The motivation for this work is the need to analyze the behavior of an engineering system subjected to the hostile environment of a fire. The specific goal is to estimate the survivability of a component potted in insulating foam. The foam undergoes an endothermic reaction and through this heat sink protects the component. Because the operating conditions are stochastic and because the properties of the foam can only be estimated, the usual deterministic analysis cannot be used. Instead, Bayesian inference is used to estimate the critical foam parameters and the operating conditions are described in terms of probabilities. The survivability is then expressed in terms of a probability distribution. Because the computations are very computationally expensive, recourse was made by expressing the computed results as a response surface defined in terms of a Gaussian process.

1.
Dowing, K. J., Hills. R. G., Leslie, I., Pilch, M., Rutherford, B. M., Hobbs, M. L., 2004, “Case Study for a Model Validation: Assessing a Model for Thermal Decomposition of Polyurethane Foam”, SAND2004–3632, Sandia National Laboratories, Albuquerque, NM
2.
Emery, A. F., Bardot. D., Modeling the response of a transient thermal system using Gaussian process,” Proc of IMECE 2005 ASME International Mechanical Engineering Congress and Exposition, Washington DC
3.
Emery
A. F.
,
Blackwell
B. F.
and
Dowding
K. J.
,
2002
, “
The Relationship Between Information, Sampling Rates, and Parameter Estimation Models
,”
ASME Journal of Heat Transfer}
,
124
(
6)
, pp.
1192
9
4.
Gelman, A., Carlin, J. B., Stern, H. S., Rubin, D. B., 2004, Bayesian Data Analysis, Chapman and Hall/CRC, Boca Raton, FL
5.
Haylock, R. G., O’Hagan, A., 1995, “Bayesian Uncertainty Analysis and Radiological Protection,” Statistics for the Environment 3: Pollution Assessment and Control (eds V. Barnett and K. F. Turkman), pp 109-128, Oxford University Press, Oxford
6.
Hobbs, M. L., Lemmon, G. H., 2003, “SPUF-a Simple Polyurethane Foam Mass Loss and Response Model”, SAND2003–2099, Sandia National Laboratories, Albuquerque, NM
7.
Kalagnanam, J. R., Diwekar., U. M., 1997, “An Efficient Sampling Technique for Off-line Quality Control”, Technometrics, v 39, n 3
8.
Oakley
JE
,
O’Hagan
A.
,
2004
, “
Probabilistic sensitivity analysis of complex models: a Bayesian approach
”,
J Roy Stat Soc Ser B
2004
;
66
:
751
69
, 2004
9.
Lee, P. M., 2004 Bayesian Statistics an Introduction, Oxford University Press, NY, NY
10.
Mathworks.com 16 June 2006. <http://www.mathworks.com/access/helpdesk/help/toolbox/stats/normpdf.html>
11.
R Project, 2004, The R project for Statistical computing, <www.r-project.com>
12.
Sivia, D. S., 1997, Data Analysis, A Bayesian Tutorial, Clarendon Press, Oxford, UK.
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