Title : Modeling the Number of Ignitions Following an Earthquake : Developing Prediction Limits for Overdispersed Count Data

This report describes an approach for modeling the number of ignitions (fires) following an earthquake. The modeling is not meant to be exact, but to provide a context for assessing the likelihood of various fire scenarios. The first component of the approach is a statistical model to predict the number of ignitions for a new earthquake event. This model is based on data for ignitions following earthquakes from 1906 to 1989 in Alaska and California. These U.S. fire data are taken from reports by fire departments on the fires they responded to immediately after the earthquakes and for several days thereafter. These data are for fires in the general built environment, including residential, commercial and industrial structures. The data contain estimates for the mean peak ground acceleration (PGA) for each earthquake, an estimate of the built area affected in million square feet (MMSF) for each earthquake, and the number of ignitions within the estimated affected area (IGNS). The statistical model uses negative binomial regression to estimate the expected number of ignitions as a function of the explanatory variables, PGA and MMSF. The associated upper confidence and prediction limits are derived from the statistical model using only spreadsheet technology. The upper prediction limit is used to determine a conservative estimate of the probability of a specified number of ignitions following a future earthquake event. The results from the spreadsheet technology are compared to more exact results based on numerical integration. The spreadsheet probability estimates are shown to be conservative. However, these fire data are limited in two ways. First, there are no estimates of the number of fires that may not have been responded to by the fire department, e.g. unreported fires following an earthquake. Second, the terms “fire” and “ignition” are used interchangeably; there are no data on the number of ignitions causing the fire. The second component of the approach provides methods for adjusting the statistical model to account for these limitations of the data. This report also provides an example of an application of this approach to a large single structure. BACKGROUND This report is concerned with determining a conservative estimate of the probability of a specified number of ignition events in buildings (including a large single structure), which might occur because of an earthquake. Conservatism is meant in the sense that the estimate of the probability of a fire is greater than the true probability. These values are not meant to be exact, but to provide a context for assessing the likelihood of various fire scenarios.