
Operator chooses 
correct heat 
treatment/quenchprogram ? 
INIT 
aceholder 
initatng 
event 
END-STATEIPHTIPHT 
10 IPHT 
12 IPHT 
HEAT_TREATMENT_SHELL - Improper heat treatment of the waste package (shel2003/0130 Page 6 
Figure 9. Event Tree for Improper Heat Treatment of the Waste Package Shell 
CAL-EBS-MD-000030 REV 00C 77 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
annunciilmiimily 
/
INIT 
Plinii# 
1 OK 
2 OK 
3 OK 
4 
5 OK 
6 OK 
7 
8 OK 
9 OK 
10 
11 OK 
12YES 
NOid) /
HT_ACR_L 
Checker detects 
operator's failure 
to respond to 
ator ? 
HT_ANN_L 
Operator responds 
to annuncator ? 
HT_PRCSS_L 
Heat treatment 
process works 
propery ? 
HT_PCR_L 
Checker 
recovers 
operator's 
stake ? 
HT_CCR_L 
Checker 
recovers 
technican's 
stake ? 
INSTLN_L 
WP thermocouples 
properinstalled ? 
HT_PRCDR_L 
Operator chooses 
correct heat 
treatmentquenching 
program ? 
aceholder 
tiatng 
event 
END-STATE 
IPHT 
IPHT 
IPHT 
IPHT 
HEAT_TREATMENT_LID - Improper heat treatment of the waste package (l2003/0130 Page 4 
Figure 10. Event Tree for Improper Heat Treatment of the Waste Package Top Lid 
CAL-EBS-MD-000030 REV 00C 78 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Based on Assumptions 5.5.1 and 5.5.2, events involved in the improper laser peening of the 
waste package outer lid weld are developed. These events are then combined into event 
sequences identifying the scenarios that could lead to improper laser peening. This is done by 
developing an event tree. This event tree is then used to quantify the corresponding probability. 
The elementary probabilities of the events involved in the improper laser peening event tree are 
as follows: 
 The probability that a process malfunction will occur during the laser peening of the 
outer lid weld is approximated by a lognormal distribution with a median of 0.005 and 
an error factor of 2. This is based on Assumption 5.5.3. 
 The probability that the operator fails to respond to an alarm (annunciator) signaling a 
process malfunction during the laser peening of the outer lid weld of a waste package is 
approximated by an HEP of 0.0001 (median) and an error factor of 10. This is based on 
Item 9 of Table 4. 
 During the QA check of the log generated by the computerized laser peening system, the 
failure of the checker to detect that the operator did not respond to an alarm generated by 
a process malfunction is approximated by an HEP of 0.02 (median) and an error factor 
of 5. The fact that an alarm was triggered during the laser peening process will be 
written in the report generated by the computerized laser peening system. It is expected 
that this alarm will catch the attention of the checker and prompt him/her to be more 
attentive of the operator response than he/she would be in the case of unannunciated 
anomalies. The corresponding HEP is based on Item 8 of Table 4, but because of the 
alarming factors, the lower bound of the HEP is chosen instead of the point estimate 
value (which is 0.1). As for the error factor, it is based on Item 2 of Table 5. 
The previous information is used to develop an event tree for the improper laser peening of the 
outer lid weld of the waste package. The software code SAPHIRE is used to perform this task, 
and the resulting event tree is shown on Figure 11. The electronic files of the SAPHIRE project 
are contained in Attachment II. Table 15 shows the events along with their mean probability. 
Note that the means are calculated based on the median and the error factor using Equation 36. 
Also, notice that none of the events are correlated together because each of them represents a 
different type of failures (see Section 6.2.4 for more information on correlation of events). 
Nevertheless, correlation classes are assigned to the events shown in Table 15; this is done in 
prevision of the quantification that will be performed in Section 6.4.8. Comparing the 
correlation classes to those given in Table 14 shows which events are determined based on the 
same state of knowledge. 
The sequence of events that leads to an improper laser peening end state on Figure 11 is labeled 
IPLP. 
There is no need to perform a Monte Carlo sampling to obtain the characteristics of the 
distribution pertaining to improper laser peening. This is because the sequence of events is the 
product of lognormal distributions and therefore is also a lognormal distribution. Application of 
Equations 37 and 38 yields a median of 1.0  10-8 per waste package and an error factor of 18. 
CAL-EBS-MD-000030 REV 00C 79 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The mean is calculated with Equation 36 and is 4.7  10-8 per waste package. Based on 
Equations 40 and 41, the 5th and the 95th percentiles are obtained by calculating the following 
equations: 
5
th 
percentile =m50 (Eq. 42) 
EF 
95
th percentile = m50  EF (Eq. 43) 
Equations 42 and 43 yield 5.6  10-10 and 1.8  10-7 for the 5th and 95th percentiles, respectively. 
In the discussion that follows, which will be used in Section 6.4.8, it is shown that the probability 
of having a waste package subjected to improper laser peening is independent of the fact that 
another waste package has already been subjected to improper laser peening. In other words, the 
fact that a waste package is affected by an improper laser peening does not increase the 
probability that the subsequent waste package to be processed is also subjected to improper laser 
peening. 
Table 15. Description of Events for Improper Laser Peening of the Waste Package Outer Lid Weld 
Event Name Event Description (Failure-Oriented) Mean 
Probability 
Correlation 
Class 
INIT Placeholder initiating event 1a N/A 
LS_PRCSS Process malfunction occurs during the laser peening 5.46  10-3 HTPC 
LS_ANN Operator fails to respond to alarm (annunciator) triggered 
by process malfunction 2.66  10-4 HTAN 
LS_ACR Checker fails to detect that operator did not respond to 
alarm triggered by process malfunction 3.23  10-2 HTAC 
a
NOTE: This is a placeholder with a value of unity. It has no uncertainty. 
CAL-EBS-MD-000030 REV 00C 80 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
ililPllinii# 
1 
2 
3 
4 
NO 
lill2002/
LS_ACR 
Checker detects 
operator's faure 
to respond to 
annunciator ? 
LS_ANN 
Operator responds 
to annuncator ? 
LS_PRCSS 
Laser peening 
process works 
propery ? 
INIT 
acehoder 
tiatng 
event 
END-STATEOKOKOKIPLP 
YES 
LASER-PEENING -Improperaser peenng of the cosure weds 11/30 Page 5 
Figure 11. Event Tree for Improper Laser Peening of the Outer Lid Weld of the Waste Package 
The rationale for this is similar to that given in Section 6.2.4 for improper heat treatment. 
Improper laser peening of a waste package will be initiated by a significant process malfunction. 
This will in turn trigger an alarm. Improper laser peening will ensue if both the operator and the 
checker fail to respond to the alarm. There is no reason other than coincidence for the 
subsequent waste package to receive an improper laser peening, unless the operator and the 
checker consider that the alarm triggered by the process malfunction is a false indication. This 
situation can be discarded from further consideration because it is incompatible with the highly 
controlled operating conditions under which laser peening of the waste package closure weld 
will be performed. Indeed, the operator and the checker would have to justify why they 
considered the alarm to be a false indication, and subsequent verifications would prove them 
wrong. The fact that the corresponding waste packages were subjected to an improper laser 
peening would thus be detected. 
Therefore, based on the previous information, occurrences of waste package improper laser 
peening events can be considered independent from each other. 
As a side remark, it is worth noting that the probability of having an undetected improper heat 
treatment (analyzed in Section 6.2.4) is much greater than the probability of having an 
undetected improper laser peening. This difference is due to the fact that, because there are 
different types of waste packages, several heat treatment programs (each applying only to a 
CAL-EBS-MD-000030 REV 00C 81 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
certain type of waste packages) were assumed (Assumption 5.4.1). This results in the possibility 
that the operator might perform an error of commission in selecting the heat treatment program 
corresponding to a given type of waste package (an error of decision was judged implausible, see 
Section 6.2.4). In comparison, the laser peening process applies to the outer lid welds only, and 
these welds are essentially the same for all types of waste packages. More precisely, as far as the 
outer lid welds are concerned, only their diameters differ according to the type of waste package 
considered, and this difference will readily be accounted for in order to enable the laser peening 
process to even begin. In other words, it is not credible that the laser peening apparatus can be 
set to an incorrect position, corresponding to the diameter of a different type of waste package, 
without that being detected. Thus, there is no opportunity for having an improper selection of a 
laser peening program, as there is for the heat treatment process. This dissimilarity explains the 
difference in the resulting probabilities. As for the other principal cause for having an 
undetected improper heat treatment or laser peening, namely an undetected significant process 
malfunction, its probability of occurrence was evaluated in the same way for both heat treatment 
and laser peening, using a deliberately undetailed but conservative approach. Consequently, the 
undetected significant process malfunction does not contribute to the difference in probabilities 
between improper heat treatment and improper laser peening. 
6.2.6 Contamination 
In order to evaluate the probability that a waste package has its surface contaminated by some 
corrosion-enhancing material, and that this contamination remains undetected, it is necessary to 
know the manipulations the waste package is going to be subjected to from its fabrication to its 
emplacement in the repository. Only preliminary information is available at this time. 
Therefore, it is necessary to make a set of assumptions on the scenario that could lead to the 
contamination of the waste package. These are given in Section 5.6. 
Two types of contamination are possible on the surface of the waste package, as explained 
below. 
The first type is a contamination that leaves visible marks on the surface of the waste package 
(such as dirt, oil, etc.). Should such contamination occur before reception at the repository 
surface facility, it is expected that during the initial waste package inspection the contamination 
will be detected (Assumption 5.6.1). Should contamination occur in the surface facilities, it is 
expected to happen prior to the final inspection of the waste package (Assumption 5.6.2). 
The second type is a contamination that does not leave visible marks on the surface of the waste 
package. The most likely source for such a contamination is an improper cleaning of the waste 
package. Assumption 5.6.3 summarizes the conditions required for this contamination scenario. 
The elementary probabilities of the events involved in the waste package contamination by 
improper cleaning are as follows: 
 The probability that the maintenance policies governing the stockage of the cleaning 
agents utilized for the waste package (use of a separate stockage area) are not observed 
has a median of 0.01 and an error factor of 5. This is based on Item 1 of Table 4. 
CAL-EBS-MD-000030 REV 00C 82 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
 Should all the cleaning agents be stocked in the same area, the probability that the 
technician in charge of the cleaning selects an improper cleaning agent is 0.003 (median) 
with an error factor of 3. This is based on Item 6 of Table 4. 
 During the QA check of the cleaning process, the failure of the checker to detect that the 
technician in charge of the waste package cleaning chose an incorrect cleaning agent is 
approximated by an HEP of 0.1 (median) with an error factor of 5. This is based on 
Item 8 of Table 4, which gives a probability value for a comparable event, namely the 
failure of an operator to select a control in a set of similar-appearing controls identified 
by labels only. 
Notice that because this type of contamination is not visible to the naked eye, it cannot be spotted 
during the inspection performed in the surface facilities of the repository. 
The elementary probabilities of the events involved in the waste package contamination inside 
the surface facilities of the repository, leaving visible traces on the metal, are as follows: 
 The probability of occurrence for the contamination has a median of 0.01 and an error 
factor of 5. This is based on the fact that for a contamination of the waste package to 
occur, the policy governing the manipulation of the waste package has to be improperly 
carried out. The probability value is based on Item 1 of Table 4. 
 The probability that the operator fails to detect visible traces of contamination during the 
final inspection of the waste package, performed remotely by camera, is estimated at 
0.002 (median) with an error factor of 3. This is based on Item 5 of Table 4, which 
gives a probability value for a comparable event, namely the failure of an operator to 
check-read a display with difficult-to-see limit marks. 
The previous information is used to develop an event tree for the contamination of the waste 
package. The software code SAPHIRE is used to perform this task, and the resulting event tree 
is shown on Figure 12. The electronic files of the SAPHIRE project are contained in Attachment 
II. Table 16 shows the events, along with their mean probability. 
The probability of contaminating the waste package during at least one of its eight cleanings 
identified in Assumption 5.6.3 is quantified using a simple fault tree, called ICLNG (given in 
Attachment II). To quantify this probability, the fault tree combines the basic events required to 
have an improper cleaning, using logic gates (OR and AND). For an improper cleaning to occur, 
three basic events are required (therefore, they are connected with an AND gate). The first is 
common to all of the eight improper cleanings. It corresponds to the failure to observe the 
maintenance policies governing the stockage of the cleaning agents. The two other basic events 
represent the failure of the cleaning itself, which requires both the failure of the operator to select 
the correct cleaning agent, and the failure of the subsequent QA check of the process. Because 
the eight cleanings are considered to be independent from each other, they are connected through 
an OR gate in the fault tree. The mean probability is calculated using a Monte Carlo sampling 
with 90,000 realizations. The seed value (randomly chosen) is 22,877. Before performing the 
calculation, nominally identical basic events are correlated together, since their distribution is 
determined with the same state of knowledge (see Section 6.2.4 for more information on 
CAL-EBS-MD-000030 REV 00C 83 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
correlation of nominally identical events). This applies to the eight basic events representing the 
improper selection of the cleaning agent on the one hand and the eight basic events representing 
the failure of the QA check on the other hand. The mean probability of fault tree ICLNG is 
shown on Table 16. It is given for information only because the real inputs that serve for the 
quantification of the event tree are the basic events on which the fault tree is developed. 
The sequences of events that lead to waste package contamination end states on Figure 12 are 
labeled CONT. 
Table 16. Description of Events for Contamination of the Waste Package 
Event Name Event Description (Failure-Oriented) Mean Probability 
INIT Placeholder initiating event 1a 
ICLNG Contamination of the waste package occurs during its cleaning 7.2  10-5 b 
CONT Visible contamination in the surface facilities of the repository 1.61  10-2 
CAM_DET Operator fails to detect visible traces of waste package contamination 
during final inspection performed via remote camera 2.50  10-3 
NOTES: a This is a placeholder with a value of unity. It has no uncertainty. 
b 
Probability value is based on quantification of associated fault tree (given in Attachment II). Only two 
significant figures are shown. 
A Monte Carlo sampling was performed with 90,000 realizations on the resultant events. Monte 
Carlo sampling is performed to propagate the variability of the events to obtain the 
characteristics of the resulting distribution. The seed value for the sampling (randomly chosen) 
is 59,027. The sample size is chosen large enough to get a good approximation on the main 
characteristics of the distribution. 
CAL-EBS-MD-000030 REV 00C 84 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
iisiblely 
clPliing 
# 
1 
2 
34YES 
NOiiCAM_DET 
Detection of 
unconformty 
on camera ? 
CONT 
No vcontamination 
of WP ? 
ICLNG 
WP propereaned ? 
INIT 
aceholder 
nitiatevent 
END-STATE 
OK 
OK 
CONT 
CONT 
CONTAMIN ATION - Contamnaton of a waste package 2002/11/30 Page 1 
Figure 12. Event Tree for Contamination of the Waste Package 
Notice that except for the basic events of the fault tree ICLNG mentioned previously, none of the 
other events need to be correlated together, because each of them represents a different type of 
failure. 
The resulting mean, median, 5th percentile, and 95th percentile are 1.1  10-4, 5.9  10-5, 
1.1  10-5, and 3.6  10-4 per waste package, respectively. 
6.2.7 Improper Handling 
This section estimates the probability that a waste package is subjected to handling damage, 
without being detected, prior to its emplacement in the repository. Handling damage is defined 
as any visible gouging or denting of the waste package surface that may jeopardize the 
performance of the Alloy 22 barrier. 
The evaluation of the probability of waste package damage by mishandling requires a set of 
assumptions in order to identify the main features that could lead to such an event. These are 
Assumptions 5.7.1 to 5.7.3. 
The elementary probabilities of the events involved in waste package mishandling are as follows: 
 The probability of damaging a waste package by mishandling is approximated by a 
lognormal distribution with a median of 4.8  10-5 per waste package handling and an 
CAL-EBS-MD-000030 REV 00C 85 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
error factor of 10. Also, there are four potential occasions during which the waste 
package may be mishandled. This is based on Assumption 5.7.4. 
 The probability that the operator fails to detect visible traces of damage during the final 
inspection of the waste package, performed remotely by camera, is estimated at 0.002 
(median) with an error factor of 3. This is based on Item 5 of Table 4, which gives a 
probability value for a comparable event, namely the failure of an operator to check-read 
a display with difficult-to-see limit marks. 
The previous information is used to develop an event tree for the damage of the waste package 
by mishandling. The software code SAPHIRE is used to perform this task, and the resulting 
event tree is shown on Figure 13. The electronic files of the SAPHIRE project are contained in 
Attachment II. Table 17 shows the events, along with their mean probability. 
Notice that the probability of damaging the waste package by mishandling during at least one of 
the four potential occasions identified in Assumption 5.7.2 is quantified using a simple fault tree 
called MISH (given in Attachment II). The four basic events (each of them representing a 
potential occasion for mishandling) are connected through an OR logic gate. The mean 
probability is calculated using a Monte Carlo sampling with 90,000 realizations. The seed value 
(randomly chosen) is 49,107. It should be noted that the four basic events are correlated 
together, since their distribution is based on the same state of knowledge (see Section 6.2.4 for 
more information on correlation of nominally identical events). The mean probability of the 
fault tree MISH is shown on Table 17. It is given for information only because the real inputs 
that serve for the quantification of the event tree are the basic events on which the fault tree is 
developed. 
The sequence of events that leads to waste package contamination end state on Figure 13 is 
labeled MISH. 
Table 17. Description of Events for Damage of the Waste Package by Mishandling 
Event Name Event Description (Failure-Oriented) Mean Probability 
INIT Placeholder initiating event 1a 
MISH Damage to the waste package occurs by mishandling 1.9  10-4 b 
CAM_DET Operator fails to detect visible traces of waste package contamination 
during final inspection performed via remote camera 2.50  10-3 
NOTES: a This is a placeholder with a value of unity. It has no uncertainty. 
b 
Probability value is based on quantification of associated fault tree (given in Attachment II). Only two 
significant figures are shown. 
CAL-EBS-MD-000030 REV 00C 86 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
MISHINIT # 
1 
2 
3NO 
iiCAM_DET 
Detection of 
unconformity 
on camera ? 
Proper handling 
of the WP ? 
Placeholder 
initiating 
event 
END-STATE 
OK 
OK 
MISH 
YES 
MISHANDLING - Damage to a waste package by mshandlng 2002/11/30 Page 6 
Figure 13. Event Tree for Damage to the Waste Package by Mishandling 
A Monte Carlo sampling was performed with 90,000 realizations on the resultant events. Monte 
Carlo sampling is performed to propagate the variability of the events to obtain the 
characteristics of the resulting distribution. The seed value for the sampling (randomly chosen) 
is 59,027. The sample size is chosen large enough to get a good approximation on the main 
characteristics of the distribution. 
Notice that except for the basic events of the fault tree MISH mentioned previously, none of the 
other events need to be correlated together because each of them represents a different type of 
failure. 
The resulting mean, median, 5th percentile, and 95th percentile are 4.8  10-7, 1.4  10-7, 
1.1  10-8, and 1.8  10-6 per waste package, respectively. 
In the discussion that follows, which will be used in Section 6.4.8, it is shown that the probability 
that a waste package is damaged by mishandling is independent of the fact that another waste 
package has already been damaged by mishandling. In other words, the fact that a waste 
package is damaged when handled does not increase the probability that the subsequent waste 
package to be processed will also be damaged through handling. 
The rationale for this is based on the fact that the dominant cause for a damage to the waste 
package by mishandling is human error (see Assumption 5.7.4). The only reason, other than 
CAL-EBS-MD-000030 REV 00C 87 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
coincidence, for two consecutive waste packages to be mishandled is that the operator makes the 
same mistake in handling the waste package. This situation is incompatible with the highly 
controlled operating conditions under which handling of the waste package will be performed. 
Indeed, handling operations will be governed by strict procedures and controls, developed to 
eliminate potentials for recurring handling errors. Such handling errors would denote a major 
flaw in handling operations that is not expected to pass the tight controls and reviews these 
handling operations will be subjected to. Furthermore, such a flaw would likely affect several 
waste packages in a row, and it is not credible that recurring damages to waste packages would 
go unnoticed. 
Therefore, based on the previous information, occurrences of waste package damage by 
mishandling can be considered independent from each other. 
6.2.8 Administrative Error Leading to Unanticipated Conditions 
Administrative error leading to an unanticipated operating environment must be more 
specifically defined for a waste package so it can be evaluated. The types of administrative 
errors that could lead to unanticipated operating conditions are those that could affect the waste 
package surface temperature and humidity history and thus impact corrosion rates, result in 
placement in prohibited areas, or allow water to contact the waste package at times earlier than 
expected. 
The temperature at the surface of the waste package is mainly governed by the temperature in the 
drift where the waste package is located rather than the heat output within the waste package. 
The reason for this is that the waste package is a metallic container with a rather large heat 
transfer area (see the dimensions of a typical waste package in Section 4.1.1). Therefore, the 
increase in heat output generated by a thermally overloaded waste package (which can be 
expected not to exceed a few kilowatts) would be quickly dissipated into the drift and is not 
expected to alter the waste package surface temperature to an extent significant enough to 
jeopardize its postclosure performance. The peak waste package temperature would envelope 
any variations in the waste package surface temperature due to thermal loading variations. 
Therefore this event will not be considered further. 
Early water contact or early exposure to rockfall could result if human error during placement of 
the drip shield results in a gap between drip shield segments or if the drip shield fails early due to 
fabrication defects; this is investigated in Section 6.3. 
6.3 MECHANISMS FOR EARLY DRIP SHIELD FAILURE 
The approach followed to investigate the mechanisms that may lead to the early failure of the 
drip shield is based on what has been done for the waste package. Of the 12 types of defects that 
are identified in Section 6.2, four are not applicable (as discussed in Section 6.2), and only the 
following eight are considered applicable to the drip shield: 
 Weld flaws 
 Base metal flaws 
 Improper weld material 
 Improper base material 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
 Improper heat treatment 
 Contaminants 
 Handling or installation damage 
 Administrative or operational error. 
These defects are evaluated in the following subsections. 
6.3.1 Weld Flaws 
No detailed information on the density and size distribution of the flaws to be expected in 
titanium welds was found in the literature. That is why it is necessary to make an assumption on 
these distributions. Based on Assumption 5.8.1, the flaw density and size distributions in 
titanium welds are taken to be the same as those of Alloy 22 weld flaws. Also, based on 
Assumption 5.8.2, the welds of the drip shield will be UT inspected. 
The previous assumptions make it possible to use the work performed in Section 6.2.1 to 
determine the characteristics of the flaws in titanium welds. Because there is no information yet 
on the precise geometry of the titanium welds, only preliminary estimates are made and a 
simplified approach is followed. 
The flaw density and size distribution of the titanium weld flaws are taken to be the same as 
those of the 25-mm thick outer lid weld of the waste package. The reason for this choice is that 
this weld geometry has been the most extensively studied in this analysis. This information is 
used in Section 6.2.2 to evaluate the volumetric flaw density in base metal. After applying a 
correction factor of one-eighth, the volumetric flaw density in inspected base metal is 
approximately 21 flaws per cubic meter of metal. Removing this correction factor yields the 
volumetric density of flaws in the welds, which is therefore 21  8 = 168 flaws per cubic meter 
of weld. 
Using the fact that there is approximately 110 kg of titanium welds in the drip shield (see 
Section 4.1.1) and that the density of titanium is about 4.51 g/cm3 (see Section 4.1.1), the volume 
3
occupied by the welds is estimated at 2.44  10-2 m. This yields an average of 
168  2.44  10-2 = 4.1 weld flaws in the drip shield. 
Also, based on Table 13, the mean size of the flaws that remain in the welds after UT inspection 
is 1.3 mm. The 5th and the 95th percentiles are 0.099 and 2.8 mm, respectively. Notice that these 
values are governed by the UT PND curve rather than the geometry of the welds (see 
Section 6.2.1.3 for more information). 
6.3.2 Base Metal Flaws 
There are mainly two types of imperfections that might affect the base metal of the titanium drip 
shield: low-density and high-density inclusions (Graham 2002). 
Low-density inclusions, also called hard-alpha defects, have been extensively studied, and 
information on their density and size distribution is presented in Section 4.1.4. Based on 
Assumption 5.9.1, this information is deemed adequate for characterizing the hard-alpha defects 
expected in the drip shield base metal. 
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High-density inclusions are typically tungsten carbide coming from tool bit or machining. Based 
on Assumption 5.9.2, the frequency of occurrence for these inclusions is taken to be the same as 
the frequency of occurrence of hard-alpha defects. Also, because these inclusions are usually 
quite small, on the order of 1 mm or less in spherical equivalent size (Graham 2002), it is 
conservative to consider that they have the same size distribution as the hard-alpha defects, 
which in comparison can reach several inches in length. 
Table 8 gives a set of data points for the hard-alpha inclusion anomaly distribution curve to be 
used in this analysis. This anomaly distribution curve gives the expected number of hard-alpha 
defects per million pounds of titanium as a function of their size or, in terms of probability, the 
probability of having an inclusion of a given size or larger per million pounds of titanium, which 
is called the exceedance probability (FAA 2001, p. A3-1). To obtain the exceedance probability 
pertaining to a given size, the anomaly distribution curve is linearly interpolated on a log-log 
scale. It should also be noted that the hard-alpha defects are supposed to be spherically shaped 
and uniformly distributed throughout the part (see Section 4.1.4 for more information on 
characteristics of anomaly distribution curves). 
Based on this information a Mathcad calculation, given in Attachment I, is performed to express 
the anomaly distribution curve in terms of the expected number of high-density and low-density 
inclusions in the drip shield as a function of the diameter of the defect in mm. The 
corresponding curve is shown on Figure 14. The total mass of the drip shield, 5000 kg, based on 
Table 3, is used to perform this calculation. 
Table 18 shows the results for inclusions of size 0.5 mm and 1 mm. A Poisson distribution is 
used to make the calculation. The parameter of the Poisson distribution is the expected number 
of flaws of 0.5 mm or 1 mm expected in the drip shield (see Attachment I for details of the 
calculation). 
Table 18. Probability of Having 0.5-mm or 1-mm Inclusions in the Drip Shield 
0 1 0 1 
i 10-2 10-3  10-2 10-5 
0.5-mm Inclusion 1-mm Inclusion 
Number of Flaws 2 or more 2 or more 
Probabilty per drip shield 0.95 5.3 1.5 0.99 1.0 5.4 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Expected Number of Inclusions of Indicated Size 
or Larger 
1 
0.1 
0.01 
10 3 
10 4 
0.11 10 
0.1 
Inclusion Size (mm) 10 
Figure 14. Anomaly Distribution Curve for Inclusions in the Drip Shield 
A basic comparison of the frequency of occurrence of inclusions in base metal titanium with the 
frequency of occurrence of flaws due to improper repairs of the base metal is performed as 
follows. 
The same approach as that of Section 6.2.2 is followed. In that section, it was assumed that the 
allowable surface of base metal Alloy 22 that could be repaired was 100 cm2. Keeping this 
surface and considering that the thickness of the titanium plates to be used in the drip shield is 
15 mm (see Section 4.1.1), a work volume of Vbm = 0.1  0.1  0.015 = 1.5  10-4 m3 is found. 
Then, using the same parameters Fbm and .bm as in Section 6.2.2, the mean number of flaws 
resulting from improper base metal repair is evaluated at: Fbm  .bm  Vbm = 6.4  10-6. A 
comparison to Figure 14 shows that the frequency of occurrence for this type of flaw is 
negligible compared to that of inclusions. 
6.3.3 Improper Weld Material or Base Metal 
The probability that improper weld material or base metal is used for the drip shield. The 
probability that this mistake goes unnoticed is evaluated in the same way as the probability of 
using improper weld material or base metal for the Alloy 22 barrier of the waste package 
analyzed in Section 6.2.3. Therefore, the assumptions used in that section also apply here. 
The results are the same as those found in Section 6.2.3 (i.e., the median, the mean, and the error 
factor are 3.5  10-8 per drip shield, 5.0  10-8 per drip shield, and 4.0, respectively). 
6.3.4 Improper Heat Treatment 
The probability of an improper heat treatment of the drip shield that would go unnoticed is 
evaluated in the same way as the probability of improper heat treatment of the waste package 
analyzed in Section 6.2.4. Therefore, the assumptions used in that section also apply here. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The evaluation is performed by developing the same event tree as that which was used for the 
improper heat treatment of the waste package. The only difference is that only one heat 
treatment is performed for the drip shield and not two as for the waste package (one for the shell, 
one for the top lid). The event tree that is used for the evaluation can be found in the SAPHIRE 
files of Attachment II. It is not given here because it is the same as that shown on Figure 9. 
A Monte Carlo sampling was performed with 90,000 realizations on the resultant events. Monte 
Carlo sampling is performed to propagate the variability of the events to obtain the 
characteristics of the resulting distribution. The seed value for the sampling (randomly chosen) 
is 59,027. The sample size is chosen large enough to get a good approximation on the main 
characteristics of the distribution. 
Nominally identical events are correlated together prior to the uncertainty analysis. 
The resulting mean, median, 5th percentile, and 95th percentile are 1.3  10-5, 1.5  10-6, 
6.1  10-8, and 5.3  10-5 per drip shield, respectively. 
6.3.5 Contamination 
The probability of a drip shield surface contamination that would remain unnoticed is evaluated 
in the same manner as the probability of contaminating the waste package analyzed in 
Section 6.2.6. The assumptions are very similar to what was done for the waste package and are 
given in Section 5.10. Notice that the inspection of the drip shield just before it leaves for the 
underground repository does not need to be performed remotely since the drip shield is not 
radioactive. Nevertheless, for the sake of simplicity and because it is conservative, the same 
HEP as for the remote inspection of the waste package is used. 
The probabilities of the events leading to contamination of the drip shield are the same as those 
used for evaluating the probability of contaminating the waste package. The quantification is the 
same. As a consequence, the resulting probability is also the same. The mean, median, 5th 
percentile, and 95th percentile are 1.1  10-4, 5.9  10-5, 1.1  10-5, and 3.6  10-4 per drip shield, 
respectively. 
6.3.6 Improper Handling 
The probability of a drip shield damage that would remain unnoticed is evaluated in the same 
way as the probability of damaging the waste package analyzed in Section 6.2.7. The 
assumptions are very similar to what was done for the waste package and are given in 
Section 5.11. Notice that the inspection of the drip shield just before it leaves for the 
underground repository does not need to be performed remotely, since the drip shield is not 
radioactive. Nevertheless, for the sake of simplicity and because it is conservative the same HEP 
as for the remote inspection of the waste package is used. 
The probabilities of the events leading to damage of the drip shield by mishandling are the same 
as those used for evaluating the probability of damaging the waste package. As a consequence, 
the resulting probability is the same. The mean, median, 5th percentile, and 95th percentile are 
4.8  10-7, 1.4  10-7, 1.1  10-8, and 1.8  10-6 per drip shield, respectively. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
6.3.7 Drip Shield Emplacement Error 
This section estimates the probability that a drip shield is improperly emplaced in the repository, 
leaving a gap between adjacent drip shields. Note that such a gap would be small. Most likely it 
would not exceed the length of the connecting plates because otherwise it would leave a readily 
visible opening between the drip shields and it is not credible that such a gap would go 
unnoticed. 
The evaluation requires making an assumption on the drip shield emplacement procedure given 
in Assumption 5.12.1. 
The elementary probabilities of the events involved in drip shield emplacement error are as 
follows: 
 The probability that the operator fails to properly interlock the drip shield to be emplaced 
with the adjacent drip shield is approximated by a lognormal distribution with a median 
of 0.003 and an error factor of 3. This is based on Item 7 of Table 4, which gives a 
probability value for a comparable event, namely the failure to correctly mate a 
connector. 
 The probability that the verification that adjacent drip shields are correctly interlocked, 
performed remotely by camera, fails to detect a gap between the drip shields, is estimated 
at 0.002 (median) with an error factor of 3. This is based on Item 5 of Table 4, which 
gives a probability value for a comparable event, namely the failure of an operator to 
check-read a display with difficult-to-see limit marks. 
The previous information is used to develop an event tree for drip shield emplacement error. 
The software code SAPHIRE is used to perform this task, and the resulting event tree is shown 
on Figure 15. The electronic files of the SAPHIRE project are contained in Attachment II. 
Table 19 shows the events along with their mean probability. Note that the means are calculated 
based on the median and the error factor using Equation 36. 
Table 19. Description of Events for Drip Shield Emplacement Error 
Event Name Event Description (Failure-Oriented) Mean 
Probability 
INIT Placeholder initiating event 1a 
DS_INTRLCK Failure to properly interlock adjacent drip shields 3.75  10-3 
CAM_DET Operator fails to detect gap between two improperly interlocked drip shields 2.50  10-3 
a
NOTE: This is a placeholder with a value of unity. It has no uncertainty. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
ililINIT 
Plii# 
1 
2 
3Iiield //
CAM_D ET 
Detection of 
unconformty 
on camera ? 
DS_INTRLCK 
Operator 
interocks 
drp shield 
propery ? 
aceholder 
initatng 
event 
END-STATE 
OK 
OK 
IDSE 
DS_EMPL ACEMENT mproper 
e mplacem ent of a d rp sh2002120 1 Page 2 
Figure 15. Event Tree for Drip Shield Emplacement Error 
The sequence of events that leads to an emplacement error end state on Figure 15 is labeled 
IDSE. 
There is no need to perform a Monte Carlo sampling to obtain the characteristics of the 
distribution pertaining to drip shield emplacement error. This is because the sequence of events 
is the product of lognormal distribution and therefore is also a lognormal distribution. 
Application of Equations 37 and 38 yields a median of 6.0  10-6 per drip shield and an error 
factor of 4.7. The mean is calculated with Equation 36 and is 9.3  10-6 per drip shield. The 5th 
(respectively 95th) percentile is obtained by dividing (respectively multiplying) the median by the 
error factor and is therefore 1.3  10-6 (respectively 2.8  10-5) per drip shield. 
6.4 CONSEQUENCES OF THE OCCURRENCE OF DEFECTS ON WASTE 
PACKAGE OR DRIP SHIELD 
The investigations described in Sections 6.2 and 6.3 have identified several types of defects that 
are applicable to the waste package or the drip shield and which also have a probability greater 
than the threshold given in Section 4.2. These types of defects are weld flaws, base metal flaws, 
improper weld material, improper heat treatment, improper laser peening, contamination, 
improper handling, and administrative error leading to unanticipated conditions (reduced down 
to drip shield emplacement error). 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The purpose of this section is to identify the consequences of the occurrence of such defects. 
Some defect types have negligible consequences while some other defect types may lead to 
stress corrosion cracking, localized corrosion, formation of grain-boundary precipitates, etc. It is 
beyond the scope of this analysis to investigate the impacts of these latter phenomena on waste 
package or drip shield performance. This will be carried out elsewhere. 
6.4.1 Consequences of Weld Flaws or Base Metal Flaws 
Any outer-surface-breaking flaws in combination with the presence of an aggressive 
environment and sufficiently high residual stresses from the weld could potentially lead to stress 
corrosion cracking. 
Another possible consequence of surface breaking flaws of any size is their growth by other 
corrosion processes. 
6.4.2 Consequences of Improper Weld Material or Base Metal 
In the case of the improper weld material used in the reactor vessel weld discussed in 
Section 6.2.3, the substituted material had a composition that was only slightly different from the 
specified material, and further impact on performance was to be minimal. However, 
Section 6.1.1 indicates that there have been pressure-vessel failures associated with the use of 
incorrect weld material, although it is not stated whether the specified material was incorrect or 
the material used was not that which was specified. Due to the strict controls that will govern the 
fabrication of the waste package and the drip shield, it is expected that the material composition 
of improper weld material or base metal would only differ slightly from the material composition 
of Alloy 22 or Titanium Grade 7. 
In view of the high corrosion resistance of the materials the consequences of the use of such 
improper material is expected to be insignificant. 
6.4.3 Consequences of Improper Heat Treatment 
While the likelihood of improper heat treatment is small, the consequences of improper heat 
treatment can be significant. Improper rate of cooling of alloys such as Alloy 22 may result in 
the precipitation of carbides and intermetallic compounds along the grain boundaries. This in 
turn enhances the susceptibility of the material to localized corrosion. Formation of grain-
boundary precipitates also enhances the susceptibility of the material to stress corrosion 
cracking. As a result of these competing effects, identification of a single and specific 
mechanism of degradation is not possible. These effects are applicable to the waste package 
Alloy 22 outer barrier and outer barrier lids (i.e., the outer lid and the middle lid). 
Concerning the drip shield, improper heat treatment could lead to susceptibility to stress 
corrosion cracking. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
6.4.4 Consequences of Improper Laser Peening 
Consequences of improper laser peening for stress mitigation may lead to the introduction of 
unacceptable amounts of cold work in the material and increased susceptibility to stress 
corrosion cracking. 
6.4.5 Consequences of Contamination 
The consequence of a contamination of the surface of the waste package or the drip shield is not 
expected to be significant from the corrosion standpoint. The waste package outer barrier is 
made of highly corrosion-resistant material over a wide range of chemical conditions. This is 
supported by the results from the ongoing long-term corrosion tests in environments with 1,000 
times the concentrations of various adverse chemical species that may be expected in the 
repository. The test environments include significantly high chloride concentrations 
(approximately 7,000 ppm) and acidic conditions (pH of 2.7) compared to the potential 
contamination and do not exhibit increased corrosion rates (BSC 2003h, Section 6.9.1). 
The same conclusion is reached with Titanium Grade 7 of the drip shield. Tests on Titanium 
Grade 16 (an analog of Grade 7) performed in the same environments as those mentioned 
previously, have not shown increased corrosion rates (BSC 2003g, Table 6 and Section 8). 
6.4.6 Consequences of Damage by Mishandling 
Gouges on the waste package outer surface may provide sites for stress corrosion cracks of 
Alloy 22 if the resulting stress profiles are conducive to the initiation and propagation of stress 
corrosion cracking. 
Concerning the drip shield, damage by mishandling could also cause increased susceptibility to 
stress corrosion cracking. 
6.4.7 Consequences of Drip Shield Emplacement Error 
As noted in Section 6.3.7, the gap between two adjacent drip shields improperly interlocked is 
expected to be small. It is not credible that the inspection performed on camera would not detect 
an incorrect emplacement leaving a gap exceeding the length of the connecting plates of the drip 
shields. That is why dripping water from the drift is not expected to fall directly onto the 
underlying waste package but will most likely hit the connecting plate first, which will divert it 
from the waste package surface. 
6.4.8 Summary and Discussion 
In light of the high corrosion resistance of Alloy 22 and Titanium Grade 7 under expected 
repository conditions, two types of defects can be discarded from further consideration. These 
are improper weld material or base metal and surface contamination (see 
Sections 6.4.2 and 6.4.5). 
Another type of defect that is not expected to affect the performance of the waste package is the 
drip shield emplacement error. As mentioned in Section 6.4.7, this defect is credible only for 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
small gaps, which will not allow for water dripping onto the waste package. Therefore, this type 
of defect is discarded from further consideration. 
Some other types of defects appear to be similar. This is the case of waste package weld flaws 
and base metal flaws. The frequency of occurrence of base metal flaws is much lower than that 
of the weld flaws. Based on the results of Section 6.2.2, the probability of having at least one 
flaw is 1.0  10-5 per waste package in the base metal. In comparison, this probability is 
1 - 0.80 = 0.20 for the outer lid weld and 1  0.77 = 0.23 for the middle lid weld, after UT 
inspection (see Table 13). Also, the discussion in Section 6.2.1.3 shows that the probability of 
occurrence for flaws in the seam welds of the waste package given in Table 13 is very 
conservative. Therefore, these flaws appear to be negligible compared to the flaws in the closure 
welds of the waste package (namely, the outer lid weld and the middle lid weld). As a 
consequence, the base metal flaws and the seam weld flaws of the waste package can be 
discarded from further consideration. Only the flaws in the closure welds are recommended to 
be investigated in further analyses. 
Improper heat treatment, improper laser peening, or mishandling of the waste package might 
have adverse consequences on waste package performance, as noted in Sections 6.4.3, 6.4.4, and 
6.4.6. A potential consequence common to the three types of defect is increased susceptibility to 
stress corrosion cracking. An evaluation is performed in SAPHIRE to quantify the probability 
that a waste package is affected by at least one of the previous defect types. To do this, 
duplicates of the event trees shown on Figures 9, 10, 11, and 13 are created in SAPHIRE, and the 
end state of the sequences of events resulting in a defective waste package are labeled DMWP. 
Also, nominally identical events are correlated together (see Section 6.2.4 for more information 
on correlation of nominally identical events). Note that these events are those which have the 
same correlation class in Tables 14 and 15. The electronic files of the SAPHIRE files are 
contained in Attachment II. 
A Monte Carlo sampling was performed with 90,000 realizations on the resultant events. Monte 
Carlo sampling is performed to propagate the variability of the events to obtain the 
characteristics of the resulting distribution. The seed value for the sampling (randomly chosen) 
is 59,027. The sample size is chosen large enough to get a good approximation on the main 
characteristics of the distribution. 
The resulting mean, median, 5th percentile, and 95th percentile are 2.8  10-5, 3.7  10-6, 
2.9  10-7, and 1.1  10-4 per waste package, respectively. The maximum value yielded by the 
Monte Carlo sampling is 7.44213  10-3. 
To make these results more tractable, they are fit to a lognormal distribution. This fit is 
supported by the fact that the basic events involved in the sequences leading to a defective waste 
package are lognormal, and that the sum and product of lognormal distributions is approximately 
lognormal (Swain and Guttmann 1983, pp. A-4 to A-6). In order to keep the most significant 
and conservative characteristics of the uncertainty analysis performed previously, a lognormal 
distribution that approximates the mean and the 95th percentile calculated by Monte Carlo 
sampling is determined. 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
To do this, the following approach is used. Equations 36 and 43 are utilized to determine the 
characteristics of the lognormal distribution. They form a system of equations in which m, m95, 
and EF (the mean, the 95th percentile, and the error factor of the lognormal distribution, 
respectively) are variables. Since m and m95 are already known from the Monte Carlo sampling, 
it is possible to combine Equations 36 and 43 together, in order to form a new equation in which 
EF is the only variable. This equation is as follows: 
2
.
.
1

..
.
ln(EF ) 
645.1
..
.
- EF 
- 
= 
0 (Eq. 44) 
..
.
..
.
m
m  
 exp
95 
2 
Calculations performed using Mathcad (see Attachment I) show that Equation 44 has no exact 
solution. Nevertheless, the function on the left side of the equation is shown to reach a minimum 
for a value of EF approximately equal to 15. This value is chosen for the fitting lognormal 
distribution. 
Therefore, the probability of a defective waste package due to improper heat treatment, improper 
laser peening, or mishandling is evaluated by a lognormal distribution with a mean of 2.8  10-5 
per waste package and an error factor of 15. Notice that this distribution has a median of 
7.2  10-6, a 5th percentile of 4.8  10-7, and a 95th percentile of 1.1  10-4 per waste package, 
respectively. When comparing to the results of the Monte Carlo sampling, these results appear 
to be conservative. 
The fact that the lognormal distribution is defined for all positive numbers leads to excessively 
conservative probability estimates when the upper percentiles of the distribution are calculated. 
That is why the lognormal distribution has been truncated. In other words, it is considered that 
the probability of having a defective waste package due to improper heat treatment, improper 
laser peening, or mishandling, will not exceed a certain maximum value. This value is selected 
as the maximum value of the Monte Carlo simulations, and is equal to 7.44213  10-3. This 
corresponds to the 99.999th percentile of the lognormal distribution. Thus, only a tiny portion of 
the original lognormal distribution is eliminated. This ensures that the resulting truncated 
distribution will provide adequate estimates of the probability of having a defective waste 
package and will prevent unrealistic upper percentiles from being considered. 
Based on the discussions in Sections 6.2.4, 6.2.5, and 6.2.7, occurrences of improper waste 
package heat treatment, laser peening, or damage by mishandling can be considered as 
independent from each other. In other words, the global probability calculated previously is 
given for each waste package individually and the fact that one waste package is affected by one 
of the defect types mentioned previously will not increase the probability that another waste 
package is affected by the same type of defect. 
As a consequence, the probability on the number of waste packages that are affected by improper 
heat treatment, improper laser peening, or damage by mishandling, and subsequently emplaced 
in the repository, can be evaluated using a Poisson distribution. The parameter of the Poisson 
distribution is calculated as the product of the probability of having a waste package affected 
with improper heat treatment, improper laser peening, or damage by mishandling (estimated 
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
previously and fitted to a lognormal distribution) and the number of waste packages to be 
emplaced in the repository. 
It is important to note that the main contributor to the probability distribution obtained previously 
is the improper heat treatment of the waste package. Additionally, any consequences of 
improper laser peening or damage by mishandling are considered subsumed by the consequences 
of improper heat treatment. Although the welding and laser peening of the weld of the outer lid 
will negate any adverse fabrication heat treatment effects, the region in which these effects is 
negated is considered small. Therefore, it is conservative to subsume the effects of improper 
laser peening into the consequences of an improper heat treatment. Damage by mishandling can 
occur at any point on the surface of the waste package and it is therefore appropriate to subsume 
its consequences into those of an improper heat treatment. 
As previously mentioned in Section 6.4.3, improper heat treatment may enhance susceptibility to 
stress corrosion cracking, but might also lead to the formation of grain-boundary precipitates. In 
fact, identification of a single and specific mechanism of degradation is not possible. Therefore, 
the following recommendations are made for evaluating the consequences of improper heat 
treatment of the Alloy 22 waste package outer barrier components. 
 A failure of the waste package outer barrier shell and outer barrier lids should be 
assumed. 
 The affected waste packages should be assumed to fail immediately upon initiation of 
degradation processes. 
 The entire waste package outer barrier surface area should be considered affected by 
improper heat treatment. 
 The materials of the entire affected area should be assumed lost upon failure of the waste 
packages because the affected area will be subjected to stress corrosion cracking and 
highly enhanced localized and general corrosion. 
These recommendations are conservative but appropriate for their intended purpose and 
represent the worst case degradation rate. 
It should be noted that a grouping of defect types similar to what was done previously for the 
waste package could be also done for the drip shield. For example, improper heat treatment and 
damage by mishandling have both in common to potentially result in increased susceptibility to 
stress corrosion cracking. The situation is also the same for weld flaws and base metal flaws, 
which are very similar types of defects. However, in this analysis, more emphasis is put on the 
defect types of the waste package than on the defect types of the drip shield. That is why 
groupings of the defect types that might affect the drip shield have not been performed nor has a 
fitting of the probabilities of occurrence of such defects to a distribution. 
6.5 FEATURES, EVENTS, AND PROCESSES INCLUDED IN MODEL 
The development of a comprehensive list of FEPs potentially relevant to postclosure 
performance of a repository at Yucca Mountain is an ongoing, iterative process based on site-
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Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
specific information, design, and regulations. The approach for developing an initial list was 
documented in The Development of Information Catalogued in REV00 of the YMP FEP 
Database (Freeze et al. 2001). To support the TSPA-LA model, the FEP list (DTN: 
MO0407SEPFEPLA.000) was re-evaluated in accordance with The Enhanced Plan for Features, 
Events, and Processes (FEPs) at Yucca Mountain (BSC 2002, Section 3.2). Table 20 provides a 
list of FEPs that are included in the TSPA-LA models described in this calculation, and provides 
specific references to sections within this document. Table 21 provides a list of the FEPs that 
have been excluded. The summary of the disposition and the details of the exclusion of these 
FEPs are documented in FEPs Screening of Processes and Issues in Drip Shield and Waste 
Package Degradation (BSC 2004b). 
Table 20. Features, Events, and Processes Included (Screened In) in TSPA-LA and Addressed in this 
Report 
FEP No. FEP Name Sections Where Disposition is Described 
2.1.03.08.0A Early Failure of Waste Package Section 6.2 
Table 21. Features, Events, and Processes Excluded (Screened Out) in this Report 
FEP No. FEP Name Sections Where Disposition is Described 
2.1.03.08.0B Early Failure of Drip Shield Section 6.3 
1.1.08.00.0A Inadequate Quality Control and Deviations from Section 6.4 
Design 
7. CONCLUSIONS 
The first part of this analysis (Section 6.1) performed a review of available literature on defect-
related early failures of welded metallic components. Types of components examined included 
boilers and pressure vessels, nuclear fuel rods, underground storage tanks, radioactive-cesium 
capsules, and dry-storage casks for spent nuclear fuel. The fractions of the total populations that 
failed due to defect-related causes during the intended lifetime of the components were generally 
in the range of 10-3 to 10-6 per container. In most cases, defects that led to failure of the 
component required an additional stimulus to cause failure (i.e., the component was not failed 
when it was placed into service). In fact, there were several examples that indicated that even 
commercial standards of quality control could reduce the rate of initially failed components well 
below 10-4 per container. 
Twelve generic types of defects that could cause early failures in the components examined were 
identified. These are weld flaws, base metal flaws, improper weld material, improper base 
metal, improper heat treatment, improper weld flux material, poor weld joint design, 
contaminants, mislocated welds, missing welds, handling or installation damage, and an 
administrative error resulting in an unanticipated environment. However, the duration of time 
required for a defect of a given type and severity to lead to failure is highly dependent on the 
service conditions to which the component is subjected. As a result, there is insufficient 
information available in the literature to defensibly relate the cumulative effect of the 
environment, or stresses to which the examined components were subjected, to the waste 
package or drip shield. In addition, factors such as the differing degrees of inspection and the 
CAL-EBS-MD-000030 REV 00C 100 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
extent to which different materials are affected by a given type of defect make direct 
extrapolations of defect-related failure rates indefensible. Accordingly, the information on the 
fraction of components that experienced defect-related failure during the components intended 
lifetime were not directly applied to waste packages or drip shields. However, information on 
the frequency of occurrence of particular types of defects was used in the estimate of waste 
package-defect occurrence rate in some cases. 
The second part of the analysis (Section 6.2) focused on estimating the probability that specific 
defect types will occur on the outer barrier of the waste package despite a set of quality controls 
designed to prevent their occurrence. This was done for eight of the 12 generic defect types 
identified in the literature review. The remaining four defect types (improper weld flux, missing 
welds, mislocated welds, and poor joint design) were judged to be inapplicable to waste 
packages (see Section 6.2 for details) or estimated to have a sufficiently low probability such that 
they could be considered incredible. Note that a defect type specific to the outer lid weld of the 
waste package was also analyzed, namely, improper laser peening of the weld. Also, only one 
type of administrative error leading to unanticipated conditions was shown to require further 
consideration, namely, the emplacement error of the drip shield, treated in Section 6.3. 
The third part of the analysis (Section 6.3) focused on the defects that could affect the drip 
shield, based on the investigations of Sections 6.1 and 6.2. The defects analyzed were weld 
flaws, base metal flaws, improper weld material, improper base metal, improper heat treatment, 
contamination, damage by mishandling, and an emplacement error. 
The fourth part of the analysis (Section 6.4) investigated the consequences of the defect types 
analyzed in Sections 6.2 and 6.3. Some defect types have been identified to have negligible 
consequences on the performance of the waste package or the drip shield (i.e., improper weld 
and base metal materials, contamination, and drip shield emplacement error). The other defect 
types have been identified to potentially increase susceptibility to stress corrosion cracking, 
localized corrosion, etc. 
For the waste package, these latter defect types are as follows: 
 Flaws in the closure welds of the waste package, namely the outer lid weld and the 
middle lid weld. 
 Improper heat treatment, improper laser peening, and mishandling of the waste package. 
These types of defects were grouped together because they all share the same 
consequence of increasing the susceptibility of the waste package to stress corrosion 
cracking. It should be noted that among these three types of defects, the improper heat 
treatment is, by far, the dominant one in terms of probability. Also, since an improperly 
heat-treated waste package might be susceptible to increased aging and phase instability, 
it is not possible to identify a single and specific mechanism of degradation. That is why 
recommendations are made for evaluating the consequences of improper heat treatment 
of the Alloy 22 waste package outer barrier (see Section 6.4.8). 
CAL-EBS-MD-000030 REV 00C 101 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
For the drip shield, the defect types that might increase susceptibility to stress corrosion cracking 
or localized corrosion are as follows: 
 Weld flaws 
 Base metal flaws 
 Improper heat treatment 
 Damage by mishandling. 
Table 22 summarizes the main results pertaining to the defect types to consider in assessing 
waste package and drip shield performance. Note that these results are suitable for their intended 
use and that they are reasonable compared to the inputs. 
As a final note, it is important to remember that a waste package or drip shield with one of the 
types of defects shown in Table 22 is not due to fail at emplacement. Failure of the waste 
package (drip shield) will only occur after degradation processes take place, which may happen 
hundreds of years after emplacement. Also, even if a waste package were to be affected by an 
early failure, its radionuclide inventory may not necessarily be available for transport. This is 
because most through-wall penetrations, especially cracks from stress corrosion cracking, are 
usually of limited length and thickness. 
Table 22. Defect Types to Consider in Assessing Waste Package and Drip Shield Performance 
Waste Package 
Defect Type 
Evaluation of Probability per 
Waste Package 
Comment 
Weld flaws See Table 11 to Table 13 Consider only closure welds 
Improper heat treatment 
grouped with improper 
laser peening and 
waste package 
damaged by 
mishandling 
Lognormal distribution: 
Median = 7.2  10-6 per waste package 
Mean = 2.8  10-5 per waste package 
Error factor = 15 
Upper truncation value = 7.44213  10-3 
per waste package 
See recommendations in Section 6.4.8. 
Use a Poisson distribution for the 
probability on the number of waste 
packages affected (parameter of the 
Poisson distribution is the product of 
probability on the left and number of 
waste packages in the repository) 
Drip Shield Defect 
Type Main Characteristics Comment 
Weld flaws 
Mean number of flaws: 4.1 per drip shield 
Mean size of flaw: 1.3 mm See Section 6.3.1 
Base metal flaws See Table 18 See Section 6.3.2 
Improper heat treatment Mean probability: 1.3  10-5 per drip shield See Section 6.3.4 
Damage by mishandling Mean probability: 4.8  10-7 per drip shield See Section 6.3.6 
This analysis contains two attachments: 
 ATTACHMENT I contains a paper copy of the Mathcad calculations performed in this 
analysis. 
 ATTACHMENT II is a CD-ROM containing the files developed for the Mathcad 
calculations of ATTACHMENT I and the SAPHIRE evaluations. 
CAL-EBS-MD-000030 REV 00C 102 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Table 23. CD-ROM Directory Listing 
File Name Date Time Size (bytes) 
Early Failure Mathcad File.mcd 09/02/2003 04:38p 213,444 
Early Failure SAPHIRE.zip 02/24/2003 09:07a 73,985 
8. INPUTS AND REFERENCES 
8.1 DOCUMENTS CITED 
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Babcock & Wilcox 1979. Records Investigation Report Related to Off-Chemistry Welds in 
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Plates, Sheet 1 of 3, Sheet 2 of 3, and Sheet 3 of 3. DWG-UDC-ME-000001 REV A. Las Vegas, 
Nevada: Bechtel SAIC Company. ACC: MOL.20020102.0174. 
CAL-EBS-MD-000030 REV 00C 103 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
BSC 2001b. Waste Package Misload Probability. CAL-WHS-MD-000001 REV 00. Las 
Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20011212.0186. 
BSC 2002. The Enhanced Plan for Features, Events, and Processes (FEPs) at Yucca Mountain. 
TDR-WIS-PA-000005 REV 00. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
MOL.20020417.0385. 
BSC 2003a. Repository Design Project, RDP/PA IED Typical Waste Package Components 
Assembly (2). 800-IED-WIS0-00202-000-00A. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: ENG.20030702.0002. 
BSC 2003b. Repository Design Project, Repository/PA IED Interlocking Drip Shield and 
Emplacement Pallet. 800-IED-WIS0-00401-000-00A. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: ENG.20030730.0004. 
BSC 2003c. Design and Engineering, D&E/PA/C IED Typical Waste Package Components 
Assembly 1 of 9. 800-IED-WIS0-00201-000-00C. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: ENG.20030917.0002. 
BSC 2003d. Repository Design Project, RDP/PA IED Typical Waste Package Component 
Assembly (6). 800-IED-WIS0-00206-000-00A. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: ENG.20030707.0002. 
BSC 2003e. Stress Corrosion Cracking of the Drip Shield, the Waste Package Outer Barrier, 
and the Stainless Steel Structural Material. ANL-EBS-MD-000005 REV 01 ICN 00. Las 
Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20030717.0001. 
BSC 2003f. 21-PWR UCF Prototype Fabrication Specification. 000-3SS-DSU0-00300-000-
00A. Las Vegas, Nevada: Bechtel SAIC Company. ACC: ENG.20030804.0001. 
BSC 2003g. General Corrosion and Localized Corrosion of the Drip Shield. ANL-EBS-MD-
000004 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20030626.0001. 
BSC 2003h. General Corrosion and Localized Corrosion of Waste Package Outer Barrier. 
ANL-EBS-MD-000003 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
DOC.20030916.0010. 
BSC 2004a. Technical Work Plan for: Regulatory Integration Modeling and Analysis of the 
Waste Form and Waste Package. TWP-WIS-MD-000009 REV 00. Las Vegas, Nevada: Bechtel 
SAIC Company. ACC: DOC.20040616.0006. 
BSC 2004b. FEPs Screening of Processes and Issues in Drip Shield and Waste Package 
Degradation. ANL-EBS-PA-000002 REV 03. Las Vegas, Nevada: Bechtel SAIC Company. 
Bush, S.H. 1983. Reliability of Nondestructive Examination. NUREG/CR-3110. Volume 3. 
Washington, D.C.: U.S. Nuclear Regulatory Commission. TIC: 218323. 
CAL-EBS-MD-000030 REV 00C 104 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
CRWMS M&O 2000. Analysis of Mechanisms for Early Waste Package Failure. ANL-EBS-
MD-000023 REV 02. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20001011.0196. 
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Textbooks and Monographs Volume 68. New York, New York: Marcel Dekker. TIC: 253256. 
DOE (U.S. Department of Energy) 2004. Quality Assurance Requirements and Description. 
DOE/RW-0333P, Rev. 16. Washington, D.C.: U.S. Department of Energy, Office of Civilian 
Radioactive Waste Management. ACC: DOC.20040823.0004. 
Doubt, G. 1984. Assessing Reliability and Useful Life of Containers for Disposal of Irradiated 
Fuel Waste. AECL-8328. Chalk River, Ontario, Canada: Atomic Energy of Canada Limited. 
TIC: 227332. 
Eide, S.A. and Calley, M.B. 1993. Generic Component Failure Data Base. PSA '93, 
Proceedings of the International Topical Meeting on Probabilistic Safety Assessment, 
Clearwater Beach, Florida, January 26-29, 1993. 2, 1175-1182. La Grange Park, Illinois: 
American Nuclear Society. TIC: 247455. 
EPA (U.S. Environmental Protection Agency) 1987a. Causes of Release from UST Systems. 
EPA 510-R-92-702. Washington, D.C.: Environmental Protection Agency. TIC: 244679. 
EPA 1987b. Causes of Release from UST Systems: Attachments. EPA 510-R-92-703. 
Washington, D.C.: Environmental Protection Agency. TIC: 244678. 
EPRI (Electric Power Research Institute) 1997. The Technical Basis for the Classification of 
Failed Fuel in the Back-End of the Fuel Cycle. EPRI TR-108237. Palo Alto, California: 
Electric Power Research Institute. TIC: 236839. 
FAA (Federal Aviation Administration) 2001. Damage Tolerance for High Energy Turbine 
Engine Rotors. Advisory Circular AC 33.14-1. Washington, D.C.: U.S. Department of 
Transportation, Federal Aviation Administration. TIC: 253277. 
Framatome Cogema Fuels. 1996. Fuel Integrity. Proprietary 12-1244558-00. Lynchburg, 
Virginia: Framatome Cogema Fuels. ACC: MOL.19990930.0110. 
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in REV00 of the YMP FEP Database. TDR-WIS-MD-000003 REV 00 ICN 01. Las Vegas, 
Nevada: Bechtel SAIC Company. ACC: MOL.20010301.0237. 
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J. Massari (Framatome Technologies), April 20, 1999. TIC: 244544. 
Heasler, P.G. and Doctor, S.R. 1996. Piping Inspection Round Robin. NUREG/CR-5068. 
Washington, D.C.: U.S. Nuclear Regulatory Commission. TIC: 244618. 
CAL-EBS-MD-000030 REV 00C 105 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Hua, F.; Sarver, J.; Jevec, J.; and Gordon, G. 2002. General Corrosion Studies of Candidate 
Container Materials in Environments Relevant to Nuclear Waste Repository. Corrosion/2002, 
57th Annual Conference & Exposition, April 7-11, 2002, Denver, Colorado. Paper No. 02530. 
Houston, Texas: NACE International. TIC: 252067. 
Hodges, M.W. 1998. Confirmatory Action Letter 97-7-001, Technical Evaluation, Docket No: 
72-1007. Washington, D.C.: U.S. Nuclear Regulatory Commission. Accessed November 2, 
1999. TIC: 244630. http://www.nrc.gov/OPA/reports/sn072298.htm 
Ikeda, B.M. and Shoesmith, D.W. 1997. Industrial Experience with Titanium. AECL-11750. 
Pinawa, Manitoba, Canada: Whiteshell Laboratories. TIC: 235003. 
Khaleel, M.A.; Chapman, O.J.V.; Harris, D.O.; and Simonen, F.A. 1999. Flaw Size 
Distribution and Flaw Existence Frequencies in Nuclear Piping. Probabilistic and 
Environmental Aspects of Fracture and Fatigue: The 1999 ASME Pressure Vessels and Piping 
Conference. PVP-386. Pages 127-144. New York, New York: American Society of 
Mechanical Engineers. TIC: 245621. 
Martz, H.F. and Waller, R.A. 1991. Bayesian Reliability Analysis. Malabar, Florida: Krieger 
Publishing Company. TIC: 252996. 
Modarres, M. 1993. What Every Engineer Should Know About Reliability and Risk Analysis. 
New York, New York: Marcel Dekker. TIC: 238168. 
NBBPVI (National Board of Boiler and Pressure Vessel Inspectors) 1999. Incident Reports. 
Columbus, Ohio: National Board of Boiler and Pressure Vessel Inspectors. Accessed 
September 29, 1999. TIC: 245629. http://www.nationalboard.com/incidents.html 
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Accident Risks in U.S. Commercial Nuclear Power Plants. WASH-1400. Washington, D.C.: 
U.S. Nuclear Regulatory Commission. TIC: 236923. 
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Washington, D.C.: U.S. Nuclear Regulatory Commission, Office of Inspection and 
Enforcement. ACC: MOL.20030922.0136. 
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Assessments for Nuclear Power Plants. NUREG/CR-2300. Two volumes. Washington, D.C.: 
U.S. Nuclear Regulatory Commission. TIC: 205084. 
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Analysis (ATHEANA). NUREG-1624, Rev. 1. Washington, D.C.: U.S. Nuclear Regulatory 
Commission. TIC: 252116. 
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D.C.: U.S. Nuclear Regulatory Commission, Office of Nuclear Material Safety and Safeguards. 
TIC: 254568. 
CAL-EBS-MD-000030 REV 00C 106 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Plinski, M.J. 2001. Waste Package Operations Fabrication Process Report. TDR-EBS-ND-
000003 REV 02. Las Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20011003.0025. 
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1994 International Topical Meeting on Light Water Reactor Fuel Performance, West Palm 
Beach, Florida, April 17-21, 1994. Pages 87-95. La Grange Park, Illinois: American Nuclear 
Society. TIC: 243043. 
Sano, Y.; Kimura, M.; Sato, K.; Obata, M.; Sudo, A.; Hamamoto, Y.; Shima, S.; Ichikawa, Y.; 
Yamazaki, H.; Naruse, M.; Hida, S.; Watanabe, T.; and Oono, Y. 2000. Development and 
Application of Laser Peening System to Prevent Stress Corrosion Cracking of Reactor Core 
Shroud. Proceedings of the 8th International Conference on Nuclear Engineering, ICONE-8, 
Baltimore, Maryland, April 2-6 2000. New York, New York: American Society of Mechanical 
Engineers. TIC: 251262. 
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Indications in PVRUF. Volume 1 of Characterization of Flaws in U.S. Reactor Pressure 
Vessels. NUREG/CR-6471. Washington, D.C.: U.S. Nuclear Regulatory Commission. 
TIC: 253278. 
Schuster, G.J.; Doctor, S.R.; Pardini, A.F.; and Crawford, S.L. 2000. Validation of Flaw 
Density and Distribution in the Weld Metal of the PVRUF Vessel. Volume 2 of Characterization 
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Regulatory Commission. TIC: 253278. 
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Industrial Heating. Pittsburgh, Pennsylvania: Business News Publishing. Accessed November 
8, 2002. TIC: 253543. 
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with Respect to Azimuth. Translated from Defektoskopiya, No. 4, 143-144. New York, New 
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in Piping Welds. Probabilistic and Environmental Aspects of Fracture and Fatigue, 1999 
ASME Pressure Vessels and Piping Conference, Boston, Massachusetts, August 1-5, 1999. 
Rahman, S., ed. PVP-Vol. 386. Pages 101-113. New York, New York: American Society of 
Mechanical Engineers. TIC: 245621. 
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S.M. Stoller and Company. TIC: 245630. 
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Standards of Construction. The Annual Winter Meeting of the American Society of Mechanical 
Engineers, San Francisco, California, December 10-15, 1978. PVP-PB-032. Pages 21-53. New 
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CAL-EBS-MD-000030 REV 00C 107 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Swain, A.D. and Guttmann, H.E. 1983. Handbook of Human Reliability Analysis with Emphasis 
on Nuclear Power Plant Applications Final Report. NUREG/CR-1278. Washington, D.C.: 
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Engineering Experience with Structural Materials. San Antonio, Texas: Center for Nuclear 
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Yang, R.L. 1997. Meeting the Challenge of Managing Nuclear Fuel in a Competitive 
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Performance, Portland, Oregon, March 2-6, 1997. Pages 3-10. La Grange Park, Illinois: 
American Nuclear Society. TIC: 232556. 
8.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
10 CFR 63. Energy: Disposal of High-Level Radioactive Wastes in a Geologic Repository at 
Yucca Mountain, Nevada. Readily available. 
14 CFR 33. Aeronautics and Space: Airworthiness Standards: Aircraft Engines. Readily 
available. 
AP-3.12Q, Rev. 2, ICN 2. Design Calculations and Analyses. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20030827.0013. 
AP-SI.1Q, Rev. 5, ICN 2. Software Management. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: DOC.20030902.0003. 
AP-SV.1Q, Rev. 1, ICN 1. Control of the Electronic Management of Information. Washington, 
D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20030902.0011. 
8.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
MO030214WPWF01.000. Waste Package Weld Flaw Data. Submittal date: 02/14/2003. 
8.4 SOFTWARE CODES 
Software Code: SAPHIRE. V7.18. PC - Windows 2000/NT 4.0. 10325-7.18-00. 
CAL-EBS-MD-000030 REV 00C 108 of 108 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
ATTACHMENT I 
MATHCAD SPREADSHEETS 
CAL-EBS-MD-000030 REV 00C I-1 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
NOTE: all calculations performed with Default values of Mathcad Built-in variables (in Math Options 
menu). 
Calculation of the weld flaw size distribution in the Y direction 
Inputs: See Section 4.1.3.2 
Location of the onset of the flaw in the Y direction, converted to mm: vector YO, i between 0 and 6.
i
3 11
YO0 := 25.4 YO4 := 25.4 
8 16 
3
YO1 := 25.4 
8 
3 
YO2 := 25.4 
11 YO5 := 25.4 
8
16
3
YO3 := 25.4 
7 YO6 := 25.4 
16
16 
Location of the end of the flaw in the Y direction, converted to mm: vector YE, i between 0 and 6.
i
7 13
YE0 := 25.4 YE4 := 25.4 
16 16 
7
YE1 := 25.4 
16 
9 
YE2 := 25.4 
13 YE5 := 25.4 
16
16
3
YE3 := 25.4 
9 YE6 := 25.4 
4
16 
.....
. 
.. 
. 
. 
. 
. 
. 
. 
.
. 
17.4625 
11.1125 
17.4625 
9.525
.
. 
.....
. 
.. 
. 
. 
. 
. 
. 
. 
.
. 
11.1125 
11.1125 
20.6375 
14.2875 
20.6375 
14.2875 
9.525 
YO 
= 
YE 
= 
9.525 
4.7625
.
19.05
.
CAL-EBS-MD-000030 REV 00C I-2 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The size of the flaws in the Y direction, given in Vector Y f, is calculated from YO and YE as: 
14.2875
. 
.. 
. 
. 
. 
. 
. 
. 
.
. 
1.5875 
1.5875 
3.175 
. 
.....
.
Yf := YE - YO Yf 
= 
3.175 
3.175 
4.7625 
6 
The sum of the flaw sizes in the Y direction, s t, is therefore:
.
st := 
Yfi 
i = 0 
mm 
Number of flaws detected through UT inspections: nf := 7 
st = 31.75 
PDF for flaw size parameter: 
Call .s the flaw size parameter in the Y direction. The posterior PDF for .s is given by Equation 2 of 
Section 6.2.1.1.1. 
nf
st nf -1
p.sx
() := ()x exp(-xst)
G nf
6 
4
x
()
p .s
2
0 
0 0.25 0.5 0.75 1 
x 
Figure I.1 Weld Flaw size PDF 
CAL-EBS-MD-000030 REV 00C I-3 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The mean (.sm), the 5th (.s0.05), and the 95th (.s0.95) percentiles are calculated based on 
Equations 3, 4, and 5 of Section 6.2.1.1.1 as: 
nf
:= .sm = 0.2205 per mm
.sm 
st 
qchisq 0.05 2 nf)
( , 
= 0.1035 per mm
.s0.05 := 
2st 
.s0.05
 
qchisq 0.95 2 nf)
( , 
= 0.373 per mm
.s0.95 := 
2st 
.s0.95
 
Flaw size distribution in the Y direction, accounting for weld thickness: 
A generalized cumulative flaw size distribution, accounting for the thickness t (in mm) of the weld, 
is defined in Equation 6 of Section 6.2.1.1.1 as: 
pexp s ,.s)
(
Psg (s ,.s , t) := 
pexp t ,.s)
( 
PDF for the flaw size distribution before UT inspection and repair (see Equation 8 of Section 
6.2.1.1.1) 
dexp s ,.s)
(
psg (s ,.s , t) := 
pexp t ,.s)
( 
Comparison with alternative flaw size distribution: 
Define alternative flaw size distribution as: 
Palt(s ,.alt, t) pexp
..
. 
:= 
s 
, 
t 
()
.alt t
.
.
Here .alt(t) is a function of t and has no dimension. To compare with Psg above, consider only the 
mean values of .s and .alt. Equation 3 of Section 6.2.1.1.1 is applied to the total size of the flaws, 
normalized to the weld thickness t. This yields: 
nf
() :=
.alt t
st 
t 
nf 
:= () := t
Because .sm we have: .alt t.smst 
Therefore, for the mean value of the flaw size parameter: Palt(s ,.alt , t) := pexp s ,.sm)
( 
Comparing Psg(s,.sm,t) to Palt(s,.alt,t) shows immediately that Palt(s,.alt,t)<Psg(s,.sm,t). Thus it is 
more conservative to use P.
sg
CAL-EBS-MD-000030 REV 00C I-4 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Verification of goodness-of-fit with chi-square test (see Equation 7 of Section 6.2.1.1.1): 
Number of cells considered: M := 3 thickness tw := 25 mm 
The cells are chosen to be approximately equiprobable (using a trial and error approach).
cell range observed frequencies expected frequencies
(from Yf) 
c1b := 0 c1e := 1.8 N1 := 2 e1 := nf(Psg (c1e,.sm, tw) - + Psg (c1b,.sm, tw)) 
c2b := 1.8 c2e := 4.9 N2 := 4 e2 := nf(Psg (c2e,.sm, tw) - + Psg (c2b,.sm, tw)) 
c3b := 4.9 c3e := 25 N3 := 1 e3 := nf(Psg (c3e,.sm, tw) - + Psg (c3b,.sm, tw)) 
e1 = 2.3023 e2 = 2.3401 e3 = 2.3577 
2
3 ( Ni - ei)
.
Pearson statistic: X2 
X2 = 1.999
:= 
e
i
i = 1 
Comparison to: qchisq 0.95 1) = 3.8415 shows that the fit is appropriate to the significance 
level considered.
( , 
Flaw size distribution: 
the PDF for the distribution is given in Equation 9 of Section 6.2.1.1.1. 
8 
the CDF is given by Equation 10 of Section 6.2.1.1.1. Pmsg(st)
, 
(.)
0 
psg (s ,.s , t) p.s().s
.s
( , ) 
d
st
:=
pmsg 
 
s
(.)
0 
1 
0.8 
0.6 
P(x25)
msg , 
0.4 
0.2
0
0 5 10 15 2025 
x 
Figure I.2 Weld Flaw Size CDF 
( , )d
:= 
ut
pmsg 
u 
(.) 
25 
,
( (s25) - 0.05, s , 0.1, 3)= 0.231 
,
pmsg(u25)u du = 4.8225 5th percentile: root Pmsg
0 root P
mean: 
( 
- 0.95, s , 3, 20)
(s25)
, 
= 15.1691
95th percentile: 
msg 
CAL-EBS-MD-000030 REV 00C I-5 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Calculation of the distribution related to the weld flaw density 
Inputs: 
total number of detected flaws: nf = 7 
breakdown by specimen ring: ring K: 2 flaws ring X: 1 flaw 
ring R: 3 flaws ring W: 1 flaw 
remaning rings (12 of them): 0 flaw 
diameter of a specimen ring (in m): Dwp := 60.765 0.0254 
 D= 1.543
wp 
length of weld in a specimen ring (in m): L:= pDwp 
L= 4.8488
wp wp 
calculations performed with: Lwp := 4.85 
total length of weld in the 16 specimen rings (in m): Lt := Lwp 16 Lt = 77.6 
PDF for flaw density parameter: 
Call .d the flaw density parameter. The posterior PDF for .d is given by Equation 12 of Section 
6.2.1.1.2. 
nf + 0.5 
Lt nf -0.5 
p.dx
() := 
G(nf + 0.5)x exp(-xLt) 
15 
10 
()
p .dx
5 
0 
0 0.13 0.25 0.38 0.5 
x 
Figure I.3 Weld Flaw Density Parameter PDF 
CAL-EBS-MD-000030 REV 00C I-6 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
The mean (.dm), the 5th (.d0.05 ), and the 95th (.d0.95 ) percentiles are calculated based on 
Equations 14, 15, and 16 of Section 6.2.1.1.2 as: 
2nf + 1
:= .dm = 0.0966 flaws per meter of weld
.dm 2Lt 

( ,
qchisq 0.05 2 nf + 1)
= 0.0468 flaws per meter of weld
.d0.05 := 
2Lt 
.d0.05

( ,
qchisq 0.95 2 nf + 1)
= 0.1611 flaws per meter of weld
.d0.95 := 
2Lt 
.d0.95
 
The CDF for the flaw density parameter is given in Equation 13. 
(.)
0 
x 
()
P.dx
:= 
()d
p.du
u 
1 
0.8 
0.6
P.dx
() 
0.4 
0.2
0
0 0.05 0.1 0.15 0.2 0.25 
x 
Figure I.4 Weld Flaw Density Parameter CDF 
Probability on the number of flaws (0,1,2 or more) with the mean flaw density parameter is: 
dpois 0 ,.dmLwp)= 0.6258
( 
dpois 1 ,.dmLwp)= 0.2933
( 
1 - ppois 1 ,.dmLwp)= 0.0809
( 
CAL-EBS-MD-000030 REV 00C I-7 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Verification of goodness-of-fit with chi-square test (see Equation 7 of Section 6.2.1.1.1 and 
information in Section 6.2.1.1.2): 
Number of cells considered: M := 4 Length of weld in a specimen ring (m): Lwp 
= 4.85 
Number of observations n := 16 
cell observed frequencies expected frequencies 
0 flaw 
N1 := 12 e1 := n dpois 0 ,.dmLwp)
( 
1 flaw N2 := 2 e2 n dpois 1 .dm Lwp ,( ):= 
2 flaws N3 := 1 e3 n dpois 2 .dm Lwp ,( ):= 
3 or more flaws N4 := 1 e4 n 1 ppois 2 .dm Lwp ,( )-( ):= 
e1 = 10.0125 e2 = 4.6934 e3 = 1.1 e4 = 0.1941 
Pearson statistic: X2 
1 
4 
i 
. 
= 
:= 
Ni( ei- )2 
ei 
X2 = 5.2962 
Comparison to: qchisq 0.95 2 ,( ) = 5.9915 shows that the fit is appropriate to the significance 
level considered. 
CAL-EBS-MD-000030 REV 00C I-8 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Calculation of the flaw depth distribution 
Inputs: the onset of the 8 UT indications in the Y direction, in mm. 
17.4625 
11.1125 
17.4625 
.....
. 
.. 
. 
. 
. 
. 
. 
. 
.
. 
9.525 
9.525 
.
YO 
= 
9.525 
4.7625
.
Verification of goodness-of-fit with uniform distribution using chi-square test (see Equation 
7 of Section 6.2.1.1.1): 
Number of cells considered: M := 3 
The cells are chosen to be equiprobable. 25 
= 8.3333 
3 
cell range observed frequencies expected frequencies 
c1b := 0 c1e := 8.33 N1 := 1 e1 nf 
1 
3 
:= 
c2b := 8.33 c2e := 16.67 N2 := 4 e2 nf 
1 
3 
:= 
c3b := 16.67 c3e := 25 N3 := 2 e3 nf 
1 
3 
:= 
Pearson statistic: 
3 Ni ei-( )2 
X2
.
:= 
X2 = 2 
e
i
i = 1 
Comparison to: qchisq 0.95 2) = 5.9915 shows that the fit is appropriate to the significance
( , 
level considered. 
CAL-EBS-MD-000030 REV 00C I-9 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Orientation of the flaws: 
inputs: See Section 4.1.3.2 
Length of the flaws in the X direction, converted in mm: vector X, i between 0 and 6.
i
1 -7
..
.
.
.
5 -1
..
.
.
.
- + 20
X4 25.4 
21
:= 
+ 
+
- + 54
X0 25.4 
54
:= 
+ 
+ 
48
82 
3 -3
- + 55+
..
.
.
.
X1 25.4 
56
:= 
+ 
84 
5 -1
..
.
.
.
7 -1
..
.
.
.
+ - + 3+ 
8 8 
11 -5
X5 25.4 
3
:=
- + 19
X2 25.4 
19
:= 
+ 
+ 
88 
..
.
.
.
5 -1
..
.
.
.
- + 4
X6 25.4 
4
:= 
+ 
+
- + 47
X3 25.4 
48
:= 
+ 
+ 
16 16
84 
Location of the flaw in the Z direction, converted in mm: vector Z, i between 0 and 6.
i
-1
-9
9 
5
..
.
.
.
..
.
.
.
Z0 25.4 
Z4 25.4
:= 
+ 
:= 
+ 
16 
8
2 
16 
9 -1
+ 
16 2 
..
.
.
.
Z1 := 25.4 
11 -9
+ 
16 16 
..
.
.
.
5 -9
+ 
8 16 
.
. 
..
. 
Z5 := 25.4 
Z2 := 25.4 
9 -1
+ 
16 2 
..
.
.
.
Z6 := 0
Z3 := 25.4 
1.5875 
Z 
= 
.. 
. 
. 
. 
. 
. 
. 
.
.
.
3.175 
= 
.. 
. 
. 
. 
. 
. 
. 
.
.
.
1.5875 
1.5875 
1.5875 
1.5875 
3.175 
.....
.
15.875 
19.05 
34.925 
9.525 
12.7 
.....
.
.
0
.
9.525 
CAL-EBS-MD-000030 REV 00C I-10 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Characterization of the angle distribution: 
The angle (converted from radians to degrees) between the flaw and the direction of the weld is 
given for each flaw by the vector. 
i .. := 6
0 
.i := atan 
2p 
.. 
..
Zi 
X
i 
.
.
.
= 
.. 
. 
. 
. 
. 
. 
. 
.
.
26.5651 
5.7106 
. 
.....
. 
.....
. 
. 
.. 
. 
. 
. 
. 
. 
. 
.
. 
14.0362 
26.5651 
0
.
2.6026 
4.7636 
4.7636 
.
:= 
()
sort .
.
=
2.6026 
5.7106 
9.4623 
9.4623 
14.0362 
0
.
The PDF of . is given in Equation 17 of Section 6.2.1.1.4 as: 
, 2 dnorm (. 0,
p.(.s) := ,s) 
The CDF is: 
,  ,s)-1
P.(.s):=2 pnorm (. 0, 
Determine the PDF for s. 
The likelihood function related to the observed angles is: 
6
():= p.(.i,s)
L.s. 
i =0 
Application of Bayes' theorem (Equation 19 of Section 6.2.1.1.4) yields the posterior PDF for s: 
()
L.s
():= 
s 
pss
(
. 
.
) 
8 
()
L.u
du 
u 
0 
CAL-EBS-MD-000030 REV 00C I-11 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
8 
The mean value fors is: sm 
:= 

xps x
()dx sm = 13.9054 
:= root 
(.)
0 
(.)
0 
.
. 
.
. 
.
a 
The 5th percentile is: 
s0.05 
()dx - 0.05, a , 2, 20 = 8.6518
ps xs0.05 
. 
(.)
0 
.
. 
.
. 
.
a 
The 95th percentile is: 
s0.95 
()dx - 0.95, a , 10, 60 = 21.5941
ps xs0.95 
.
:= root 
Maximum likelihood estimator for s: use formula given in Martz and Waller 1991, p. 225: 
smle 
:= 
0 
6 
i 
. i()2.
= 
nf 
= 12.2727
smle 
Verification of goodness-of-fit with chi-square test (see Equation 7 of Section 6.2.1.1.1): 
Number of cells considered: M := 3
The cells are chosen to be approximately equiprobable.
cell range observed frequencies expected frequencies
c1b := 0 c1e := 5.6 N1 := 3 e1 := nf(P.(c1e,sm)- P.(c1b,sm)) 
c2b := 5.6 c2e := 12.7 N2 := 2 e2 := nf(P.(c2e,sm)- P.(c2b,sm)) 
-
c3b := 12.7 N3 := 2 e3 := nf(1P.(c3b,sm)) 
e1 = 2.1899 e2 = 2.2825 e3 = 2.5275 
2
3 ( Ni - ei)
.
Pearson statistic: X2 
X2 = 0.4447
:= 
e
i
i = 1 
CAL-EBS-MD-000030 REV 00C I-12 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Comparison to: qchisq 0.95 1) = 3.8415 shows that the fit is appropriate to the significance 
level considered.
( , 
Expected fraction of flaws with an angle . greater than 45 degrees 
(Equation 20 of 6.2.1.1.4): 
8
(.)
0 
(1P. 45 u )
-
F. 
:= 
() 
 
()du
ps u
, 
F.= 8.0502 10- 3 This corresponds to around 0.8% of the flaws. 
CAL-EBS-MD-000030 REV 00C I-13 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Characterization of UT inspection on WP closure weld: 
flaw size s in mm 
UT reliability curve given in Equation 21:
e := 0.005 . := 3 s01 := 5 mm alternative value of s0 is: s02 := 2.5 mm
(PND1( s e , , s0. ,) e 0.5 1 - e) erfc . ln
..
. 
..
. 
s 
s0 
.
. 
.
. 
:= 
+ 
 
 
UT reliability curve given in Equation 22: 
 1 := - 2.67 2 := 1.6709 per mm 
PND2( s , 1, 2) := 1 - 
1 + exp(- 
1 
+ - 2 s)
1 
1 
0.8
PND1( xe ,, . ,)
s01 
0.6 
PND1( xe ,, . ,)
s02
PND2( x, 1, 2) 0.4
0.2
0
01 23 4 56 78 910 
x 
Figure I.5 UT Weld Flaw Detection Reliability Curve 
In the following, the UT PND curve considered is that given by PND1(s,e ,s0,. ), with s0 := 2.5 mm 
-
1PND1( 2.5e , , 2.5. , )= 0.4975 
CAL-EBS-MD-000030 REV 00C I-14 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Flaw size distribution after UT inspection and repair: 
Fraction of flaws that remain in the weld after UT inspection and repair (Equation 23): 
t 
PDF for the flaw size after UT inspection and weld repair (Equation 25), accounting for all possible 
values of .s, weighted by their probability: 
(.)
0 
FND(t .s ) 
psg (s ) PND1(s e , , s0. , )
e , , s0. , 
.s 
ds
:= 
, t 

, 
, 
8 
psg (s ,.s , t)PND1(s e , , s0. , ) 
) 
Corresponding CDF (Equation 26): 
(
. 
. 
.)
0 
pmsgut (st) 

p.s 
.s
() 
d.s
,
,e, s0. , 
:= 
FND(t ,.s e , , s0. , 
s 
pmsgut (ut)
(.)
0 
Pmsgut (st)
,
,e, s0. , 
,
,e, s0. , 
du
:= 
Graphical representation for outer closure weld of WP (t=25mm): 
- 3

t := 25 e= 510 s0 = 2.5 .= 3 
The CDF is calculated for 100 points between 0 and the 99.6th percentile 
s0.996 ( ,e, s0. , )- 0.996, s , 3, 10):= root Pmsgut (st, 
s0.996 = 6.1177 
ns := 100 i := 1.. ns 

is0.996
S:=
i0
, 
ns 
CAL-EBS-MD-000030 REV 00C I-15 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
t
Si1, := Pmsgut ( Si0,,e,, s0. , ) 
Also we have: S00, := 0 S01, := 0 
1 
0.8 
0.6 
<>
S1
0.4 
0.2
0
01 2 3 4 5 6 7 8 
<>
S0
Figure I.6 Weld Flaw Size CDF After UT Inspection & Weld Flaw Repair 
The mean flaw size is calculated using the formula given in Equation 27. 
t
(.)
0 
smgut( t e , ) 
pmsgut ( ut)
. , 
,e,, s0. , 
 u 
d
:=
s0 
u
, 
smgut( t e , , s0. , )= 1.2527 mm 
5th percentile: root Pmsgut ( st
( ,e,, s0. , )- 0.05, s , 0.01, 1)= 0.09853 
95th percentile: root Pmsgut ( st
( ,e,, s0. , )- 0.95, s , 1, 5)= 2.7585 
CAL-EBS-MD-000030 REV 00C I-16 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Flaw density parameter after UT inspection and weld repair: 
The flaw density parameter after UT inspection and weld repair.dut is given in Equation 28. 
t,
.dut (.d ,.s ,e, s0. , ):=.dFND(t ,.s e , , s0. , ) 
It is a function of 2 independent random variables: .d and .s. The CDF is calculated using latin 
hypercube sampling. 
size of the sampling: ns := 2000 
i := 1.. ns 
:= i
-
RDi1, 0 RK1 and RK2 are two matrixes 
(
- := rnd 1.0) whose first column contain aRDi1, 1 permutation on the integers on the 
(
- := rnd 1.0) interval [1,ns].
RDi1, 2 
( , ( ,
RK1 := csort RD 1) RK2 := csort RD 2) 
Define two sets of random values. Each random value is selected within one of the equiprobable 
ns intervals that partition [0,1]. 2 sets are created, one for each random variable. 
<>
<> <>
RK1 0- 1 + runif ns , 0, 1) X1:= 
RK2 0- 1 + runif ns , 0, 1)
<> 
X0 := 
( 
n( 
n s 
s 
Calculate a set of sample values for each of the random variables: 
a := 0.1 
.
.
.
.
a 
a
(.)
.
0 
(.)
.
.
0 
.
.
.
.
q.s(y) 
:= root 
()du
p.su
- y 
, a 
, 0, 1q.d(y) 
()d
p.du
u 
- y 
, a 
, 0, 1
:= root 
.
i := 0 .. ns - 1 
:= q.s( Xi0) := q.d( Xi1)
Yi0, Yi1,
, , 
Calculate a set of sample values for .dut defined in Equation 28: 
- 3
t25 e= 510 s0 = 2.5 .= 3
= 
CAL-EBS-MD-000030 REV 00C I-17 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
t,
Zi0:= .dut (Yi1, Yi0,e, s0. , )
, ,, 
Sort the sample values and rank them on [0,1] 
Z := sort Z
() 
i1
+ 
:=
Zi1
, 
ns 
1 
0.8 
0.6 
<>
Z1
0.4 
0.2 
0 
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 
<>
Z0
Figure I.7 Weld Flaw Density CDF After UT Inspection and Weld Flaw Repair 
Estimated mean of .dut, based on sample values (see Equation 29): 
n-1
s 
,
= 0.0407 flaw per meter of weld
.dmut := . 
Zni0.dmut .dmut25 := .dmut 
i = 0s 
<> <>
(
5th percentile: linterp Z 1, Z0, 0.05)= 0.0166 flaws / m 5th percentile and 95th 
percentiles calculated by 
linear interpolation on 
<> <> sample values.
(
95th percentile: linterp Z 1, Z0, 0.95)= 0.0756 flaws / m 
Probability on the number of flaws (0,1, 2 or more) with the mean flaw density parameter is: 
dpois 0 ,.dmutLwp)= 0.8207
( 
dpois 1 ,.dmutLwp)= 0.1622
( 
1 - ppois 1 ,.dmutLwp)= 0.0171
( 
CAL-EBS-MD-000030 REV 00C I-18 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Calculation sheet for characterizing flaws in the other welds of the WP: 
e = 510 - 3 s0 = 2.5 mm . = 3 
flat closure lid weld: 
(see Table 2 for input 
diameter: Dflat 1.527:= m length of weld: Lflat p Dflat:= 
values) Lflat 4.7972= m 
rounded up to: Lflat 4.80:= m 
lid thickness: tflat 10:= mm 
after UT, the CDF on the flaw size accounting Pmsgut ( stflate , , s0. , )for uncertainties on . s is given by: 
, 
tflat 
mm
smgut( tflate , , s0. , )= 1.2252 
(,
5th percentile: root Pmsgut ( stflate , , s0. , )- 0.05, s , 0.01, 1)= 0.09835 
(.)
0 
(,
95th percentile: root Pmsgut ( stflate , , s0. , )- 0.95, s , 1, 5)= 2.7389 
Before UT, the mean, the 5th and the 95th percentiles were: 
smgut( tflate , ) 
pmsgut ( utflat )
mean flaw size: 
. , 
e , , s0. , 
du
:=
s0 
 u
, 
, 
10 
0 
,
95th percentile: root Pmsg( stflat)- 0.95, s , 3, 20)= 8.5759 
(.
) 
( 
the main features of the flaw density parameter after UT are determined by latin 
hypercube sampling:
ns = 2103 samples

Z := 0 (initialization of vector)
Zi0, :=. dut ( Yi1,, Yi0,, tflate , , s0. , ) 
Sort the sample value and rank them on [0,1] 
() i1+
Zi1, := 
ns
Z := sort Z
(,
5th percentile: root Pmsg( stflat)- 0.05, s , 0.1, 3)
mean: 
(u10 , ) u d 3.3395 
0.204
pmsg 
u = 
= 
CAL-EBS-MD-000030 REV 00C I-19 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Estimated mean of .dut, based on sample values (see Equation 29): 
n-1
s
,
= 0.0463 flaw per meter of weld
.dmut := . 
Zni0.dmut 
i = 0s 
<> <>
(
5th percentile: linterp Z 1, Z0, 0.05)= 0.0211 flaw / m 
<> <>
(
95th percentile: linterp Z 1, Z0, 0.95)= 0.0809 flaw / m 
Probability on the number of flaws (0,1, and 2 or more) with the mean flaw density 
parameter is: 
before UT: after UT: 
((
dpois 0 ,.dmLflat)= 0.6288 dpois 0 ,.dmutLflat)= 0.8006 
dpois 1 ,.dmLflat)= 0.2917 dpois 1 ,.dmutLflat)= 0.178
(( 
1 - ppois 1 ,.dmLflat)= 0.0795 1 - ppois 1 ,.dmutLflat)= 0.0213
(( 
Seam welds of the WP: 
- 3

e= 510 s0 = 2.5 mm .= 3 
Length of weld in the bottom lid weld taken to be the same as for the outer closure lid weld: 
L= 4.85 m
wp 
Length of the weld seaming the two half-cylinder:
Diameter taken at Dseam := 1.544 m (average of inner and outer diameter of WP, see Table 2
Length of one longitudinal seam taken at: Llong
:= 5.165 m 
So the total length of weld is: 
:= Lwp +pDseam += 14.8656 m
Lseam Llong Lseam 
rounded to: Lseam := 15 m 
Thickness of the weld is conservatively taken at: tseam := 20 mm 
after UT, the CDF on the flaw size is given by: Pmsgut (st, seam e , , s0. , ) 
CAL-EBS-MD-000030 REV 00C I-20 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
the main features of the flaw size after UT are: 
t
seam 
smgut( tseam e , , s0. , )= 1.247 
mm 
(,
5th percentile: root Pmsgut ( stseam e , , s0. , )- 0.05, s , 0.01, 1)= 0.09851 
(,
95th percentile: root Pmsgut ( stseam e , , s0. , )- 0.95, s , 1, 5)= 2.7558 
Before UT, the mean, the 5th and the 95th were: 
(.)
0 
smgut( tseam e , ) 
pmsgut ( utseam )
mean flaw size: 
. , 
e , , s0. , 
 u 
du
:=
s0
, 
, 
20 
(,
95th percentile: root Pmsg( stseam)- 0.95, s , 3, 20)= 13.8487 
the main features of the flaw density parameter after UT are determined by latin hypercube 
sampling on: 
2103 samples
ns = 
Z := 0 (initialization of vector) 
Zi0, :=. dut ( Yi1,, Yi0,, tseam e , , s0. , ) 
Sort the sample value and rank them on [0,1] 
() i1+
Z := sort Z
:=
Zi1, ns 
(.)
0 
Estimated mean of . dut, based on sample values (see Equation 29): 
n- 1
s 
Zi0, 
(,
5th percentile: root Pmsg( stseam)- 0.05, s , 0.1, 3)
mean: 
(u20 , ) u d 4.5543 
0.2283
pmsg 
u = 
= 
.
flaw per meter of weld
. 
0.0413
. dmut
:= 
=
dmut 
n
s
i = 0 
<> <>
(
5th percentile: linterp Z 1, Z0, 0.05)= 0.0173 flaw / m 
<> <>
(
95th percentile: linterp Z 1, Z0, 0.95)= 0.0759 flaw / m 
CAL-EBS-MD-000030 REV 00C I-21 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Probability on the number of flaws (0,1, and 2 or more) with the mean flaw density 
parameter is: 
before UT: after UT: 
dpois 0 ,.dmLseam)= 0.2346 dpois 0 ,.dmutLseam)= 0.5385
(( 
dpois 1 ,.dmLseam)= 0.3402 dpois 1 ,.dmutLseam)= 0.3333
(( 
1 - ppois 1 ,.dmLseam)= 0.4252 1 - ppois 1 ,.dmutLseam)= 0.1282
(( 
Comparison with results from Khaleel et al. (1999) 
Flaw size for 25-mm thick weld: 
s50k 
:= 
25.4 
..
.
0.1169 
+ 
-0.0445 
2
25
.
.
. 
25 
25.4 
+
..
.
.
.
0.00797 
25.4 
mm
s50k = 2.0529 
2
25
..
.
25 
25.4 
.
.
sk 
:= 0.09733+ 0.345 
+ 
-0.07268 
25.4 
sk = 0.3665 
mean size of the flaw (See Equation 34 of Section 6.2.1.1.3):
..
:= s50kexp 0.5 sk
smk 
2
.
.
 
mm
smk = 2.1955 
mm
5th percentile: qlnorm 0.05 ln s50k),sk)= 1.1235
( ,( 
mm
95th percentile: 
qlnorm 0.95 ln s50k),sk)= 3.7511
( ,( 
Apply a UT inspection of the same type that the one used in the analysis (i.e., using P 
ND1): 
Fraction of remaining flaws: 
25
(.
) 
dlnorm u ln s50k),sk) PND1(u e , , s0. , )
(, ( 
0 
Fk 
:= 
du Fk = 0.6761
 
CAL-EBS-MD-000030 REV 00C I-22 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
PDF for the size of the remaining flaws: 
dlnorm s , ln s50k),sk)PND1(s e , , s0. , )
((
() :=
pskut sFk 
CDF for the size of the remaining flaws: 
mean size of the flaws remaining in the weld: 
(.)
0 
s 
()
Pskut s
:= 
()du
pskut u
5th percentile: root Pskut(s) - 0.05, s , 1, 5)= 1.0507
( 
95th percentile: root Pskut(s) - 0.95, s , 1, 5)= 2.7312
( 
Flaw density for non-inspected welds: 
.dk := 0.0448 
1000 
.dk = 1.7638 flaws per meter of weld (no inspection) 
25.4 
(.)
0 
.dk 
= 18.2492
.dm
25 
:=
smkut 
() u du smkut = 1.8168
pskut u mm 
CAL-EBS-MD-000030 REV 00C I-23 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Base-metal flaws: see Section 6.2.2 
Frequency of occurrence for base metal flaws in the Alloy 22 barrier of the WP: 
inputs for HEPs: med1 := 0.01 EF1 := 3 Item 2 of Table 4 
med2 := 0.1 EF2 := 5 Item 8 of Table 4 
mean of resulting frequency of occurrence fbm : 
exp 0.5  
.
. 
.
. 
.. 
.
.
2....
2.
...
(ln EF1))
( 
2 
(ln EF2))
(
+ 
med1med2
Fbm 
:= 
1.645 
- 3 
= 2.017 10
Fbm 
Calculation of the cross-area of weld in a specimen ring: Refer to Section 4.1.3.1 for 
schematic representation and dimensions. 
surface of the half-disk delimited by A 1A2O: 
2
radius is r0 := 0.125 inch so surface is: S1 := 0.5p  0.125S1 = 0.0245 inch2 
surface of triangle delimited by B 3A1B1 and triangle delimited by B 2A2B4: 
distance A1B1 = distance A 2B2 = OC-BC-r0 = L1 L1 := 0.97 - 0.43 - 0.125
L1 = 0.415 inch
p
angle B3A1B1 is: a1 := 
32a1 = 0.0524 radians 
360
p
angle B2A2B4 is: a2 := 
62a2 = 0.1047 radians 
360
length B3B1 is: L2 := L1tan a1
() L2 = 0.0217 inch 
length B2B4 is: L3 := L1tan a2
() L3 = 0.0436 inch 
CAL-EBS-MD-000030 REV 00C I-24 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
 
2
surface of triangle delimited by B3A1B1 is: S2 := 
L1L2 
S2 = 4.513 10- 3 inch2 
 
2
surface of triangle delimited by B2A2B4 is: S3 := 
L1L3 
S3 = 9.0508 10- 3 inch2 
surface of triangle delimited by C 5B3C3 and triangle delimited by C 4B4C6: 
distance B3C3 = distance B 4C4 = BC = L4 L4 := 0.43 inch 
p
angle C5B3C3 is: a3 := 
25 2a3 = 0.4363 radians 
360
p
angle C4B4C6 is: a4 := 
29 2a4 = 0.5061 radians 
360
length C5C3 is: L5 := L4tan a3
() L5 = 0.2005 inch 
length C4C6 is: L6 := L4tan a4
() L6 = 0.2384 inch 
 
surface of triangle delimited by B3A1B1 is: S4 := 
L4L5 
S4 = 0.0431 inch2 
2 
 
surface of triangle delimited by B2A2B4 is: S5 := 
L4L6 
S5 = 0.0512 inch2 
2 
surface of rectangle delimited by A 1B1B2A2and rectangle delimited by C 4B4B3C3: 
rectangle delimited by A1B1B2A2 is: S6 := 2r0L1 S6 = 0.1038 inch2 
 
2
rectangle delimited by C4B4B3C3 is: S7 := (2r0 + L2 + L3)L4 S7 = 0.1356 inch
Calculation of the cross-area: 
total surface is: S := S1 + S2 + S3 + S4 + S5 + S6 + S7 S = 0.3718 inch2 
CAL-EBS-MD-000030 REV 00C I-25 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
in metric system: S S 0.02542 := 
S = 2.3988 10- 4 m 2 
Estimation of the total volume of weld in the 16 specimen rings (in mm3): 
16p  Dwp  S 10003  = 18610540.3277924 
Volumetric weld flaw density of flaws after UT inspection and repair: 
.bm := 
.dmut25 
8S 
.bm = 21.2339 flaws /m3 
Probability on the number of flaws in the Alloy 22 barrier of a WP: See Equation 39 of 
Section 6.2.2. 
Volume of base metal affected: Vrbm := 0.1 0.1 0.02 Vrbm = 210 - 4 m3
 
-
Pnbm(n ,.bm, Vwp) := 1Fbm + Fbmppois (n ,.bmVwp)
- 3
= 4.2468 10
.bm Vrbm
- 3 - 6
= 2.017 10 Fbm .bmVrbm = 8.5659 10
Fbm 
Probability of having at least one flaw on a randomly selected WP: 
- ,,= 8.5477 10- 6 (rigorous evaluation)
1Pnbm(0 .bm Vrbm)
= 8.5659 10- 6 (simpler evaluation)
Fbm .bm Vrbm 
CAL-EBS-MD-000030 REV 00C I-26 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Characterization of anomaly distribution curve in base-metal titanium used for the drip 
shield: 
Express the Anomaly distribution curve in units of the metric system: 
See Section 4.1.4 
defect inspection area in square mils put in Column 0 of Matrix E
Exceedance probability per million pounds of titanium put in Column 1 of Matrix E
E := 
.
..........................
.
100 
200 
300 
400 
500 
600 
700 
800 
900 
1000 
2000 
3000 
4000 
5000 
6000 
7000 
8000 
9000 
10000 
20000 
6.6 
3.6 
2.6 
2.0 
1.7 
1.3 
1.1 
0.90 
0.75 
0.65 
0.21 
0.084 
0.051 
0.037 
0.028 
0.022 
0.020 
0.017 
0.016 
0.010 
. 
.......................
. 
.
<>
<>
Anomalies are spherically shaped so their diameter in mm is: M0:= 0.0254 2  
E0
 
p 
The number of defect per million pound of titanium is converted to the number of defect per million 
kg of titanium. Also, the number if multiplied by 2 to account for both low- and high-density 
inclusions. 
CAL-EBS-MD-000030 REV 00C I-27 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
<>
<>  
M1:= 
2E1
0.45359237
In the metric system, the set of data points for the anomaly distribution curve is: 
Column 0: diameter of the defect in mm 
Column 1: expected number of defects per 
million kg of titanium
M = 
0 1 
0 0.2866 29.101 
1 0.4053 15.8733 
2 0.4964 11.464 
3 0.5732 8.8185 
4 0.6409 7.4957 
5 0.702 5.732 
6 0.7583 4.8502 
7 0.8107 3.9683 
8 0.8598 3.3069 
9 0.9063 2.866 
10 1.2818 0.9259 
11 1.5698 0.3704 
12 1.8127 0.2249 
13 2.0266 0.1631 
14 2.2201 0.1235 
15 2.3979 0.097 
16 2.5635 0.0882 
17 2.719 0.075 
18 2.8661 0.0705 
19 4.0533 0.0441 
A linear interpolation on a log-log scale is done to these data to get the anomaly exceedance 
curve for any defect size. 
<> ( <>
(( () )
10linterp log M 0), log M 1), log x
dx
() := 
CAL-EBS-MD-000030 REV 00C I-28 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
0.1 10.01 
0.1 
1 
10 
100 
1 .103 
dx() 
10 
x
Figure I. 8 Titanium Weld Anomaly Distribution Curve 
The density of inclusions in the DS is obtained by multiplying the function above by the mass of 
the DS, expressed in million kg. 
mds := 0.005 million kg of titanium (see table 3 of Section 4.1.1) 
1
0.1 
dx
() mds 0.01 
1 .10 3
1 .10 4
0.1 1 10
x
Figure I. 9 Titanium Mass Weld Anomaly Distribution Curve 
CAL-EBS-MD-000030 REV 00C I-29 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Probability on the number of flaws in the DS: 
.5 mm 1 mm 
(, () mds )= 0.945 dpois 0 d 1
0 flaw dpois 0 d.5 (, () mds )= 0.9897
- 2 - 2
(, () mds )= 5.3462 10 dpois 1 d 1 
1 flaw dpois 1 d.5 (, () mds )= 1.0292 10
- 3 - 5
(, ( (, () mds )= 5.3699 10
2 or more flaws 1 - ppois 1 d 0.5)mds )= 1.5412 10 1 - ppois 1 d 1
CAL-EBS-MD-000030 REV 00C I-30 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Fitting of distribution related to defective WP due to improper heat treatment, improper 
laser peening, or damage by mishandling to lognormal distribution 
mean of distribution: m := 2.8 10 - 5 
 

95th percentile: m95 := 1.1 10 - 4 
Lognormal fitting performed by keeping the mean value and calculating the error factor that 
approximates the 95th percentile above. 
Call f(x) the function defined by: 
() :=
fxm95 
- 
mx
 
exp -0.5 
..
. 
..
.
2
ln x
()
.
.
. 
.
.
1.645 
1 .10 7 
1 .10 6 
1 .10 5 
1 .10 4 
fu() 
5 1015202530 
u 
Figure I.10 Minimum Error Factor Determination Curve 
x5
:= 
Minimize f , x) = 14.9697
( 
Take EF := 15 
the median of the lognormal distribution is: 
ml := 
...
m exp 
 
-0.5
..
.
.
.
. 
2
ln EF
()
.
.
1.645 
- 6
ml = 7.2222 10 
- 7
95th percentile is: ml EF = 1.0833 10- 4 5th percentile: ml 
EF 
 = 4.8148 10 
percentile of the lognormal distribution at the upper value yielded by Saphire results: 
... 
- 3 ( 
ln 15
()
plnorm 7.4421310 , ln 7.2 10 - 6)
.
.
= 0.99999
 
, 
1.645 
CAL-EBS-MD-000030 REV 00C I-31 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
INTENTIONALLY LEFT BLANK 
CAL-EBS-MD-000030 REV 00C I-32 of I-32 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
ATTACHMENT II: LISTING OF FILES ON CD-ROM 
CAL-EBS-MD-000030 REV 00C II-1 of II-4 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Listing of Files Contained In Compressed Folder Early Failure SAPHIRE.zip (Part 1 of 3) 
CAL-EBS-MD-000030 REV 00C II-2 of II-4 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Listing of Files Contained In Compressed Folder Early Failure SAPHIRE.zip (Part 2 of 3) 
CAL-EBS-MD-000030 REV 00C II-3 of II-4 August 2004 

Analysis of Mechanisms for Early Waste Package/Drip Shield Failure 
Listing of Files Contained In Compressed Folder Early Failure SAPHIRE.zip (Part 3 of 3) 
CAL-EBS-MD-000030 REV 00C II-4 of II-4 August 2004