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Determining confidence intervals, and convergence, for parameters in stochastic evacuation models

Determining confidence intervals, and convergence, for parameters in stochastic evacuation models

Grandison, Angus ORCID: 0000-0002-9714-1605 (2020) Determining confidence intervals, and convergence, for parameters in stochastic evacuation models. Fire Technology. ISSN 0015-2684 (Print), 1572-8099 (Online) (In Press) (doi:https://doi.org/10.1007/s10694-020-00968-0)

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Abstract

An issue when using stochastic egress models is how many simulations are required to accurately represent the modelled scenario? Engineers are mostly interested in a representative Total Evacuation Time (TET). However, the convergence of the TET may not ensure that the full range of evacuation dynamics has been adequately represented. The average total egress curve (AC) has been suggested as an improved measure. Unfortunately, defining a confidence interval (CI) for the AC is problematic. CIs can robustly quantify the precision of many statistics and have been used to define convergence in egress modelling and other research fields. This paper presents a novel application of bootstrapping, functional analysis measures (FAMs), and a bisection algorithm, to derive three FAM-based CIs representing the precision of the AC. These CIs were tested using a theoretical model to demonstrate the consistency of the coverage probability, the actual percentage of CIs that contain the theoretical parameter, with the nominal 95% confidence level (NCL). For two of the FAM-based CIs, it was found that the coverage probability was between 94.2% and 95.6% for all tested sample sizes between 10 to 4000 simulations. The third FAM-based CI’s coverage probability was always greater than the NCL and was a conservative estimate, but this presented no problems in practice. A FAM-based CI may suggest if there is more or less variability in an earlier phase of the evacuation. A convergence scheme based on statistical precision, CI widths, is proposed and verified. The method can be extended to other statistics.

Item Type: Article
Additional Information: © 2020 The Author(s). Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Uncontrolled Keywords: Convergence criteria; Evacuation modelling; Bootstrapping; Functional analysis; Confidence interval
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Liberal Arts & Sciences
Faculty of Liberal Arts & Sciences > Centre for Numerical Modelling & Process Analysis (CNMPA)
Faculty of Liberal Arts & Sciences > Centre for Numerical Modelling & Process Analysis (CNMPA) > Fire Safety Engineering Group (FSEG)
Faculty of Liberal Arts & Sciences > Department of Mathematical Sciences
Last Modified: 04 Mar 2020 17:26
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/27065

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