Applications of p-boxes and probability bounds analysis

P-boxes and probability bounds analysis have been used in many applications spanning many disciplines in engineering and environmental science, including:

• Engineering design^[1]
• Expert elicitation^[2]
• Analysis of species sensitivity distributions^[3]
• Sensitivity analysis in aerospace engineering of the buckling load of the frontskirt of the Ariane 5 launcher^[4]
• ODE models of chemical reactor dynamics^[5][6]
• Pharmacokinetic variability of inhaled VOCs^[7]
• Groundwater modeling^[8]
• Bounding failure probability for series systems^[9]
• Heavy metal contamination in soil at an ironworks brownfield^[10][11]
• Uncertainty propagation for salinity risk models^[12]
• Power supply system safety assessment^[13]
• Contaminated land risk assessment^[14]
• Engineered systems for drinking water treatment^[15]
• Computing soil screening levels^[16]
• Human health and ecological risk analysis by the U.S. EPA of PCB contamination at the Housatonic River Superfund site^[17][18]
• Environmental assessment for the Calcasieu Estuary Superfund site^[19]
• Aerospace engineering for supersonic nozzle thrust^[20]
• Verification and validation in scientific computation for engineering problems^[21]
• Toxicity to small mammals of environmental mercury contamination^[22]
• Modeling travel time of pollution in groundwater^[23]
• Reliability analysis^[24]
• Endangered species assessment for reintroduction of Leadbeater's possum^[25]
• Exposure of insectivorous birds to an agricultural pesticide^[26]
• Climate change projections^[10][27][28]
• Waiting time in queuing systems^[29]
• Extinction risk analysis for spotted owl on the Olympic Peninsula^[30]
• Biosecurity against introduction of invasive species or agricultural pests^[31]
• Finite-element structural analysis^[32][33]
• Cost estimates^[34]
• Nuclear stockpile certification^[35]
• Fracking risks to water pollution^[36]

References

1. Aughenbaugh, J. M., and C.J.J. Paredis (2007). Probability bounds analysis as a general approach to sensitivity analysis in decision making under uncertainty. SAE 2007 Transactions Journal of Passenger Cars: Mechanical Systems, (Section 6) 116: 1325–1339, SAE International, Warrendale, Pennsylvania.
2. Flander, L., W. Dixon, M. McBride, and M. Burgman. (2012). Facilitated expert judgment of environmental risks: acquiring and analysing imprecise data. International Journal of Risk Assessment and Management 16: 199–212.
3. Dixon, W.J. (2007). The use of Probability Bounds Analysis for Characterising and Propagating Uncertainty in Species Sensitivity Distributions. Technical Report Series No. 163, Arthur Rylah Institute for Environmental Research, Department of Sustainability and Environment. Heidelberg, Victoria, Australia.
4. Oberguggenberger, M., J. King and B. Schmelzer (2007). Imprecise probability methods for sensitivity analysis in engineering. Proceedings of the 5th International Symposium on Imprecise Probability: Theories and Applications, Prague, Czech Republic.
5. Enszer, J.A., Y. Lin, S. Ferson, G.F. Corliss and M.A. Stadtherr (2011). Probability bounds analysis for nonlinear dynamic process models. AIChE Journal 57: 404–422.
6. Enszer, Joshua Alan, (2010). Verified Probability Bound Analysis for Dynamic Nonlinear Systems. Dissertation, University of Notre Dame.
7. Nong, A., and K. Krishnan (2007). Estimation of interindividual pharmacokinetic variability factor for inhaled volatile organic chemicals using a probability-bounds approach. Regulatory Toxicology and Pharmacology 48: 93–101.
8. Guyonnet, D., F. Blanchard, C. Harpet, Y. Ménard, B. Côme and C. Baudrit (2005). Projet IREA—Traitement des incertitudes en évaluation des risques d'exposition, Annexe B, Cas «Eaux souterraines». Rapport BRGM/RP-54099-FR, Bureau de Recherches Géologiques et Minières, France.
9. Fetz, T., and F. Tonon (2008). Probability bounds for series systems with variables constrained by sets of probability measures. International Journal of Reliability and Safety 2: 309–339. doi:10.1504/IJRS.2008.022079.
10. Augustsson, A., M. Filipsson, T. Öberg, B. Bergbäck (2011). Climate change—an uncertainty factor in risk analysis of contaminated land. Science of the Total Environment 409: 4693–4700.
11. Baudrit, C., D. Guyonnet, H. Baroudi, S. Denys and P. Begassat (2005). Assessment of child exposure to lead on an ironworks brownfield: uncertainty analysis. 9th International FZK/TNO Conference on Contaminated Soil – ConSoil2005, Bordeaux, France, pages 1071–1080.
12. Dixon, W.J. (2007). Uncertainty Propagation in Population Level Salinity Risk Models. Technical Report Technical Report Series No. 164, Arthur Rylah Institute for Environmental Research. Heidelberg, Victoria, Australia
13. Karanki, D.R., H.S. Kushwaha, A.K. Verma, and S. Ajit. (2009). Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment. Risk Analysis 29: 662–75.
14. Sander, P., B. Bergbäck and T. Öberg (2006). Uncertain numbers and uncertainty in the selection of input distributions—Consequences for a probabilistic risk assessment of contaminated land. Risk Analysis 26: 1363–1375.
15. Minnery, J.G., J.G. Jacangelo, L.I. Boden, D.J. Vorhees and W. Heiger-Bernays (2009). Sensitivity analysis of the pressure-based direct integrity test for membranes used in drinking water treatment. Environmental Science and Technology 43(24): 9419–9424.
16. Regan, H.M., B.E. Sample and S. Ferson (2002). Comparison of deterministic and probabilistic calculation of ecological soil screening levels. Environmental Toxicology and Chemistry 21: 882–890.
17. U.S. Environmental Protection Agency (Region I), GE/Housatonic River Site in New England
18. Moore, D.R.J., R.L Breton, T.R DeLong, S. Ferson, J.P Lortie, D.B MacDonald, R. McGrath, A. Pawlisz, S.C Svirsky, R.S. Teed, R.P Thompson, and M. Whitfield Aslundz (2015). Ecological risk assessment for mink and short-tailed shrew exposed to PCBs, dioxins, and furans in the Housatonic River area. Integrated Environmental Assessment and Management. doi:10.1002/ieam.1661.
19. U.S. Environmental Protection Agency (Region 6 Superfund Program), Calcasieu Estuary Remedial Investigation
20. Roy, C.J., and M.S. Balch (2012). A holistic approach to uncertainty quantification with application to supersonic nozzle thrust. International Journal for Uncertainty Quantification 2: 363-381. doi:10.1615/Int.J.UncertaintyQuantification.2012003562.
21. Oberkampf, W.L., and C. J. Roy. (2010). Verification and Validation in Scientific Computing. Cambridge University Press.
22. Regan, H.M., B.K. Hope, and S. Ferson (2002). Analysis and portrayal of uncertainty in a food web exposure model. Human and Ecological Risk Assessment 8: 1757–1777.
23. Ferson, S., and W.T. Tucker (2004). Reliability of risk analyses for contaminated groundwater. Groundwater Quality Modeling and Management under Uncertainty, edited by S. Mishra, American Society of Civil Engineers Reston, VA.
24. Crespo, L.G., S.P. Kenny, and D.P. Giesy (2012). Reliability analysis of polynomial systems subject to p-box uncertainties. Mechanical Systems and Signal Processing 37: 121–136. doi:10.1016/j.ymssp.2012.08.012
25. Ferson, S., and M. Burgman (1995). Correlations, dependency bounds and extinction risks. Biological Conservation 73: 101–105.
26. Ferson, S., D.R.J. Moore, P.J. Van den Brink, T.L. Estes, K. Gallagher, R. O'Connor and F. Verdonck. (2010). Bounding uncertainty analyses. Pages 89–122 in Application of Uncertainty Analysis to Ecological Risks of Pesticides, edited by W. J. Warren-Hicks and A. Hart. CRC Press, Boca Raton, Florida.
27. Kriegler, E., and H. Held (2005). Utilizing belief functions for the estimation of future climate change. International Journal of Approximate Reasoning 39: 185–209.
28. Kriegler, E. (2005). Imprecise probability analysis for integrated assessment of climate change, Ph.D. dissertation, Universität Potsdam, Germany.
29. Batarseh, O.G.Y., (2010). An Interval Based Approach to Model Input Uncertainty in Discrete-event Simulation. Ph.D. dissertation, University of Central Florida.
30. Goldwasser, L., L. Ginzburg and S. Ferson (2000). Variability and measurement error in extinction risk analysis: the northern spotted owl on the Olympic Peninsula. Pages 169–187 in Quantitative Methods for Conservation Biology, edited by S. Ferson and M. Burgman, Springer-Verlag, New York.
31. Hayes, K.R. (2011). Uncertainty and uncertainty analysis methods: Issues in quantitative and qualitative risk modeling with application to import risk assessment ACERA project (0705). Report Number: EP102467, CSIRO, Hobart, Australia.
32. Zhang, H., R.L. Mullen, and R.L. Muhanna (2010). Finite element structural analysis using imprecise probabilities based on p-box representation. Proceedings of the 4th International Workshop on Reliable Engineering Computing (REC 2010).
33. Zhang, H., R. Mullen, R. Muhanna (2012). Safety Structural Analysis with Probability-Boxes. International Journal of Reliability and Safety 6: 110–129.
34. Mehl, C.H. (2013). P-boxes for cost uncertainty analysis. Mechanical Systems and Signal Processing 37: 253–263. doi:10.1016/j.ymssp.2012.03.014
35. Sentz, K., and S. Ferson (2011). Probabilistic bounding analysis in the quantification of margins and uncertainties. Reliability Engineering and System Safety 96: 1126–1136.
36. Rozell, Daniel J., and Sheldon J. Reaven (2012). Water pollution risk associated with natural gas extraction from the Marcellus Shale. Risk Analysis 32: 1382–1393.