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Uncertainty and Risk Analysis in Fire Safety Engineering Frantzich, Håkan Uncertainty and Risk Analysis in Fire Safety Engineering Frantzich, Håkan 1998 Link to publication Citation for published version (APA): Frantzich, H. (1998). Uncertainty and Risk Analysis in Fire Safety Engineering. Department of Fire Safety Engineering and Systems Safety, Lund University. Total number of authors: 1 General rights Unless other specific re-use rights are stated the following general rights apply: Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Read more about Creative commons licenses: https://creativecommons.org/licenses/ Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. LUND UNIVERSITY PO Box 117 221 00 Lund +46 46-222 00 00 LUND UNIVERSITY • SWEDEN INSTITUTE OF TECHNOLOGY DEPARTMENT OF FIRE SAFETY ENGINEERING REPORT LUTVDG/(TVBB-1016) Uncertainty and Risk Analysis in Fire Safety Engineering Håkan Frantzich Lund 1998 Uncertainty and Risk Analysis in Fire Safety Engineering Uncertainty and Risk Analysis in Fire Safety Engineering Håkan Frantzich ISSN 1102-8246 ISRN LUTVDG/TVBB--1016--SE Keywords: Risk analysis, uncertainty analysis, Monte Carlo simulation, FOSM, reliability index, fire engineering design, event tree, response surface. Abstract: Two Quantitative Risk Analysis (QRA) methods are presented which can be used to quantify the risk to occupants in, for example, a building in which a fire has broken out. The extended QRA considers the inherent uncertainty in the variables explicitly. The standard QRA does not consider the uncertainties in the variables and must be complemented by a sensitivity analysis or an uncertainty analysis. Both methods provide risk measures, such as individual risk and FN curves. In the extended QRA these are presented in terms of statistical distributions. The standard QRA is more simple to perform and has been used extensively in many engineering fields. Both QRA methods have been applied to an example, structured with the event tree technique, to determine the risk to patients on a hospital ward. In addition to the two risk analysis methods, separate uncertainty analysis methods are also presented. Both stochastic uncertainty and knowledge uncertainty are considered in the analysis, separately and combined. The importance of the variables is also investigated. As both QRA methods are rather complex to use, a more simple method using design values in deterministic equations would be preferable for fire safety design purposes. A method of deriving these design values, based on quantified risk, is presented and complemented with an example which provides design values for a class of buildings. When these design values are known, so-called partial coefficients can be derived. © Copyright Institutionen för brandteknik Lunds Tekniska Högskola, Lunds universitet, Lund 1998 Front page photo: Typical societal risks (hospital, shopping centre and transportation of hazardous goods). S-I Granemark and H Frantzich. Department of Fire Safety Engineering ⋅ Lund Institute of Technology ⋅ Lund University Postal Address Telephone Telefax E-mail Box 118 046 - 222 73 60 046 - 222 46 12 SE-221 00 LUND +46 46 222 73 60 +46 46 222 46 12 [email protected] Contents Contents Nomenclature 1 Introduction 1 1.1 Background 1 1.2 Purpose of the study 5 1.3 Risk management 6 1.3.1 Qualitative methods 7 1.3.2 Semi-quantitative methods 8 1.3.3 Quantitative methods 9 1.4 Uncertainty 11 1.5 Overview of this thesis 11 1.6 Limitations 13 2 Sources of failure 15 2.1 Error classification 15 2.2 Gross errors 16 2.2.1 Human error 16 2.3 Random variability 17 2.3.1 Uncertainty caused by randomness 18 2.4 Handling gross errors 20 2.5 Systematic errors 20 2.6 Uncertainty in subscenarios 21 3 Logical systems 23 3.1 Event tree 23 3.2 Fault tree 26 3.3 Problems with logical trees 28 4 The unwanted consequences 31 4.1 Model for consequence calculation 31 4.1.1 The limit state function 31 4.1.2 Untenable conditions 33 4.1.3 The values of variables 36 Uncertainty and Risk Analysis in Fire Safety Engineering 4.2 Sensitivity analysis 38 4.3 System analysis 38 4.4 Response surface method 40 4.5 Creating the response surface equation 42 4.5.1 The linear two-dimensional case 42 4.5.2 Nonlinear problems 46 4.5.3 Design of experiments 48 5 Describing random variables 51 5.1 Statistical distributions 51 5.2 Correlated variables 53 5.3 The choice of distribution 53 5.3.1 The classical approach 54 5.3.2 The Bayesian approach 55 5.3.3 Bayes' theorem 56 5.4 Fire safety engineering data 59 5.5 Distributions used in fire safety engineering 60 6 Quantitative methods 63 6.1 Introduction 63 6.2 Performing a QRA 66 6.3 Risk measures 68 6.3.1 Individual risk 69 6.3.2 Societal risk 69 6.4 Standard quantitative risk analysis 70 6.4.1 Societal risk 71 6.4.2 Individual risk 74 6.4.3 Limitations 76 6.5 Uncertainty analysis 77 6.6 The single subscenario 79 6.6.1 The analytical reliability index β method 80 6.6.2 Reliability index β method with multiple failure modes 88 6.6.3 Numerical sampling methods 91 6.6.4 Importance of variables 97 Contents 6.7 Extended quantitative risk analysis 100 6.7.1 Societal risk 100 6.7.2 Individual risk 106 6.7.3 Application of the method 107 7 Sample risk analysis of a hospital ward 109 7.1 Introduction 109 7.2 Definition of the system 110 7.3 Standard QRA 113 7.3.1 Societal risk 113 7.3.2 Individual risk 117 7.4 Extended QRA 117 7.4.1 Societal risk 117 7.4.2 Individual risk 127 7.5 Uncertainty analysis of individual subscenarios 128 7.5.1 The analytical reliability index β method 129 7.5.2 Numerical sampling methods 134 7.6 Concluding remarks 140 8 Risk evaluation 143 8.1 Tolerable risk 143 8.2 Risk measures 144 8.3 Uncertainty in QRA 146 9 Design values based on risk 149 9.1 Introduction 149 9.2 Theory of the method 150 9.3 The design problem 151 9.4 Method 153 9.5 Design values 159 9.6 Problems with the method 162 10 Summary, conclusions and future work 165 Uncertainty and Risk Analysis in Fire Safety Engineering Acknowledgements 169 References 171 Appendix A "Description of Matlab files" Appendix B "General assumptions for the sample scenario" Nomenclature Nomenclature * ai vector of direction cosines 2 Ar room area, m ci subscenario consequences e regression error Fs specific flow rate through a doorway, persons/(m+s) Hr room height, m M escape time margin, s MS model uncertainty correction factor Ni number of fatalities 2 No occupant density, persons/m NoPat number of patients on the ward NoStaff number of nurses on the ward PatInRm number of patients in a patient room pday fraction of fires occurring during the day pdetection operation probability for detection system pdoor probability that door to the fire room is open pET,i event tree branch probability pfire fire occurrence rate, fires/year p probability of failure for single failure mode f j pflaming probability of flaming fire phelp fraction that require help during evacuation pi subscenario probability pinitial scenario probability psleeping probability of sleeping patients psprinkler operation probability for sprinkler system psuppressed probability that the fire will be suppressed by a member of staff or is selfextinguished ptarget specified target probability of failure pu,i subscenario probability of failure R2 coefficient of determination r correlation coefficient si subscenario description StaffInRm number of nurses in patient room Uncertainty and Risk Analysis in Fire Safety Engineering tcare time taken to prepare a patient, s tdet time taken to detect the fire, s Tg temperature in hot smoke layer, °C tmove time required to move to a safe location, s corr tmove movement time from corridor, s room tmove movement time from patient room, s tpatM movement time for a patient, s tresp response and behaviour time, s tresp,d response and behaviour time (design value), s staff tresp member of staff response and behaviour time, s tstaffM movement time for a member of staff, s tu time taken to reach untenable conditions, s corr tu time taken to reach untenable conditions in corridor, s room tu time taken to reach untenable conditions in fire room, s W door width, m * xi vector of "design point" in original space '* xi vector of "design point" in standardised space xi,ch characteristic value xi,d design value z smoke layer height, m 2 αf fire growth rate, kW/s 2 αf,d fire growth rate (design value), kW/s β reliability index βC reliability index according to Cornell βHL reliability index according to Hasofer and Lind γi partial coefficient δ regression coefficient ε experimental data Θ general random variable λ regression coefficient µ mean value ρ correlation coefficient σ standard deviation Introduction 1 Introduction The research work presented in this thesis is a partial fulfilment of the Doctor of Philosophy in Engineering (PhD Eng.) requirement at the department of Fire Safety Engineering at Lund University.
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