Statistical methods in risk evaluation

Response surface modelling of monte carlo fire data

“…Therefore, an advanced engineering methodology for the cost -effective design of fire safety and protection in buildings has been proposed and widely accepted [5]. The risk analysis should incorporate an uncertainty analysis because many variables of fire are associated with uncertainty [3][71] [72] [73]. However, a detailed methodology for implementing a realistic risk analysis, which can nevertheless be used by practising engineers, has not been developed to date.…”

“…The current compartment flame spread model assumes that the lateral flame spread rate depends on the net external radiative heat flux to the combustible and the oxygen (O 2 ) concentration in the compartment [6]: where Y O2i is the oxygen mass fraction in the compartment and V f is the lateral flame spread velocity. V fo is the radiation-dependent flame velocity, given by: Heat fed back to the fuel by the compartment enclosure can be expressed as: [3][4] where σ is the Stefan Boltzmann constant (W/m 2 K 4 ), ε is the gas emissivity, and T, T W and T S are the gas, inner wall and fuel surface temperatures, respectively.…”

“…Cooper and Yung modified the above R by taking into account the reduction in mass loss rate due to oxygen concentration and fuel consumption as follows: [3][4][5][6][7][8][9][10] where Y o2F is the mass fraction of post-combustion oxygen, m o is the initial mass of the fuel and m c is the mass of fuel that has been consumed by the fire. n = 1 at CESARE-RISK model for CESARE-Risk's experimental building fire facility instead of Cooper and Yung's n = 2 (see [18]).…”

“…Input parameter distributions were subjectively quantified and classified with respect to category: knowledge or stochastic uncertainty. Risk assessment results comprised probability of failure, reliability index and complementary cumulative distribution function for evacuation time-margin deficit [3][71] [72][73] [74]. Of special interest is the calculation of confidence intervals for the distribution of complementary cumulative distribution functions obtained by the two-phase Monte Carlo sampling procedure, allowing a distinction between knowledge and stochastic uncertainty.…”

“…The mass loss rate R of the fuel for flaming fires depends on the ignited area, the concentration of oxygen in the burning environment and the radiative heat flux to the fuel [18]. (3)(4)(5)(6)(7)(8) where m ideal is the free vaporization/pyrolysis rate of the fuel (kg/m 2 s) and ∆r is the enhancement to the mass loss rate due to heat radiation by the compartment walls: (3)(4)(5)(6)(7)(8)(9) where ∆H v is the heat of vaporization (J/kg fuel).…”