A PREDICTION MODEL FOR BROKEN RAILS AND AN ANALYSIS OF THEIR ECONOMIC IMPACT

Broken rails are the leading cause of major derailments in North America. Class I freight railroads average 84 mainline broken-rail derailments per year with an average track and equipment cost of approximately $525,000 per incident. The number of mainline broken-railcaused derailments has increased from 77 in 1997, to 91 in 2006; therefore, efforts to reduce their occurrence remain important. We conducted an analysis of the factors that influence the occurrence of broken rails and developed a quantitative model to predict locations where they are most likely to occur. Among the factors considered were track and rail characteristics, maintenance activities and frequency, and on-track testing results. Analysis of these factors involved the use of logistic regression techniques to develop a statistical model for the prediction of broken rail locations. For such a model to have value for railroads it must be feasible to use and provide information in a useful manner. Consequently, an optimal prediction model containing only the top eight factors related to broken rails was developed. The economic impact of broken rail events was also studied. This included the costs associated with broken rail derailments and service failures, as well as the cost of typical prevention measures. A train delay calculator was also developed based on industry operating averages. Overall, the information presented here can assist railroads to more effectively allocate resources to prevent the occurrence of broken rails. INTRODUCTION Understanding the factors related to broken rails is an important topic for U.S. freight railroads and is becoming more so because of the increase in their occurrence in recent years. This increase is due to several factors, but the combination of increased traffic and heavier axle loads are probably the most important. Broken rails are generally caused by the undetected growth of either internal or surface defects in the rail (1). Previous research has focused on both mechanistic analyses (2-8) and statistical analyses (9-13) in order to understand the factors that cause crack growth in rails and ultimately broken rails. The first objective of this analysis was to develop a predictive tool that will enable railroads to identify locations with a high probability of broken rail. The possible predictive factors that were evaluated included rail characteristics, infrastructure data, maintenance activity, operational information, and rail testing results. The second objective was to study the economic impact of broken rails based on industry operating averages. Our analysis on this topic incorporates previous work that developed a framework for the cost of broken rails (14). The purpose of this paper is to provide information to enable more efficient evaluation of options to reduce the occurence of broken rails. DEVELOPMENT OF SERVICE FAILURE PREDICTION MODEL The first objective of this paper was to develop a model to identify locations in the rail network with a high probability of broken rail occurrence based on broken rail service failure data and possible influence factors. All of the factors that might affect service failure occurrence and for which we had data were considered in this analysis. Several broken rail predictive models were developed and evaluated using logistic regression techniques. Data Available for Study In order to develop a predictive tool, it is desirable to initially consider as many factors as possible that might affect the occurrence of broken rails. From the standpoint of rail maintenance planning it is important to determine which factors are and are not correlated with broken rail occurence. Therefore the analysis included a wide-range of possible variables for which data were available. This included track and rail characteristics such as rail age, rail curvature, track speed, grade, and rail weight. Also, changes in track modulus due to the presence of infrastructure features such as bridges and turnouts have a potential effect on rail defect growth and were examined as well. Additionally, maintenance activities were included that can reduce the likelihood of broken rail occurrence, such as rail grinding and tie replacement. Finally, track geometry and ultrasonic testing for rail defects were used by railroads to assess the condition of track and therefore the results of these tests are included as they may provide predictive information about broken rail occurrence. The BNSF Railway provided data on the location of service failures and a variety of other infrastructure, inspection and operational parameters. In this study a “service failure” was defined as an incident where a track was taken out of service due to a broken rail. A database was developed from approximately 23,000 miles of mainline track maintained by the BNSF Railway covering the four-year period, 2003 through 2006. BNSF’s network was divided into 0.01-mile-long segments (approximately 53 feet each) and the location of each reported service failure was recorded. BNSF experienced 12,685 service failures during the four-year study period. For the case of modeling rare events it is common to sample all of the rare events and compare these with a similar sized sample of instances where the event did not occur (15). Therefore an additional 12,685 0.01-mile segments that did not experience a service failure during the four-year period were randomly selected from the same network. Each non-failure location was also assigned a random date within the four-year time period for use in evaluating certain temporal variables that might be factors. Thus, the dataset used in this analysis included a total of 25,370 segment locations and dates when a service failure did or did not occur in the railroad’s network during the study period. All available rail characteristics, infrastructure data, maintenance activity, operational information, and track testing results were linked to each of these locations, for a total of 28 unique input variables. Evaluation of Previous Service Failure Model In a previous study Dick developed a predictive model of service failures based on relevant track and traffic data for a two-year period (10, 11). The outcome of that study was a multivariate statistical model that could quantify the probability of a service failure at any particular location based on a number of track and traffic related variables. Dick‘s model used 11 possible predictor factors for broken rails and could correctly classify failure locations with 87.4% accuracy using the dataset provided to him. Our first step was to test this model using data from a more recent two-year period. From 2005 through 2006, the BNSF experienced 6,613 service failures and data on these, along with 6,613 randomly selected non-failure locations, were analyzed. 7,247 of the 13,226 cases were classified correctly (54.8%), considerably lower than in the earlier study causing us to ask why the predictive power seemed to have declined. Examination of the service failure dataset used previously revealed that it may not have included all the trackage from the network. This resulted in a dataset that generated the particular model and accuracy levels reported in the earlier study (10, 11). Therefore a new, updated statistical model was developed to predict service failure locations. Development of Updated Statistical Classification Model The updated model that was developed to predict service failure locations used similar logistic regression techniques. Logistic regression was selected because it is a discrete choice model that calculates the probability of failure based on available input variables. These probabilities are used to classify each case as either failure or non-failure. A statistical regression equation was developed based on the significant input parameters to determine the probability of failure. To find the best classification model, the input parameters were evaluated with and without multiple-term interactions allowed. Logistic Regression Methodology and Techniques The model was developed as a discrete choice classification problem of either failure or non-failure using the new dataset described above. The objective was to find the best combination of variables and mathematical relationships among the 28 available input variables to predict the occurrence of broken rails. The service failure probability model was developed using Statistical Analysis Software (SAS) and the LOGISTIC procedure (16). This procedure fits a discrete choice logistic regression model to the input data. The output of this model is an index value between zero and one corresponding to the probability of a service failure occurrence. Four commonly used variable selection techniques were evaluated in this analysis to find the best model. The simplest method is referred to as “full-model”, or variable selection type “none” in SAS. The full-model method uses every available input variable to determine the best regression model. The next technique examined was selection type “forward”, which evaluates each input variable and systematically adds the most significant variables to the model. The forward selection process continues adding the most significant variable until no additional variables meet a defined significance level for inclusion in the model. The entry and removal level used in this analysis for all variable selection techniques was a 0.05 significance threshold. The “backward” variable selection technique was also used. This method starts with all input variables included in the model. In the first step, the model determines the least significant variable that does not meet the defined significance level and removes it from the model. This process continues until no other variables included in the model meet the defined criteria for removal. The final logistic regression selection technique used was “step-wise” selection. The step-wise selection method is s