QUANTITIVE SENSITIVITY AND IMPORTANCE ANALYSIS OF PARAMETERS IN MONTE CARLO MODELS Page: 1 of 3
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SAiO a17l m'ocik
Quantitative Sensitivity and Importance Analysis
of Parameters in Monte Carlo Models
Sean A. McKenna and Bill W. Arnold
Sandia National Laboratories
P. O. Box 5800, MS-1324
Albuquerque, NM 87185-1324
In a performance assessment of a nuclear waste
repository, the modeling of many subsystems and pro-
cesses is accomplished using Monte-Carlo methods.
Monte-Carlo techniques are necessary to assess the magni-
tude of uncertainty in system or subsystem performance
due to uncertainty in parameters. In all cases, it is desir-
able to determine the relative importance of the various
input parameters through a sensitivity analysis. While
results may be sensitive to various parameters, those
parameters only become important if they also control reg-
ulatory failure or acceptance of the model results. The sen-
sitivity and importance analysis results can then be used to
guide further site characterization activities and/or to deter-
mine if the given uncertainty in a parameter is consequen-
tial to the overall performance assessment.
II. SENSITIVITY ANALYSIS
In many cases, sensitivity analyses performed on the
results of nuclear waste repository performance assessment
calculations have focused on parameter sensitivity to all
model results regardless of any regulatory driver (e.g., ').
The difficulty with this approach is that while model results
may be sensitive to a given parameter, if all results are still
below (or above) the regulatory limit, then the final regula-
tory decision is insensitive to that parameter, and the
importance of that parameter in future modeling or site
characterization studies may be negligible.
A smaller volume of work (e.g., 2) has considered a
regulatory constraint in determining the sensitivity and
importance of parameters in Monte Carlo models. Gener-
alized sensitivity analysis (GSA)3 is a technique that con-
siders the sensitivity of model parameters to the final
regulatory decision against which the model results are
being judged. GSA has recently been used in a decision
analysis of different approaches to aquifer remediation4 but
has not been applied to sensitivity analysis of nuclear waste
repository performance assessment models.
The essence of GSA is the placement of each vector
of model input parameters into one of two sample sets:
those that produced model results that failed the regulatory
requirement and those that produced model results that
passed the regulatory requirement. This behavioral classi-
fication of the input vectors into two sample sets allows for
the quantitative examination of the differences between the
two sample sets as a function of any parameter contained
within the input vectors. This process allows for determi-
nation of whether or not the differences between a "fail"
sample set of input parameters and a "pass" sample set is
significant and also for the relative ranking of all input
parameters in terms of the sensitivity of the results to the
given parameter. For those parameters where the distribu-
tion of values in the fail sample set is statistically indistin-
guishable from those in the pass the sample set, the model
results are insensitive to that parameter.
An example GSA of input parameters to an analytical
solution for solute transport through a single fracture with
matrix diffusion and sorption onto the matrix is presented.
Given a continuous source, the expression for the relative
concentration at the fracture outlet is 5:
= erfc[(DaPB) LQ
The hypothetical example problem to be addressed is
the time to a relative concentration (C/C,) of 0.90 when
there is uncertainty in the values of the distribution coeffi-
cient (Kd), the bulk density (pg), the length and width of
the fracture (L and W) and the flux through the fracture (Q).
The advective travel time (tadv,) is calculated using Q, L,
and the cross-sectional area of the fracture where the cross-
sectional area is calculated as (W * aperture) and aperture
is also considered an uncertain parameter. For this exam-
ple, 10,000 vectors of the 6 uncertain parameters were
drawn using the latin hypercube sampling program LHS6
and the program BETA*. The type of distribution and the
*. BETA: A visual BASIC program for calculation of beta
distributions, L. Yarrington, 1995, Sandia.
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McKenna, Sean A. & Arnold, Bill W. QUANTITIVE SENSITIVITY AND IMPORTANCE ANALYSIS OF PARAMETERS IN MONTE CARLO MODELS, report, February 18, 1998; Las Vegas, Nevada. (digital.library.unt.edu/ark:/67531/metadc724405/m1/1/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.