Linking Safety Factor and Probability of Failure Based on Monte Carlo Simulation in Fire Safety Design

Abstract

Ensuring occupants’ safety in building fires is one of the most important aspects for fire safety engineering. Many uncertainties are inevitably introduced when estimating the occupant safety level, due to the high complexity of fire dynamics and the human behavior in fires. Safety factor methods are traditionally employed to deal with such uncertainties. This kind of methods is easy to apply but leaves fire safety engineers unsure of the margin by which the design has failed. An investigation of a method linking safety factors and probability of failure in building fire safety design is conducted in this paper. Given to ASET and RSET uncertainties, the concept of random safety factor is proposed as a random parameter. Once the distribution of the random safety factor is known, a specific random safety factor, whose cumulative probability corresponds to the target probability of failure, can then always be found within that distribution. A relationship between safety factors and the probability of failure can be established. Due to the complexity of ASET and RSET distributions, the distribution of the random safety factor is difficult to determine analytically. Instead, Monte Carlo simulation using Latin hypercube sampling is employed to determine the distribution of the random safety factor. A case study is presented to illustrate the usage of this method to calculate the required safety factor for a given target probability of failure, as well as determining the probability of failure for a selected safety factor.