A Simple and Practical Application of Quantitative Risk Analysis in PBFSE
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A Simple and Practical Application of Quantitative Risk Analysis in Performance-Based Fire Safety Engineering

By Greg Baker


There is a growing awareness and focus, both in Europe and internationally, on risk analysis in fire safety engineering, particularly in relation toperformance-based fire safety engineering (PBFSE). To clarify the terminology, in this article PBFSE refers to alternative methods of achieving compliance with the fire safety performance requirements in legislation, where the ‘alternative methods’ differ from the pre-accepted solutions in the building regulations. The reality is that the majority of fire safety engineering involves a combination of a performance-based and pre-accepted approach. The other term to clarify in the context of this article is ‘quantitative risk analysis’ (QRA). Unpacking the term QRA word-by-word, ‘quantitative’ refers to describing the risk with numbers, ‘risk’ relates to the uncertainty that is inherent in PBFSE, and ‘analysis’ means some form of numerical analysis/assessment of the risk. In PBFSE, risk has two components – ‘probability’ and ‘consequences’, and when a risk analysis is conducted, the analyst answers three simple questions [1]:


  1. What can happen? (i.e., what can go wrong?) – this is called a ‘scenario’ in PBFSE
  2. How likely is it that will happen? – this is the probability component of risk
  3. If it does happen, what are the consequences? – this is the second component of risk.

A relevant question to ask at this point is “OK - how important is quantitative risk analysis in PBFSE?” The best way to answer that question is to quote Notarianni [2] who expresses the view that the “treatment of uncertainty is key to ensuring and maintaining an appropriate level of public safety while allowing the flexibility necessary to reduce costs.” In a similar vein, ISO 16732-1 [3] states that “all fire safety decisions involve uncertainty” and that “probabilities are the mathematical representation of uncertainty, and risk assessment is the form of fire safety analysis that most extensively uses probabilities and so most extensively addresses all types of uncertainty.”

Another related question is “where does this uncertainty in PBFSE come from?” Several authors and publications describe the sources of uncertainty, but the document that best summarises the issue is the International Fire Engineering Guidelines (IFEG) [4], which lists the following sources:

  • Applying engineering judgement to quantify design fires
  • Lack of quantification of performance requirements
  • Deficiencies in methods and data to evaluate whether acceptance criteria have been met
  • Input data
  • Uncertainties inherent in methods used
  • Poor conceptualisation of the problem being investigated
  • Inadequate formulation of conceptual or computational model being used
  • Calculation and document errors

The focus of this article is the first of these items, namely the subjectivity that applies when quantifying design fires. The traditional approach to quantifying the design fire(s) to use in deterministic ASET/RSET modelling is to take a parametric approach, as follows:

  1. Select an alpha-t-squared fire for the occupancy in question to represent the growth phase of the fire.
  2. Determine the ventilation-limited HRR that will apply for the compartment of fire origin.
  3. Use the design fire load density for the occupancy to determine the duration of the post-flashover, fully-developed phase of the fire.
  4. Apply some generic decay phase algorithm, also based on the fire load density from step 3.

The problem with this approach is described by Fleischmann [5] who notes that if only a few specific scenarios are considered and single-point values for key design parameters incorporated into the calculation procedures, no allowance is made for the probability of these scenarios occurring or the uncertainty/variability of input parameters [6]. Even if you apply a factor of safety, you still cannot say confidently what level of safety is being achieved by the fire engineering design.

A new QRA fire modelling tool, called B-RISK [7], has been developed which provides a rational way to address these concerns. To firstly describe the general QRA functionality in B-RISK, the model uses a combination of iterative Monte Carlo simulation and deterministic zone modelling. Essentially how it works is that for each Monte Carlo iteration B-RISK samples from distributions for key input parameters, and then calculates a value for the different tenability criteria (the ASET part of the analysis). By doing multiple (say, one thousand) Monte Carlo iterations a probability distribution for each tenability criterion is produced – specifically a cumulative distribution function (or cdf for short). If, for example, you want to avoid a threshold value for the tenability criterion in 90% of cases, you simply determine the 90-percentile value from the cdf curve. It is obviously more complicated than this simple explanation, but this gives the flavour of the functionality of B-RISK.

With regard to design fires, B-RISK has a special module called the Design Fire Generator (DFG). The purpose of the DFG is to ‘generate’ a heat release rate (HRR) curve as input for each Monte Carlo iteration, rather than the model user inputting their own ‘subjective’ HRR curve. With the compartment of fire origin having been defined by the model user, the DFG then randomly populates that compartment with combustible items from an Item Database that are appropriate for the occupancy in question. The number of items is determined by the value of the fire load density that has been sampled, from a distribution, for that iteration. Each item has a number of parameters defined, including a HRR curve and ignition properties. Figure 1 shows an example of an armchair item and the various input data for the armchair

Once the DFG has populated the compartment with items, one item is randomly selected as the first item to ignite, and that burning items starts emitting radiation to adjacent items in the compartment, and a hot upper layer starts forming. As the fire develops, the radiation from the first item is sufficient to ignite secondary items. In Figure 1, there is ignition data for vertical surfaces (which accounts for radiation from the flames of burning items) and also horizontal surfaces (which accounts for radiation from the hot upper layer). As soon as secondary items ignite, their own HRR contributes to the accumulating HRR in the compartment – this is how the DFG ‘generates’ a HRR curve for each Monte Carlo iteration. Figure 2 shows an example of the HRR curves for 100 iterations.



It is a bit difficult to pick all the curves in Figure 2 but for this particular scenario, the ventilation limits the HRR to about 4.8 MW, and the duration of each curve is governed by the fire load density value selected for the particular iteration. The very lowest curve shows an example where only the first item ignited, peaked at approximately 200 kW, and then burnout without any other items getting involved. There is another curve where the ignition of a second item doesn’t occur until approximately 400 s, but then flashover occurs for that scenario.

In effect what happens with the multiple Monte Carlo iterations is that the whole range of possible scenarios is generated by the DFG. The model user (the fire safety engineer) therefore has a much better feel for the likelihood of different scenarios occurring, and can therefore make life safety decisions with more confidence. When compared to the simple QRA approached of B-RISK described here, a deterministic-only approach focuses just on the consequences component of risk, without any allowances being made for the likelihood of the scenario actually occurring. One problem that this can create is unnecessary investment in life safety, that is, spending money for very little benefit.

Greg Baker is with SP Fire Research AS, Trondheim, Norway


  1. Kaplan, S., & Garrick, B. J. (1981). On the Quantitative Definition of Risk. Risk Analysis, 1(1), 11-27. doi:10.1111/j.1539-6924.1981.tb01350.x
  2. Notarianni, K.A., (2002) Uncertainty. In: P.J. DiNenno, D. Drysdale, C.L. Beyler, W.D. Walton, R.P. Custer, J.R. Hall (Jr.), & J.M. Watts (Jr.), SFPE Handbook of Fire Protection Engineering, Section 5, Chapter 4 (3rd ed.), NFPA, Quincy, MA, USA
  3. ISO, (2012) International Standard ISO 16732-1:2012(E) Fire safety engineering – Fire risk assessment – Part 1: General, International Organization for Standardization, Geneva, Switzerland
  4. ABCB, (2005) International Fire Engineering Guidelines, Edition 2005, Australian Building Codes Board, Canberra, ACT
  5. Fleischmann, C.M., (2011) Is prescription the future of performance-based design?, In: M. Spearpoint, Fire Safety Science – Proceedings of the Tenth International Symposium, College Park, MD, USA, IAFSS, pp. 77-94
  6. Baker, G., Frank, K., Spearpoint, M., Fleischmann, C., and Wade, C., (2013) The next generation of performance-based fire safety engineering in New Zealand. In: S. Kajewski, K. Manley, and K. Hampson, Proceedings of the 19th International CIB World Building Congress, Brisbane, QLD, Australia, May 2013, Queensland University of Technology, QLD, Australia
  7. Wade, C., Baker, G., Frank, K., Robbins, A., Harrison, R., Spearpoint, M., and Fleischmann, C., (2013) B-RISK user guide and technical manual, BRANZ Study Report SR 282, BRANZ Ltd, Porirua, New Zealand
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