Hazard based models for freeway traffic incident duration

Assessing and prioritising cost-effective strategies to mitigate the impacts of traffic incidents and accidents on non-recurrent congestion on major roads represents a significant challenge for road network managers. This research examines the influence of numerous factors associated with incidents of various types on their duration. It presents a comprehensive traffic incident data mining and analysis by developing an incident duration model based on twelve months of incident data obtained from the Australian freeway network. Parametric accelerated failure time (AFT) survival models of incident duration were developed, including log-logistic, lognormal, and Weibul—considering both fixed and random parameters, as well as a Weibull model with gamma heterogeneity. The Weibull AFT models with random parameters were appropriate for modelling incident duration arising from crashes and hazards. A Weibull model with gamma heterogeneity was most suitable for modelling incident duration of stationary vehicles. Significant variables affecting incident duration include characteristics of the incidents (severity, type, towing requirements, etc.), and location, time of day, and traffic characteristics of the incident. Moreover, the findings reveal no significant effects of infrastructure and weather on incident duration. A significant and unique contribution of this paper is that the durations of each type of incident are uniquely different and respond to different factors. The results of this study are useful for traffic incident management agencies to implement strategies to reduce incident duration, leading to reduced congestion, secondary incidents, and the associated human and economic losses.     

Competing risks mixture model for traffic incident duration prediction

Traffic incident duration is known to result from a combination of multiple factors, including covariates such as spatial and temporal characteristics, traffic conditions, and existence of secondary accidents but also the clearance method itself. In this paper, a competing risks mixture model is used to investigate the influence of clearance methods and various covariates on the duration of traffic incidents and predict traffic incident duration. The proposed mixture model considers the uncertainty in any of five clearance methods that occurred. The probability of the clearance method is specified in the mixture by using a multinomial logistic model. Three candidate distributions, namely, generalized gamma, Weibull, and log-logistic are tested to determine the most appropriate probability density function of the parametric survival analysis model. The unobserved heterogeneity is also incorporated into the mixture model in a way that allows parameters to vary across observations based on the three candidate distributions. The methods are illustrated with incident data from Singaporean expressways from January 2010 to December 2011. Regression analysis reveals that the probability of different clearance methods and the duration of traffic incidents are both significantly affected by various factors, such as traffic conditions and incident characteristics. Results show that the proposed mixture model is better than the traditional accelerated failure time model, and it predicts traffic incident duration with reasonable accuracy, as shown by the mean average percent error.     

An accelerated failure time model for investigating pedestrian crossing behavior and waiting times at signalized intersections

The waiting process is crucial to pedestrians in the street-crossing behavior. Once pedestrians terminate their waiting behavior during the red light period, they would cross against the red light and put themselves in danger. A joint hazard-based duration model is developed to investigate the effect of various covariates on pedestrian crossing behavior and to estimate pedestrian waiting times at signalized intersections. A total of 1181 pedestrians approaching the intersections during red light periods were observed in Beijing, China. Pedestrian crossing behaviors are classified into immediate crossing behavior and waiting behavior. The probability and effect of various covariates for pedestrians’ immediate crossing behavior are identified by a logit model. Four accelerated failure time duration models based on the exponential, Weibull, lognormal and log-logistic distributions are proposed to examine the significant risk factors affecting duration times for pedestrians’ waiting behavior. A joint duration model is developed to estimate pedestrian waiting times. Moreover, unobserved heterogeneity is considered in the proposed model. The results indicate that the Weibull AFT model with shared frailty is appropriate for modelling pedestrian waiting durations. Failure to account for heterogeneity would significantly underestimate the effects of covariates on waiting duration times. The proposed model provides a better understanding of pedestrian crossing behavior and more accurate estimation of pedestrian waiting times. It may be applicable in traffic system analysis in developing countries with high flow of mixed traffic.     

Modelling total duration of traffic incidents including incident detection and recovery time

Traffic incidents are key contributors to non-recurrent congestion, potentially generating significant delay. Factors that influence the duration of incidents are important to understand so that effective mitigation strategies can be implemented. To identify and quantify the effects of influential factors, a methodology for studying total incident duration based on historical data from an ‘integrated database’ is proposed. Incident duration models are developed using a selected freeway segment in the Southeast Queensland, Australia network. The models include incident detection and recovery time as components of incident duration. A hazard-based duration modelling approach is applied to model incident duration as a function of a variety of factors that influence traffic incident duration. Parametric accelerated failure time survival models are developed to capture heterogeneity as a function of explanatory variables, with both fixed and random parameters specifications. The analysis reveals that factors affecting incident duration include incident characteristics (severity, type, injury, medical requirements, etc.), infrastructure characteristics (roadway shoulder availability), time of day, and traffic characteristics. The results indicate that event type durations are uniquely different, thus requiring different responses to effectively clear them. Furthermore, the results highlight the presence of unobserved incident duration heterogeneity as captured by the random parameter models, suggesting that additional factors need to be considered in future modelling efforts.     

The Weibull log-logistic mixture distributions: Model,theory and application to lifetime data

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing, which makes standard lifetime models inadequate. Finite mixture models provide more flexibility for modeling such data. In this paper, the Weibull-log-logistic mixture distributions model is introduced as a new class of flexible models for heterogeneous lifetime data. Some statistical properties of the model are presented including the failure rate function, moments generating function, and characteristic function. The identifiability property of the class of all finite mixtures of Weibull-log-logistic distributions is proved. The maximum likelihood estimation (MLE) of model parameters under the Type I and Type II censoring schemes is derived. Some numerical illustrations are performed to study the behavior of the obtained estimators. The model is applied to the hard drive failure data made by the Backblaze data center, where it is found that the proposed model provides more flexibility than the univariate life distributions (Weibull, Exponential, logistic, log-logistic, Frechet). The failure rate of hard disk drives (HDDs) is obtained based on MLE estimates. The analysis of the failure rate function on the basis of SMART attributes shows that the failure of HDDs can have different causes and mechanisms.     

Accelerated failure time models for reliability data analysis

Despite the popularity of the proportional hazards model (PHM) in analysing many kinds of reliability data, there are situations in which it is not appropriate. The accelerated failure time model (AFT) then provides an alternative. In this paper, a unified treatment of the accelerated failure time model is outlined for the standard reliability distributions (Weibull, log-normal, inverse Gaussian, gamma). The problem of choosing between the accelerated failure time models and proportional hazard models is discussed and effects of misspecification are reported. The techniques are illustrated in the analysis of data from a fatigue crack growth experiment.     

Development of an accident duration prediction model on the Korean Freeway Systems

Since duration prediction is one of the most important steps in an accident management process, there have been several approaches developed for modeling accident duration. This paper presents a model for the purpose of accident duration prediction based on accurately recorded and large accident dataset from the Korean Freeway Systems. To develop the duration prediction model, this study utilizes the log-logistic accelerated failure time (AFT) metric model and a 2-year accident duration dataset from 2006 to 2007. Specifically, the 2006 dataset is utilized to develop the prediction model and then, the 2007 dataset was employed to test the temporal transferability of the 2006 model. Although the duration prediction model has limitations such as large prediction error due to the individual differences of the accident treatment teams in terms of clearing similar accidents, the results from the 2006 model yielded a reasonable prediction based on the mean absolute percentage error (MAPE) scale. Additionally, the results of the statistical test for temporal transferability indicated that the estimated parameters in the duration prediction model are stable over time. Thus, this temporal stability suggests that the model may have potential to be used as a basis for making rational diversion and dispatching decisions in the event of an accident. Ultimately, such information will beneficially help in mitigating traffic congestion due to accidents.     

Lower Percentile Estimation of Accelerated Life Tests with Nonconstant Scale Parameter

Lower percentiles of product lifetime are useful for engineers to understand product failure, and avoiding costly product failure claims. This paper proposes a percentile re‐parameterization model to help reliability engineers obtain a better lower percentile estimation of accelerated life tests under Weibull distribution. A log transformation is made with the Weibull distribution to a smallest extreme value distribution. The location parameter of the smallest extreme value distribution is re‐parameterized by a particular 100pth percentile, and the scale parameter is assumed to be nonconstant. Maximum likelihood estimates of the model parameters are derived. The confidence intervals of the percentiles are constructed based on the parametric and nonparametric bootstrap method. An illustrative example and a simulation study are presented to show the appropriateness of the method. The simulation results show that the re‐parameterization model performs better compared with the traditional model in the estimation of lower percentiles, in terms of Relative Bias and Relative Root Mean Squared Error. Copyright © 2017 John Wiley & Sons, Ltd.     

On the upper truncated Weibull distribution and its reliability implications

The characteristics and application of the truncated Weibull distribution are studied in this paper. This distribution is applicable to the situation where the test data are bounded in an interval because of test conditions, cost and other restrictions. An important property of the truncated Weibull distribution is that it can have bathtub-shaped failure rate function. In this paper, the parametric analysis and parameter estimation methods of the distribution are investigated. Both the graphical approach and the maximum likelihood estimation are considered. The applicability of this distribution to modeling lifetime data is illustrated by an example and the results of comparisons to other competitive models in modeling the given data are also presented. Moreover, the possible application of the distribution to modeling component or system failure is discussed.     

Parametric study of multiplicative model involving two Weibull distributions

The multiplicative model involving two Weibull distributions is characterized by four independent parameters. The shapes of the density and failure rate functions for the model depend on the parameter values. A complete parametric characterization of these shapes is presented in this paper.