The Probability of Death in the Room of Fire Origin: an Engineering Formula

Abstract

The paper presents a partial safety factor approach to the problem of evaluating competing designs for fire safety in the room of fire origin in a building. A partial safety factor is defined as the ratio of the design value to the characteristic value for a load type variable and its inverse for a resistance type variable. The safety criterion considered is the expected number of deaths in the room or, alternatively, the probability of any death. A death is assumed to occur when the time, X between the occurrence of the alerting cue and the onset of untenable conditions is shorter than the time, Y to evacuation.

First, a safety index, β is obtained, based on the means and standard deviations of the logarithms of X and Y. Partial safety factors for X and Y can then be calculated.

It is further shown that there are theoretical reasons as well as empirical evidence for assuming that X and Y both have approximately a lognormal distribution. There is then a direct connection between the probability of death and the safety index β, which leads to a rationale for selecting appropriate values of β. A discussion of the choice criteria for characteristic values and code calibration procedure is also included.