Project Sponsored By:
Mr. Fred Woodaman

The Department of the Navy desires a tool for analyzing the effects of budgetary changes upon Fire and Emergency Services provided upon Naval Installations throughout the world.  The diversity of these installations suggests that across the board funding changes may affect each location differently.  This project presents a Fire Loss Model to support the continued development of the analysis tool.

In the Fall of 2011 a George Mason University (GMU) project team created an Excel based modeling tool called “FESEBLE”.  This model used real data from Key West, FL, and a grid map system of a city (GMU Fairfax Campus) to evaluate call events that resulted in a “LOSS”.  This loss determination was based on all required resources being able to respond to a fire event.  The loss classification was binary in nature, either a loss occurred or did not occur.

This Spring 2012 project focuses on quantifying this loss in a method such that a change in expected loss for a given event can be estimated using varying resource manning levels and event response times.  Our objective is to accurately model the behavior of fire and expected loss given varying response parameters and to provide the capability to simulate expected loss at a customer installation.

An understanding of basic fire science and the firefighting process was important to establishing a reasonable model foundation.    A far reaching internet review was performed exploring numerous fire science topics, and two subject matter experts (SME) were interviewed.  As the group’s knowledge increased frequent feedback from our experts was obtained.  This feedback assisted us in focusing the scope of the material search and in pinpointing questions we needed to find answers to as the model components were created.  Evaluating available data related to the frequency and severity of fire the loss model was developed based on a 1-2 story family residence with possible fire ignition sites of a downstairs living room or upstairs bedroom.  This limitation in fire type, however, does not eliminate variability in the fire process.

The firefighting process was researched by reviewing federal regulations, recommended standards, and expert experience.  Our determination is that the arrival times of the first two fire suppression resources, and the level at which they are staffed, are key factors in limiting fire growth.  A delay in firefighter arrival or reduction in manpower may allow for the fire to increase in energy to its flashover point, greatly increasing the amount of damage.  Flashover is when heat from the growing fire is absorbed into the walls and contents of the room, heating up the combustible gases and furnishings until they burst into flames. 

The Fire Loss Model is based on using the curve of a Weibull function to imitate the expected damage from a fire. Two methods are used to model the variability in fire.  To initiate a model fire a [0,1] random number is generated.   This random number will fall within a probability bin and that type of fire will be used throughout the remaining calculations.  The probability bins are based on researched data as to ignition location and fire spread within the structure. By varying the alpha and beta parameters of the function, different types and growth rates of a fire can be generated.  Two main fires (upstairs and downstairs) with five different levels of expected damage can be initiated. These probabilities can be adjusted to add additional types of fires or by altering the probability range of those currently modeled as new research and data are available.

Each of these general probability bins correspond to an assigned alpha and beta parameter. General damage curves can be produced to show the expected loss rate over time.  By manually inputting the appropriate parameters a specific fire can be selected by the user for detailed study.

Research showed that even in experiments with repeatable laboratory conditions, multiple fire growth rates were measured for fixed parameters. After the main fire type is determined the rate of fire growth is varied.  We have modeled this uncertainty by using a gamma distribution to randomly adjust the base fire parameters.

The effects of firefighting efforts to mitigate damage are assumed to be linear in nature.  The model determines the start time based on given arrival times of the first two resources.  These arrival times are currently inputted manually and could be obtained from existing information about fire response times for any given Naval installation.  Additionally, the user can vary the number of people assigned to a resource.  Our model currently allows for 3 or 4 people to be assigned.  A reduction in personnel adds a time penalty to the fire mitigation process.  Being Excel based, it is expected that future work evaluating the effects of resource changes will be able to generate response time data.  If there is a larger than expected delay between the first and second units, mitigation efforts will cease when the first unit expends their available water and resume when additional support arrives.

After each of the component parts are determined, a Monte Carlo simulation is initiated.  This simulation keeps the base parameters fixed, generates multiple results with new variability, and reports the average expected damage from the entire simulation.  The number of trials is chosen by the user.  These results are reported with a histogram showing the frequency of expected loss events.

By keeping either the crew size or arrival times fixed and varying the other,  the change in expected loss can be estimated by comparing the average damage results from each simulation.  A user with a proposed change in resources and its possible effects on arrival times will be able to use this model to estimate additional damage risk to property.