6.5. VADER: Trending Analysis for Code/Data Validation
S. Hart, J. Clarity
VADER (Validation Analysis Data Evaluation Resource) is a new module in SCALE 6.3 derived from the legacy USLSTATS program. VADER is a tool that allows the determination of bias and bias uncertainty for criticality safety computational methods. The older USLSTATS program, written in Java, existed outside of SCALE and provided tools to calculate only the confidence band with administrative margin (sometimes called USL1) and the singlesided uniform width closed interval (USL2). For normality testing it offered only a crude chisquared normality test that had no userconfigurable options and presented a simple pass/nopass functionality.
VADER has been completely written in C++ using modern coding practices and standards. It has been moved to be part of the SCALE code package and is run through the normal SCALE executables. To support the VADER methods, large updates were made to the statistical capabilities of SCALE. Interfaces to known statistical distributions were added and many of the statistical calculations required for VADER were made available to all SCALE sequences. In addition to being able to process legacy USLSTATS inputs, VADER adds support for the singlesided tolerance band method (from NUREG/CR6698) as well as two nontrending methods: the “historical” nonparametric and parametric methods, also as described in NUREG/CR6698. VADER also includes several new tests for normality in addition to adding user control options on the original chisquared normality test. A new ttest for the statistical significance of the trend is included.
VADER has also been integrated into the Fulcrum GUI used by SCALE. This allows VADER to benefit from the autocomplete, templating, and input validation features offered by Fulcrum. In addition, Fulcrum can plot the results given by VADER, and the plot files have been expanded to include the new methods available in VADER.
6.5.1. Theory
The methods and theory for VADER are largely taken from NUREG/CR6698. That document contains equations and descriptions of the methods used in VADER. It also includes working examples, some of which data was used to verify the results and create example problems for VADER.
6.5.2. Input
The VADER input is based on the SON input syntax common in other modernized SCALE codes such as ORIGEN and ORIGAMI. The SON input format consists of key/value pairs where the value can be either a single item, an array of items, or other SON blocks.
The VADER input generally just has one level of depth. There are no SON blocks inside of SON blocks. All input is mostly arrays at the top level of the tree. A quick look at all the top level items is given in Table 6.5.1. Each top level input will then be described in detail in the next section.
Keyword 
Required 
Description 
Yes 
Data entered in triplets in the form 

No 
Title to give the case. 

No 
Global parameters that apply to each test or trend. 

No 
User desired trend values to run the tests on. 

Yes 
Methods that the user wishes to apply to the data. 

No 
Statistical checks that the user wishes to apply to the data. 
6.5.3. Detailed Input
6.5.3.1. data
The data
input array is a flat array consisting of data triplets. There is
no punctuation between the triplets. The data is entered in the order
\(X_1 \, Y_1 \, \sigma_1 \; X_2 \, Y_2 \, \sigma_2 \; ... \; X_N \, Y_N \, \sigma_N\).
Where
X 
The trended value, usually something like enrichment or moderator density. 
Y 
The y value, usually something like C/E or eigenvalue. 
\(\sigma\) 
The standard deviation of Y. 
VADER will emit an error if the number of entries in this array is not divisible by three.
data=[2.4 0.9976 0.00122 2.6 0.9978 0.00022
...
1.9 1.0011 0.00213 1.99 1.013 0.00012]
6.5.3.2. title
The title
entry allows the user to specify a title for the case. The title
is cosmetic and doesn’t affect any of the results. The title is echoed to the
output in several places and is included on some of the graphs generated by
VADER.
title="My Very First VADER Case"
6.5.3.3. parameters
The parameters
section can exist outside of any test or method. If a parameter
is listed in this global section, then it will apply to any method or test that has
that parameter available instead of the default value. Values in this global
parameters
section can be overridden in the specific method or test block for
which the user wishes to override the global parameter. For a list of all
parameters, their default values, and which tests and methods they are applied
to, see Sect. 6.5.6.
parameters {extrapolate=yes admin_margin=0.03}
6.5.3.4. trend_values
This array allows the user to insert values at which they wish the trend Y (typically the upper subcritical limit) values to be calculated. Extrapolation outside of the data range is only available if the method supports it and extrapolation is enabled.
trend_values=[0.1 0.2 2.4 10.0]
6.5.3.5. methods
This is where the user specifies the methods to enable and, optionally, gives methodspecific parameters. Each method is followed by an array of the parameters the user wishes to set. Any omitted parameters are initialized with the default value (see Table 6.5.2). If the user wishes to enable a method with all default values, then an empty array can be given.
methods {
USL1 {} % uses default parameters
CR6698 {weighted=yes admin_margin=0.03 chi_p=0.97}
Parametric {confidence=0.9}
}
6.5.3.6. tests
This block is similar to the methods block, but it allows the user to specify which tests they wish to enable. These tests are run on the data and generally either pass or fail and give a few statistical values as their result. Most of the tests implemented for VADER for now are normality tests.
tests {
chisq {} % default parameters
ttest {confidence=0.98}
}
6.5.4. Available Methods
The sections below indicate the input name to be used to activate the available method. Details on the methods can currently be found in NUREG/CR6698.
6.5.4.1. USL1
 Confidence Band with Administrative Margin
6.5.4.2. USL2
 SingleSided Uniform Width Closed Interval Approach
6.5.4.3. CR6698
 SingleSided Lower Tolerance Band
6.5.4.4. NonParametric
 Historical NonParametric Method
6.5.4.5. Parametric
 Historical Parametric Method
6.5.5. Available Tests
The sections below indicate the input name to be used to activate the available test. Details on the tests can currently be found in NUREG/CR6698.
6.5.5.1. chisq
 \(\chi^2\) Normality Test
6.5.5.2. ttest
 Trend Significance ttest
6.5.5.3. anderson_darling
 AndersonDarling Normality Test
6.5.6. Available Parameters
Table 6.5.2 shows all of the available parameters, their default
value, and the methods and tests to which they apply. Any parameter can be
put into the global parameters
block. Only
parameters that apply to a specific method or test can be put into that method
or tests parameters
block. Following the table is a more detailed description
of each parameter.
Keyword 
Default Value 
Available In 
Off 
USL1 USL2 

Off 
USL1 

0.95 
USL1 USL2 

0.05 
USL1 USL2 CR6698 NonParametric Parametric 

All X Values 
USL1 USL2 CR6698 NonParametric Parametric 

0.95 
USL2 

0.95 
USL2 

0.95 
CR6698 

0.95 
CR6698 

0.95 
CR6698 

No 
CR6698 NonParametric Parametric 

0.95 
NonParametric Parametric 

0.95 
NonParametric Parametric 

No 
NonParametric 
6.5.6.1. tsunami
This enables a TSUNAMImode calculation for VADER. It requires that all X values be between 1.0 and 1.0.
6.5.6.2. extrapolate
This allows extrapolation past the data values entered by the user. This is generally only applicable when the user has input values in the trend_values block.
6.5.6.3. fit_confidence
Confidence in the statistical result. Sometimes referred to as \(1  \gamma\). In USL1 this is used to calculated the tstatistic quantile.
6.5.6.4. admin_margin
Administrative margin subtracted from the result. This can be used to add an extra layer of confidence that the value reported is below criticality.
6.5.6.5. xrange
Allows the user to tailor X values for each method or test or change the values for all tests without having to change the data block. Data is entered as an array of two values. By default all of the X values are used.
xrange=[0.5 2.5]
6.5.6.6. proportion_confidence
In USL2 this controls the confidence on the proportion that is in the confidence band.
6.5.6.7. proportion
In USL2 this controls the proportion of the data points that will be inside the confidence band.
6.5.6.8. f_p
The percentile used for the Fdistribution in the singlesided lower tolerance band method.
6.5.6.9. normal_p
The percentile used for the normal distribution in the singlesided lower tolerance band method.
6.5.6.10. chi_p
The percentile used for the \(\chi^2\) distribution in the singlesided lower tolerance band method.
6.5.6.11. weighted
Whether to use the weighted version of the mean and standard deviation equations when calculating the statistics for this method.
6.5.6.12. confidence
Statistical confidence that the proportion calculated to be above the cutoff is correct.
6.5.6.13. proportion_of_pop
Proportion of the population that will be above the cutoff value in the nonparametric method.
6.5.6.14. use_npm
Use (add) nonparametric margin to the nonparametric method.