Roache,
P. J.
, 1998, Verification and Validation in Computational Science,
Hermosa,
Albuquerque, NM.

Oberkampf,
W. L.
, and
Roy,
C. J.
, 2010, Verification and Validation in Scientific Computing,
Cambridge University Press,
Cambridge, UK.

Roy,
C. J.
, and
Oberkampf,
W. L.
, 2011, “
A Complete Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing,” Comput. Methods Appl. Mech. Eng.,
200(25–28), pp. 2131–2144.

[CrossRef]
Zipay,
J. J.
,
Modlin,
C. T.
, and
Larsen,
C. E.
, 2016, “
The Ultimate Factor of Safety for Aircraft and Spacecraft—Its History, Applications and Misconceptions,” AIAA Paper No. AIAA 2016-1715.

Ferson,
S.
,
Kreinovich,
V.
,
Ginzburg,
L.
,
Myers,
D. S.
, and
Sentz,
K.
, 2003, “
Constructing Probability Boxes and Dempster-Shafer Structures,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2002-4015.

Ferson,
S.
, and
Ginzburg,
L. R.
, 1996, “
Different Methods Are Needed to Propagate Ignorance and Variability,” Reliab. Eng. Syst. Saf.,
54(2–3), pp. 133–144.

[CrossRef]
Hoffman,
F. O.
, and
Hammonds,
J. S.
, 1994, “
Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability,” Risk Anal.,
14(5), pp. 707–712.

Ferson,
S.
, and
Tucker,
W. T.
, 2006, “
Sensitivity Analysis Using Probability Bounding,” Reliab. Eng. Syst. Saf.,
91(10–11), pp. 1435–1442.

[CrossRef]
Roy,
C. J.
, and
Balch,
M. S.
, 2012, “
A Holistic Approach to Uncertainty Quantification With Application to Supersonic Nozzle Thrust,” Int. J. Uncertainty Quantif.,
2(4), pp. 363–381.

[CrossRef]
Baraldi,
P.
, and
Zio,
E.
, 2008, “
A Combined Monte Carlo and Possibilistic Approach to Uncertainty Propagation in Event Tree Analysis,” Risk Anal.,
28(5), pp. 1309–1326.

Baudrit,
C.
,
Dubois,
D.
, and
Guyonnet,
D.
, 2006, “
Joint Propagation and Exploitation of Probabilistic and Possibilistic Information in Risk Assessment,” IEEE Trans. Fuzzy Syst.,
14(5), pp. 593–608.

Kentel,
E.
, and
Aral,
M. M.
, 2005, “
2D Monte Carlo Versus 2D Fuzzy Monte Carlo Health Risk Assessment,” Stochastic Environ. Res. Risk Assess.,
19(1), pp. 86–96.

[CrossRef]
Ali,
T.
,
Boruah,
H.
, and
Dutta,
P.
, 2012, “
Modeling Uncertainty in Risk Assessment Using Double Monte Carlo Method,” Int. J. Eng. Innovative Technol.,
1(4), pp. 114–118.

Denoeux,
T.
, and
Li,
S.
, 2018, “
Frequency-Calibrated Belief Functions: Review and New Insights,” Int. J. Approximate Reasoning,
92, pp. 232–254.

[CrossRef]
Montgomery,
V. J.
,
Coolen,
F. P. A.
, and
Hart,
A. D. M.
, 2009, “
Bayesian Probability Boxes in Risk Assessment,” J. Stat. Theory Pract.,
3(1), pp. 69–83.Vol.

[CrossRef]AIAA 1998, “
Guide for the Verification and Validation of Computational Fluid Dynamics Simulations,” AIAA Paper No. AIAA-G-077-1998.

ASME, 2006, “
Guide for Verification and Validation in Computational Solid Mechanics,” ASME, New York, Standard No. V V 10-2006.

Gelman,
A.
,
Carlin,
J. B.
,
Stern,
H. S.
, and
Rubin,
D. B.
, 1995, Bayesian Data Analysis,
Chapman and Hall,
London.

Freeman,
J. A.
, and
Roy,
C. J.
, 2016, “
Global Optimization Under Uncertainty and Uncertainty Quantification Applied to Tractor-Trailer Base Flaps,” J. Verif., Validation Uncertainty Quantif.,
1(2), p. 021008.

Welch,
L. A.
,
Beran,
P. S.
, and
Freeman,
J. A.
, 2017, “
Computational Optimization Under Uncertainty of an Active Flow Control Jet,” AIAA Paper No. AIAA 2017-3913.

Syamlal,
M.
,
Celik,
I. B.
, and
Benyah,
S.
, 2017, “
Quantifying the Uncertainty Introduced by Discretization and Time‐Averaging in Two‐Fluid Model Predictions,” AIChE J,
63(12), pp. 5343–5360.

[CrossRef]
Black,
D. L.
, and
Ewing,
M. E.
, 2017, “
A Comprehensive Assessment of Uncertainty for Insulation Erosion Modeling,” 64th JANNAF Propulsion Meeting, Kansas City, MO, Paper No. 2017-0003AD.

Harmel,
R. D.
, and
Smith,
P. K.
, 2007, “
Consideration of Measurement Uncertainty in the Evaluation of Goodness-of-Fit in Hydrologic and Water Quality Modeling,” J. Hydrology,
337(3–4), pp. 326–336.

[CrossRef]
Johnson,
J. S.
,
Gosling,
J. P.
, and
Kennedy,
M. C.
, 2011, “
Gaussian Process Emulation for Second-Order Monte Carlo Simulations,” J. Stat. Plann. Inference,
141(5), pp. 1838–1848.

[CrossRef]
Sun,
S.
, 2010, “
Decision-Making Under Uncertainty: Optimal Storm Sewer Network Design Considering Flood Risk,” Ph.D. thesis, University of Exeter, Exeter, UK.

Simon,
T.
, 1999, “
Two-Dimensional Monte Carlo Simulation and Beyond: A Comparison of Several Probabilistic Risk Assessment Methods Applied to a Superfund Site,” Hum. Ecol. Risk Assess.,
5(4), pp. 823–843.

[CrossRef]
Ewing,
M. E.
, and
Isaac,
D. A.
, 2015, “
Mathematical Modeling of Multi-Phase Chemical Equilibrium,” J. Thermophys. Heat Transfer,
29(3), pp. 551–562.

[CrossRef]
Ewing,
M. E.
,
Laker,
T. S.
, and
Walker,
D. T.
, 2013, “
Numerical Modeling of Ablation Heat Transfer,” J. Thermophys. Heat Transfer,
27(4), pp. 615–632.

[CrossRef]
Ewing,
M. E.
,
Hernandez,
M. J.
, and
Griffin,
D. R.
, 2016, “
Thermal Property Characterization of an Ablative Insulator,” J. Propul. Energ.,
7(1), pp. 89–106.

Lachaud,
J. R.
,
Martin,
A.
,
van Eekelen,
A.
, and
Cozmuta,
I.
, (2012) “
Ablation Test-Case Series 2,” 5th Ablation Workshop, Lexington, KY, February 28 – March 1, No. AW05-051.