Competing Risks Models for the Assessment of Intelligent Transportation Systems Devices: A Case Study for Connected and Autonomous Vehicle Applications

: Intelligent transportation system (ITS) has become a crucial section of transportation and tra ﬃ c management systems in the past decades. As a result, transportation agencies keep improving the quality of transportation infrastructure management information for accessibility and security of transportation networks. The goal of this paper is to evaluate the impact of two competing risks: “natural deterioration” of ITS devices and hurricane-induced failure of the same components. The major devices employed in the architecture of this paper include closed circuit television (CCTV) cameras, automatic vehicle identiﬁcation (AVI) systems, dynamic message signals (DMS), wireless communication systems and DMS towers. From the ﬁndings, it was evident that as ITS infrastructure devices age, the contribution of Hurricane Category 3 as a competing failure risk is higher and signiﬁcant compared to the natural deterioration of devices. Hurricane Category 3 failure vs. natural deterioration indicated an average hazard ratio of 1.5 for CCTV, AVI and wireless communications systems and an average hazard ratio of 2.3 for DMS, DMS towers and portable DMS. The proportional hazard ratios of the Hurricane Category 1 compared to the devices was estimated as < 0.001 and that of Hurricane Category 2 < 0.5, demonstrating the lesser impact of the Hurricane Categories 1 and 2. It is expedient to envisage and forecast the impact of hurricanes on the failure of wireless communication networks, vehicle detection systems and other message signals, in order to prevent vehicle to infrastructure connection disruption, especially for autonomous and connected vehicle systems. signs (horizontal and vertical members), traffic signals, small signs, lights and fixtures and roadway and bridge operation facilities.


Introduction
Intelligent transportation systems (ITS) and their associated technologies have been employed for the past decades to improve mobility and accessibility on roadways. The United States Department of Transportation (USDOT) and the Federal Highway Administration (FHWA) keep refining standards and engaging in programs to upgrade the overall performance on roadways. With the projected impact of connected and autonomous vehicle systems' (CAVs) traffic data collection, management and analysis remain crucial for decision-making. As such, innovative travel time reliability, safety and operational measures on corridors remain critical for effective navigation, trip virtualization, intersection crossing and way-finding purposes. As part of the goal of enhancing the ITS on roadways, highway cameras, Additionally, hurricane hazards have resulted in the failure and fracture-critical assessment of traffic signal systems, sign cantilevers and high masts, as well as sign-span and cables elements [21,28]. According to the Federal Highway Authority (FHWA), knock-downs, lightning, floods and other unforeseen events also engender failure of ITS infrastructures [29].
Past investigations have employed the traditional survival analysis concept to evaluate the reliability of transportation infrastructure components. However, the complex impact of failures using the dependent failure assumption and the competing risks scenario remains an area to be explored. The competing risks model employed in this research evaluates the impact of the different risks of failure in the event of multiple failures by determining the main failure event among the other competing causes.
The concept of competing risks has been employed in studies involving risk stratification and degradation of electronic systems, as well as the recurrence and relapse of diseases in patients [30,31]. In the field of transportation, the concept of competing risks has been utilized by experts to investigate traffic choice models and vehicle transaction behaviors. Additionally, other transportation infrastructure performance assessments have been analyzed using the dependent failure assumption [26,[32][33][34]. Other researchers have employed machine-learning models and artificial intelligence frameworks to evaluate traffic signal communications, hybrid electric vehicles' performance costs and other transportation infrastructure operations [10,11,35,36].
Like the already-mentioned investigations, this paper aims at estimating the performance of selected ITS infrastructures using the competing risks model and the dependent failure assumption in the presence of three major failure modes: natural deterioration, mechanical and electrical failures and hurricane-induced failures.

Methodology
This section of the paper discusses the competing risks model and the dependent failure assumption. The authors build up the competing risks scenario from the traditional survival analysis and the independent failure assumption and then explains the nonparametric (Kaplan Meier estimates) and parametric survival analyses (Weibull analysis), as well as the cumulative incidence function (CIF) for the performance assessment. A schematic representation of the roadway ITS infrastructure is shown from which time the failure and survival probabilities are computed using historic data on natural deterioration, hurricane exposure and vulnerability information.

Competing Risk Model
A competing risk is an event that hinders the observation of an event of interest [37]. As discussed by David and Moeschberger [38], Prentice et al. [39] and Gail [40], for any failure event, there is only one cause of failure among the m competing causes. Competing risks problems are often formulated in terms of latent or potential failure times, µ 1 , µ 2 , . . . , µ j corresponding to j failure types with the observed failure time T = min µ 1 , µ 2 , . . . , µ j .
The concepts of the net and crude lifetimes are required for competing event analysis. The lifetime analyses employ different assumptions for risk assessment. That is, the net probability formulation adopts the independence assumption where the specific risk present C j , j = 1, 2, . . . , k is analyzed as the only risk. That is, the subjects present are impacted by the one and only risk present. The net probability of failure in [p, q) by failure risk j could be described as shown below: with the cumulative hazard function given as H(τ) = e − q p h µ j (τ)dτ . The crude lifetime and probabilities are evaluated in the presence of all other j causes. That is, assuming all risks are present, the crude probability of failure by failure risk j, in the time interval [p, q) given the survival of a specific component or the ITS device until time p, is described as Additional computational expressions on competing risks are outlined in Klein and Moeschberger [41] and Crowder et al. [42]. From the above concepts, the three competing events evaluated are natural deterioration, electrical and mechanical failures and hurricane-induced failures. The deterioration of the selected ITS components are modeled for their survival probabilities using estimators such as the hazard ratios, log-rank statistics and the Kaplan-Meier statistics. The log-rank test is used to evaluate whether there is enough evidence that the survival probabilities due to the risks present are significantly different, while the hazard ratios estimate the hazard rates due to the failure time covariate.

Natural Deterioration, Electrical and Mechanical Failures
Traffic management system life-cycle includes assessment of the overall functionality of ITS infrastructures during its lifetime. The overall performance is measured based on key operational factors such as construction/installation programs, maintenance procedures, emergency assessment and decommissioning planning programs and associated cost analyses. Most departments of transportation and transportation agencies inspect infrastructures annually or biennially for maintenance, rehabilitation and repair purposes. Elements are monitored from which forecasting models are generated for future performance analyses. Past investigations have associated high annual maintenance costs with different ITS devices. These include devices such as signal controllers, weigh-in motions and communications hubs and consoles. The least costly of the maintenances have been affiliated with radio, sonic and radar detectors, as well as automatic vehicle identification readers ( Figure 1).
Infrastructures 2020, 5, x FOR PEER REVIEW 5 of 16 Additional computational expressions on competing risks are outlined in Klein and Moeschberger [41] and Crowder et al. [42]. From the above concepts, the three competing events evaluated are natural deterioration, electrical and mechanical failures and hurricane-induced failures. The deterioration of the selected ITS components are modeled for their survival probabilities using estimators such as the hazard ratios, log-rank statistics and the Kaplan-Meier statistics. The log-rank test is used to evaluate whether there is enough evidence that the survival probabilities due to the risks present are significantly different, while the hazard ratios estimate the hazard rates due to the failure time covariate.

Natural Deterioration, Electrical and Mechanical Failures
Traffic management system life-cycle includes assessment of the overall functionality of ITS infrastructures during its lifetime. The overall performance is measured based on key operational factors such as construction/installation programs, maintenance procedures, emergency assessment and decommissioning planning programs and associated cost analyses. Most departments of transportation and transportation agencies inspect infrastructures annually or biennially for maintenance, rehabilitation and repair purposes. Elements are monitored from which forecasting models are generated for future performance analyses. Past investigations have associated high annual maintenance costs with different ITS devices. These include devices such as signal controllers, weigh-in motions and communications hubs and consoles. The least costly of the maintenances have been affiliated with radio, sonic and radar detectors, as well as automatic vehicle identification readers ( Figure 1). ITS devices and their signages are constantly monitored for natural deterioration, as well as electrical and mechanical failures. Most transportation infrastructure conditioned states have been modeled using regression and deterioration models based on condition ratings. Remedial actions (repair or replacement) of installed transportation management system components because of natural or other causes of failure are also undertaken by required agencies [7].
Also, TMS life-cycle metrics evaluate the degradation and obsolescence of system components with time. Parameters such as mean time between failure of components, mean time to repair and average cost of repair are used in evaluating the condition of components. Table 1 and Figure 2 are representations of TMS components and their life expectancy.  To evaluate the operational characteristics of ITS devices using competing risks models, the failure times of the various ITS control devices are modeled based on the Weibull distribution family. The distribution family was chosen to simulate random failure arrival times to mimic the mode of degradation of electrical, mechanical and structural systems. The wireless communication systems, hubs and consoles which perform like computer systems were modeled using the exponential distribution (Poisson point process) with their mean time to failure expressed as the inverse of the failure rates, while the dynamic message sign towers and portable message signs are modeled using the Weibull distribution based on past literature [43][44][45][46][47]. The data is generated based on the life expectancy data from Table 1 using the algorithm shown below. Distributions of the failure times are shown in Figure 3.

Algorithm 1: Exponential and Weibull Data Generation
#Generate N number of variables with mean λ data2 = rand(weibull, β, µ) #Generate N number of variables with shape β and scale µ end for return data1, data2 Infrastructures 2020, 5, x FOR PEER REVIEW 7 of 16

Hurricane Hazard and Exposure Probabilities
According to the FDOT traffic operations [7], operation and maintenance (O&M) personnel often monitor the ITS infrastructure for effective deployment and operability through daily maintenance and emergency management evaluations. The evaluations are characterized by pre-trip diagnostics, configuration management, routine repair and replacement activities while updating the associated databases with all the conditions and needs of the systems for asset management operations, especially in the event of hazards.
Previous hazard impact assessments on civil infrastructures have been conducted on roadway and bridge components and subsystems using historical records from hurricanes, storm surges and earthquake occurrences [25,41,42,48]. Damage of roadway infrastructures have been quantified as slight, moderate, extensive or complete based on the level of vulnerability due to hazard impacts [49]. Qualitative damage states describing hurricane-induced damage for structural and nonstructural elements employed in this paper are provided in detail in the Hazards United States, HAZUS-MH [21,26]. Due to limited data, the vulnerability weights assigned to traffic sign structure failures due to past hurricane damages as reported in [21] are employed to estimate expected damages and associated probabilities of the failure of signs, poles, mast and signals. Hurricane wind data from the Hazards United States database are used to compute occurrence probabilities for Hurricane Categories 1, 2 and 3 storms.
The exposure probability at traffic sign structure locations on roadways per year is expressed mathematically as shown in Equations (6) and (7).
where P β -probability of β number of storms occurring in a specified year, ϑ-mean rate of storms per year, P(T ≤ τ)-cumulative distribution function and τ is a random variable representing a given period.
To evaluate the hurricane arrival rates along with vulnerability ratings, the concept of interarrival times are utilized. That is, for a sequence of interarrival times, the time between (a − 1)st and the ath hurricane event is expressed as the mean arrival time and computed as 1/λ. The arrival time S a of the ath event is given as and the expectation of the arrival time is computed as With the hurricane event being modeled as a Poisson process with rate λ, the hurricane event in a particular location could belong to s number of groups (that is, different hurricane categories, locations (coastal or noncoastal) or roadway functional classes (interstate or noninterstate)). With a specified hurricane event being independent of all other events, the probability of being in group I among an s hurricane event is given as P(E) = probability of hurricane failure of element i, P( j X) = probability of damage j given element vulnerability level X. P(X|H) = element vulnerability level X given hurricane category H occurrence and P(H) = probability of occurrence of the hurricane category.  To estimate the risks outcomes for the already-mentioned hazards, outcomes of the exposure probabilities computed, vulnerability weights and fragility outputs are used to estimate final failure probabilities and expected failure times for competing risks analysis. Data on hurricane damages, including those from Florida, Texas, Louisiana and Alabama, are used as supplementary data for engineering assessments and validation of failure times based on historical data of these states. Records of hurricane-induced failures of sign structures [21,[48][49][50][51], shown in Figure 4, are employed in estimating the probabilities of damage due to signs, signals and other operation facilities on roadways ( Figure 5). From the computed probabilities of failure, the Poisson processes of L 1 (t), t ≥ 0 , L 2 (t), t ≥ 0 L 3 (t) and t ≥ 0 to L s (t), t ≥ 0 of the s events would yield rates λp 1 , λp 2 , λp 3 . . . . . . to λp k , with the processes being independent and the probability of event L i (t) is given as e −λp i (t) .
To estimate the risks outcomes for the already-mentioned hazards, outcomes of the exposure probabilities computed, vulnerability weights and fragility outputs are used to estimate final failure probabilities and expected failure times for competing risks analysis. Data on hurricane damages, including those from Florida, Texas, Louisiana and Alabama, are used as supplementary data for engineering assessments and validation of failure times based on historical data of these states. Records of hurricane-induced failures of sign structures [21,[48][49][50][51], shown in Figure 4, are employed in estimating the probabilities of damage due to signs, signals and other operation facilities on roadways ( Figure 5).

Results and Discussion
This section discusses risks of failure of ITS devices (by natural deterioration, electrical or mechanical) in the presence of hurricanes. The competing risk model is applied to assess the performance of six ITS components, namely, CCTV, AVI, wireless communication systems, DMS and portable DMS, and their failure due to the impact of Hurricane Categories 1, 2 and 3. The various risks are compared using the hazard ratios of the competing events with age as the covariate along with the cumulative incidence curves.
From the output of the product-limit survival estimates and the cause-specific hazard outputs for the DMS system (Figures 6 and 7), it is estimated that the impact of Hurricanes Category One (1) would not fail the devices as a competing event compared to the deterioration of the devices either through wear-out or electrical/mechanical failures. From the analyzed data, it is realized that the

Results and Discussion
This section discusses risks of failure of ITS devices (by natural deterioration, electrical or mechanical) in the presence of hurricanes. The competing risk model is applied to assess the performance of six ITS components, namely, CCTV, AVI, wireless communication systems, DMS and portable DMS, and their failure due to the impact of Hurricane Categories 1, 2 and 3. The various risks are compared using the hazard ratios of the competing events with age as the covariate along with the cumulative incidence curves.
From the output of the product-limit survival estimates and the cause-specific hazard outputs for the DMS system (Figures 6 and 7), it is estimated that the impact of Hurricanes Category One (1) would not fail the devices as a competing event compared to the deterioration of the devices either through wear-out or electrical/mechanical failures. From the analyzed data, it is realized that the

Results and Discussion
This section discusses risks of failure of ITS devices (by natural deterioration, electrical or mechanical) in the presence of hurricanes. The competing risk model is applied to assess the performance of six ITS components, namely, CCTV, AVI, wireless communication systems, DMS and portable DMS, and their failure due to the impact of Hurricane Categories 1, 2 and 3. The various risks are compared using the hazard ratios of the competing events with age as the covariate along with the cumulative incidence curves.
From the output of the product-limit survival estimates and the cause-specific hazard outputs for the DMS system (Figures 6 and 7), it is estimated that the impact of Hurricanes Category One (1) would not fail the devices as a competing event compared to the deterioration of the devices either through wear-out or electrical/mechanical failures. From the analyzed data, it is realized that the contribution of wear-out or electrical/mechanical failures of DMS, DMS towers and portable DMS is significantly higher and different from the Hurricane Categories 1 and 2 impacts as demonstrated by the chi-square estimates and the corresponding p-value (<0.05) from the CIF (Tables 2 and 3). The point estimate of the hazard ratios due to the impact of the deterioration of the DMS, the DMS towers, and the portable DMS are of the order of 0.293 (with confidence intervals of 0.267 and 0.322), 0.314 (with confidence bounds of 0.287 and 0.344) and 0.425 (with confidence bounds of 0.392 and 0.460), compared to the impact of Hurricane Category 3. As such, the average hazard ratio for Hurricane Category 3 compared to the devices is estimated to be more than twice the impact of the DMS deterioration, indicating the severity of the impact of Hurricane Category 3 compared to the natural deterioration of components. It is postulated from the results that the impact of Hurricane Category 3 could undermine the reliability of the dynamic message signal components during its service life ahead of natural wear-out, electrical or mechanical failures. Autonomous and connected vehicles research would therefore have to envisage and forecast the impact of hurricanes on the vehicle to infrastructure connection disruption due to hurricane-induced failures of towers and other message signals. The results described above also suggest that, in the event of hurricane-induced failures, departments of transportation (DOTs) would have to plan for the repercussions of the net effect of the hazards that could lead to road-posting and the partial or complete closure of roadways. point estimate of the hazard ratios due to the impact of the deterioration of the DMS, the DMS towers, and the portable DMS are of the order of 0.293 (with confidence intervals of 0.267 and 0.322), 0.314 (with confidence bounds of 0.287 and 0.344) and 0.425 (with confidence bounds of 0.392 and 0.460), compared to the impact of Hurricane Category 3. As such, the average hazard ratio for Hurricane Category 3 compared to the devices is estimated to be more than twice the impact of the DMS deterioration, indicating the severity of the impact of Hurricane Category 3 compared to the natural deterioration of components. It is postulated from the results that the impact of Hurricane Category 3 could undermine the reliability of the dynamic message signal components during its service life ahead of natural wear-out, electrical or mechanical failures. Autonomous and connected vehicles research would therefore have to envisage and forecast the impact of hurricanes on the vehicle to infrastructure connection disruption due to hurricane-induced failures of towers and other message signals. The results described above also suggest that, in the event of hurricane-induced failures, departments of transportation (DOTs) would have to plan for the repercussions of the net effect of the hazards that could lead to road-posting and the partial or complete closure of roadways.
Also, the vehicle detection and tracking devices demonstrated rapid failures with time. From the pairwise comparison of the CCTV, AVI and wireless communications systems with Hurricane Categories 1 and 2, the results showed a high likelihood of failure of vehicle detections systems due to deterioration as a competing event (Figures 8 and 9). The proportion hazard ratios of the Hurricane Category 1 compared to the devices was < 0.0001 and that of Hurricane Category 2 < 0.5, demonstrating the lower impact of the Hurricane Categories 1 and 2 (Tables 4 and 5). Like the results for the DMS components, Hurricane Category 3 was observed to be significant and statistically different in its impact (based on the hazard ratios and the cumulative incidence functions) compared to the AVI and the CCTV. The hazard ratios of Hurricane Category 3 compared to the CCTV, AVI and wireless communication systems were 1.51, 1.54 and 3.41 times, respectively.  Also, the vehicle detection and tracking devices demonstrated rapid failures with time. From the pairwise comparison of the CCTV, AVI and wireless communications systems with Hurricane Categories 1 and 2, the results showed a high likelihood of failure of vehicle detections systems due to deterioration as a competing event (Figures 8 and 9). The proportion hazard ratios of the Hurricane Category 1 compared to the devices was < 0.0001 and that of Hurricane Category 2 < 0.5, demonstrating the lower impact of the Hurricane Categories 1 and 2 (Tables 4 and 5). Like the results for the DMS components, Hurricane Category 3 was observed to be significant and statistically different in its impact (based on the hazard ratios and the cumulative incidence functions) compared to the AVI and the CCTV. The hazard ratios of Hurricane Category 3 compared to the CCTV, AVI and wireless communication systems were 1.51, 1.54 and 3.41 times, respectively.
Infrastructures 2020, 5, x FOR PEER REVIEW 6 of 16 Additionally, the CCTV and the AVI showed faster deterioration than DMS and DMS towers. This was not unexpected, since the vehicle detection devices are more prone to electrical and mechanical failures [29]. As such, preventive maintenance and monitoring would be required for efficient functionality of the devices. To maintain the overall reliability of the ITS systems, roadway communications and detection devices would have to be evaluated for deterioration on a regular basis and inspected after hurricanes to maintain a high standard of operation of ITS systems.        Figure 9. Cumulative incidence function estimates for vehicle-tracking and detection systems compared with hurricane failure intensities.      Additionally, the CCTV and the AVI showed faster deterioration than DMS and DMS towers. This was not unexpected, since the vehicle detection devices are more prone to electrical and mechanical failures [29]. As such, preventive maintenance and monitoring would be required for efficient functionality of the devices. To maintain the overall reliability of the ITS systems, roadway communications and detection devices would have to be evaluated for deterioration on a regular basis and inspected after hurricanes to maintain a high standard of operation of ITS systems.

Conclusions
This paper has employed the competing risks model to estimate the performance of ITS infrastructures. The product-limit survival estimates and the cumulative incidence functions were used to depict the risks of failure of CCTV, AVI, wireless communication systems and DMS due to natural deteriorations in the presence of hurricane-induced failures of the devices from Hurricane Categories 1, 2 and 3.
It was demonstrated that, as ITS infrastructure devices age, the contribution of Hurricane Category 3 as a competing failure risk is higher and significant compared to natural deterioration. This was evident as the Hurricane Category 3 failure vs. natural deterioration yielded an average hazard ratio of 1.5 for CCTV, AVI and wireless communications system and an average hazard ratio of 2.3 for DMS, DMS towers and portable DMS. The proportion hazard ratios of the Hurricane Category 1 compared to the devices was < 0.0001 and that of Hurricane Category 2 < 0.5, demonstrating the lower impact of the Hurricane Categories 1 and 2. Survival probabilities also indicated that Hurricane Categories 1 and 2 caused relatively low impacts as competing events compared to DMS components and vehicle detection systems.
Also, the results demonstrated that the chance of "failure" of ITS infrastructures declining in their reliabilities could not only be with affiliated with natural deterioration only but also electrical and mechanical failures, as well as hurricane failures. As such, institutions would have to envisage and forecast the impact of hurricanes on vehicle to infrastructure connection disruptions due to hurricane-induced failures of towers and other message signals, especially for autonomous and connected vehicle systems. Overall, it was successfully demonstrated that competing risk models were effective in assessing the performance of ITS devices based on the dependent modes of failure and their extent and contribution to the holistic failures of ITS infrastructures.