Intervention Model Technical Documentation Overview The Intervention Model measures the effectiveness of the Federal Motor Carrier Safety Administration’s (FMCSA) Roadside Inspection and Traffic Enforcement programs in terms of safety. The majority of roadside inspections and traffic enforcements are conducted by state personnel under the Motor Carrier Safety Assistance Program (MCSAP) grant program. Effectiveness, for the purposes of this analysis, is defined as the estimated reduction in commercial motor vehicle crashes attributable to the existence and implementation of the aforementioned safety programs. The model is a key element of the FMCSA's Safety Program Performance Measures project. Intervention Data Raw intervention data serve as the inputs from which all further determinations flow. The data consist of individual records of roadside inspections and traffic enforcements carried out during a given period. The model creates a crashes-avoided figure for each intervention based on the number and type of violations detected. Roadside Inspections Roadside inspections are interventions performed by qualified safety inspectors using the North American Standard (NAS) guidelines. The NAS is a vehicle and driver inspection structure established by the FMCSA and the Commercial Vehicle Safety Alliance (CVSA). Traffic Enforcements MCSAP traffic enforcements are a subset of traffic enforcements in general. MCSAP traffic enforcements include only those enforcement stops that lead to an on-the-spot roadside inspection. The enforcement agent, if qualified, performs the subsequent roadside inspection. Otherwise, a safety inspector is called to the scene to conduct it. Since a traffic infraction precipitates the ensuing roadside inspection, 17 moving violations are incorporated into the driver section of the roadside checklist. The model classifies an intervention as a traffic enforcement intervention when at least one traffic enforcement violation is present in the intervention record. The only exception is when one or more drug and alcohol violations (392.4A and 392.5A) are the only traffic enforcement violations present. These interventions are counted as roadside inspection interventions rather than traffic enforcement-initiated interventions. Intervention Level Impact As the name implies, the Intervention Model places a great deal of importance on individual interventions. The reason for this is that violation tabulations come from interventions and those tabulations are matched against a Violation Crash Risk Probability Profile (VCRPP), which then serves as a basis for determining the number of crashes avoided for a given intervention. Aggregates developed from the intervention-level crashes avoided numbers eventually form national and state statistics. Violation Crash Risk Probability Profile The model assumes that observed deficiencies (OOS and non-OOS violations) can be converted into crash risk probabilities. This assumption is based on the belief that detected defects represent varying degrees of mechanical or judgmental faults and, as a result, some are more likely than others to play contributory roles in causing commercial motor vehicle crashes. These differences can be estimated and ranked into discrete risk categories. Thus, the VCRPP contains all violation codes, each with an assigned risk category and a corresponding crash probability. Using Cycla's risk categories and the relative weights assigned to the categories, the Volpe Center analysts sought to account for error margins by opting for two probability sets - a Higher Bound set and a Lower Bound set. The outputs computed from the two sets are used to compute a mean with a range of ± 20 percent. Because crash causation data is still forthcoming, users are reminded to employ caution interpreting the Model's results. The values in Table 1 and Table 2 indicate the Lower Bound and Higher Bound numbers of violations that would have to be discovered to cause the model to credit one of the programs with an avoided crash. Keep in mind, however, the numbers in the tables are not meant to be definitive. They constitute the “best guesses” of industry experts interpreting available data. Volpe Center analysts used these figures to test and calibrate the model. As more reliable crash causation statistics become available, table quantities may have to be revised. These revisions will not affect the overall soundness of the model. Note that in moving from Risk Category (RC) 1 to RC 2, from RC 2 to RC 3, and so on, each step varies by a factor of ten. This tracks Cycla's variation in designated relative weights between risk categories. Note further that the weight given to traffic enforcement violations is four times that of the roadside inspection counterpart violations. Table 1 and Table 2 illustrate the factor and weighting differences. For example, the tenfold factor variation can be seen when Traffic Enforcement RC1 OOS Violations jump from 30 to 300 when stepping to Traffic Enforcement OOS Violations RC2. Additionally, it takes quadruple the number of Roadside Inspection OOS Violations in RC1 (120) to have the same impact as Traffic Enforcement OOS Violations in RC1 (30), demonstrating the reduced weight given to roadside inspection violations vis-à-vis traffic enforcement violations. Volpe Center analysts used the latest, preliminary data available from ongoing crash causation studies to support this difference. The studies found that driver faults represented by traffic enforcement violations are more likely to lead to motor carrier crashes than are roadside inspection driver or vehicle faults of an equivalent risk category. Table 1. Lower Bound of Number of Violations to Avoid One Crash Risk Category Roadside Inspection Traffic Enforcement OOS Non-OOS OOS Non-OOS 1 120 240 30 60 2 1,200 2,400 300 600 3 12,000 24,000 3,000 6,000 4 120,000 240,000 30,000 60,000 5 1,200,000 2,400,000 300,000 600,000 Table 2. Higher Bound of Number of Violations to Avoid One Crash Risk Category Roadside Inspection Traffic Enforcement OOS Non-OOS OOS Non-OOS 1 80 160 20 40 2 800 1,600 200 400 3 8,000 1,600 2,000 4,000 4 80,000 16,000 20,000 40,000 5 800,000 160,000 200,000 400,000 Table 3 and Table 4 display the higher bound and lower bound probabilities, respectively. The crash reduction probabilities are the reciprocals of the numbers in Table 1 and Table 2, so it follows that the probabilities also experience a tenfold change between steps. The crash reduction probabilities associated with each violation form the VCRPP. Table 3. Lower Bound Crash Reduction Probabilities Risk Category Roadside Inspection Traffic Enforcement OOS Non-OOS OOS Non-OOS 1 8.33 x 10-3 4.167 x 10-3 0.033 0.0167 2 8.33 x 10-4 4.167 x 10-4 3.3 x 10-3 1.67 x 10-3 3 8.33 x 10-5 4.167 x 10-5 3.3 x 10-4 1.67 x 10-4 4 8.33 x 10-6 4.167 x 10-6 3.3 x 10-5 1.67 x 10-5 5 8.33 x 10-7 4.167 x 10-7 3.3 x 10-6 1.67 x 10-6 Table 4. Higher Bound Crash Reduction Probabilities Risk Category Roadside Inspection Traffic Enforcement OOS Non-OOS OOS Non-OOS 1 0.0125 6.25 x 10-3 0.05 0.025 2 1.25 x 10-3 6.25 x 10-4 5.0 x 10-3 2.5 x 10-3 3 1.25 x 10-4 6.25 x 10-5 5.0 x 10-4 2.5 x 10-4 4 1.25 x 10-5 6.25 x 10-6 5.0 x 10-5 2.5 x 10-5 5 1.25 x 10-6 6.25 x 10-7 5.0 x 10-6 2.5 x 10-6 Examples Applied to Recorded Violations Because each inspection used in the analysis has one or more violations, the model classifies recorded violations according to their VCRPP ratings. Table 5 and Table 6 display the classification process for two example interventions. Intervention A is a roadside-initiated intervention, since no traffic enforcement violations are present. It contains roadside RC 1 OOS violations and both OOS and non-OOS RC 2 violations. Using the VCRPP, the violations receive their respective probabilities from the Higher Bound and Lower Bound probability sets. The VCRPP is also applied to Intervention B. Unlike Intervention A, Intervention B is classified as a traffic enforcement-initiated intervention, because it has at least one traffic enforcement violation. Additionally, several roadside inspection violations were identified during the subsequent roadside inspection. Table 5. Violations for Intervention A Violation Number Violation Description Violation Type OOS Risk Category Lower Risk Probability Higher Risk Probability 392.5C Operating a CMV while fatigued Roadside Yes 1 8.33 x 10-3 0.0125 393.9H Inoperable head lamps Roadside Yes 1 8.33 x 10-3 0.0125 395.3A1 10 hour rule violation Roadside Yes 2 8.33 x 10-4 1.25 x 10-3 392.14 Failed to use caution for hazardous condition Roadside Yes 2 8.33 x 10-4 1.25 x 10-3 393.201B Bolts securing cab broken Roadside Yes 2 8.33 x 10-4 1.25 x 10-3 393.9T Inoperable tail lamp Roadside No 2 4.167 x 10-4 6.25 x 10-4 393.60C Use of vision reducing matter on windows Roadside No 2 4.167 x 10-4 6.25 x 10-4 392.9A3 Driver’s view is obstructed Roadside No 2 4.167 x 10-4 6.25 x 10-4 393.77 Prohibited heaters Roadside No 2 4.167 x 10-4 6.25 x 10-4 Table 6. Violations for Intervention B Violation Number Violation Description Violation Type OOS Risk Category Lower Risk Probability Higher Risk Probability 393.48A Inoperative brakes Roadside Yes 1 8.33 x 10-3 0.0125 393.209D Inoperative steering system component Roadside Yes 1 8.33 x 10-3 0.0125 393.17B No deflective side marker Roadside No 2 4.167 x 10-4 6.25 x 10-4 392.9A Failure to secure load Roadside No 2 4.167 x 10-4 6.25 x 10-4 392.5A Possession/use/under influence of alcohol Traffic Yes 1 0.033 0.05 392.2C Failure to obey traffic control device Traffic Yes 2 3.3 x 10-3 5.0 x 10-3 392.2P Improper passing Traffic Yes 2 3.3 x 10-3 5.0 x 10-3 Occurrences per Risk Category After the application of the VCRPP, the model aggregates violations occurring in a particular risk category. Table 7 continues with the example interventions from Table 5 and Table 6 by exhibiting the results of the aggregation. Table 7. Violation Occurrences per Risk Category Inspection Roadside Inspection Traffic Enforcement RC 1 Viol. RC 2 Viol. RC 1 Viol. RC 2 Viol. OOS Non-OOS OOS Non-OOS OOS Non-OOS OOS Non-OOS A 2 0 3 4 0 0 0 0 B 2 0 0 2 1 0 2 0 Crashes Avoided per Intervention To generate an intervention's crashes avoided, the number of violation occurrences per risk category is multiplied by the crash probability associated with that risk category. For instance, if four occurrences of roadside inspection OOS violations in RC 1 were noted on an inspection report, then the model would multiply four by the roadside OOS RC 1 probability from the VCRPP. This would be done for all roadside inspection OOS and non-OOS violations, along with all traffic enforcement OOS and non-OOS violations. Summing the products creates an initial crash risk reduction for the inspection's risk category being evaluated. [1] where: Variable Description Values Initial Crash Risk Reduction 0... Number of Violations 0... Crash Risk Probability Table 5, Table 6 Risk Category 1,2,3,4,5 Type of Violation Roadside, Traffic Out of Service Yes, No Next, all violations recorded for a risk category during an intervention, roadside inspection OOS and non-OOS and, if applicable, traffic enforcement OOS and non-OOS, are added together. Multiplying the total by the initial crash risk reduction calculated in Equation [1] produces the final crash risk reduction for a given risk category in a particular intervention. Equation [2] is designed to capture the increased risk arising from the discovery and correction of numerous violations during a single intervention. The logic behind this is that, while each violation carries a certain degree of crash risk in isolation, additional violations occurring in tandem elevate the crash risk beyond the mere combined, additive, risk levels caused by each violation alone. In essence, the final crash risk reduction per risk category equation measures the multiplicative crash risk effect of compound safety defects. [2] where is the final calculated crash risk reduction for a given risk category within an intervention. Equation [1] and Equation [2] must be calculated for each of the five risk categories. When all five risk categories have had their respective crash risk reductions determined, the model calculates the intervention's crashes avoided by adding the five numbers as shown in Equation [3]. A cap of 0.75 is placed on the outcome for each intervention, thus ensuring that the model never produces a crashes avoided total greater than one. Volpe Center analysts chose three-quarters of a crash avoided as a cap to maintain a more conservative tendency in the model, given the lack of empirical crash causation data. [3] where is the calculated crashes avoided due to an intervention. Repeating this process using both Higher Bound and Lower Bound probabilities yields the crashes avoided range for each intervention. Examples Intervention A For Intervention A (see Table 5), a vehicle given a roadside inspection is found to have two out-of-service violations in Risk Category 1, three out-of-service violations in Risk Category 2, and four non-out-of-service violations in Risk Category 2. The calculation of the total crashes avoided of this single inspection, using Higher Bound probabilities, appears below. Multiplying the crash reduction probability for each risk category by the number of out-of-service violations in that risk category and adding it to the product of the risk reduction probability and the number of non-out-of-service violations gives the initial crash risk reduction as formalized by Equation [1]. Risk Category Higher Bound Calculation 1 2 Final crash risk reduction becomes known after multiplying the initial crash risk reduction for each risk category by the number of violations in that risk category. The model supplies total crashes avoided for the intervention by tallying the final crash risk reduction from each risk category as formalized by Equation [2] and Equation [3]. Risk Category Higher Bound Calculation 1 2 Total Therefore, Inspection A's range of crashes avoided begins at the Higher Bound result, 0.09375, and would extend to the Lower Bound output. Intervention B For Intervention B (see Table 6), a traffic enforcement stop has resulted in both traffic enforcement violations and roadside inspection violations. The intervention involved one traffic enforcement out-of-service violation in Risk Category 1 and two out-of-service violations in Risk Category 2. In addition, the inspection involved two roadside inspection out-of-service violations in Risk Category 1 and two non out-of-service violations in Risk Category 2. Inspection B's computations follow: Risk Category Higher Bound Calculation 1 2 To account for multiple violations, the model makes the following intensification adjustments to calculate the final crash risk reduction for each risk category: Risk Category Higher Bound Calculation 1 2 Total The crashes avoided range for Inspection B starts at 0.27 at the higher bound and extends down to the lower bound. Program Level Impact Measuring interventions at the program level is next. It is here, however, that the model follows two divergent paths, one measuring direct effects and the other measuring indirect effects. Direct effects, it should be remembered, are the immediate products of roadside inspections and traffic enforcement stops performed in a given year, while indirect effects are based on behavioral changes caused by program awareness. Figure 1 provides an overview of the Intervention Model. Figure 1. Overview of the Intervention Model Direct Effect Approach This section outlines the development of direct-effect crashes-avoided estimates. Figure 2 shows the process used to determine the direct effects of the programs. First, there is a primary crashes avoided computation that calculates crashes avoided for each program. Afterwards, the Traffic Enforcement Program is further analyzed to better understand how each Traffic Enforcement Program activity contributes to the number of crashes avoided. Figure 2 provides an overview of the direct effects approach. Figure 2. Direct-Effect Approach Primary Determination The model initially examines all inspections in a given year in terms of the numbers and types of violations associated with each individual inspection. Based on the VCRPP described above, inspection violations (both OOS and non-OOS) are matched with their respective crash risk reduction probabilities, to produce an estimated range of crashes avoided for that inspection. The model next segregates the complete set of inspections into two groups, depending on whether the initiating intervention was a roadside inspection or a traffic enforcement. Interventions with drug and alcohol violations (392.4A and 392.5A) as the only traffic enforcement violations are counted as roadside inspection interventions. The logic behind this is the only way an officer could have identified drug and alcohol violations is by stopping the vehicle, and if the vehicle was not stopped for a moving violation, then it must have been detained as a part of a roadside inspection. Thus these types of interventions are counted as part of the Roadside Inspection Program, but the drug and alcohol violations are assigned the traffic enforcement crash reduction probabilities. Once all of the inspections have been divided among the two programs, the estimated crashes-avoided ranges are summed across all inspections in each program. Two overall estimates of crashes avoided emerge: one for the Roadside Inspection Program and one for the Traffic Enforcement Program. [4] [5] Traffic Enforcement Program Since the Traffic Enforcement Program is broken out into both traffic enforcement activities and roadside inspection activities, the next step in the model is to understand the contribution each type of activity makes to the number of crashes avoided. In previous years, a roadside inspection allocation was calculated to credit a portion of traffic enforcement crashes avoided back to the Roadside Inspection Program, recognizing the contribution to the traffic enforcement total made by the ensuing roadside inspection, however, this approach has been modified. The current methodology provides a breakdown of the Traffic Enforcement Program and analyzes the contribution of each type of activity separately and in combination within the Traffic Enforcement Program. To analyze the benefits of each activity type individually, the same calculations are applied as in determining the impact of the Traffic Enforcement Program as a whole, but the data for traffic enforcement activities and roadside inspection activities are treated separately. To calculate the initial crash risk reduction for a risk category for each type of activity, Equation [1] is modified to look at the roadside inspection violations and traffic enforcement violations that make up the Traffic Enforcement Program independently, where represents the initial crash risk reduction for roadside inspection activities within each risk category and represents the same for traffic enforcement activities: [6] [7] where: Variable Description Values Initial Crash Risk Reduction 0... Number of Violations 0... Crash Risk Probability Table 5, Table 6 Risk Category 1,2,3,4,5 Out of Service Yes, No To determine the final calculated crash risk reduction per risk category for Traffic Enforcement Program roadside inspection activities and traffic enforcement activities, Equation [2] can be modified as follows: [8] [9] Where is the final calculated crash risk reduction for a given risk category gained through roadside inspection activities and is the final calculated crash risk reduction for a given risk category gained through traffic enforcement activities. Equation [3] can be modified to determine the number of crashes avoided as a result of roadside inspection activities or traffic enforcement activities within one intervention: [10] [11] Finally, the total crashes avoided as a result of the Traffic Enforcement Program activities can be determined by summing up across all interventions: [12] [13] Where is the total number of crashes avoided through Traffic Enforcement Program roadside inspection activities and where is the total number of crashes avoided through the program’s traffic enforcement activities: [14] [15] Equation [14] and Equation [15] describe the contribution of both traffic enforcement activities and roadside inspection activities to the crashes avoided through the entire Traffic Enforcement Program, where represents the effect of the combined activity of uncovering both roadside inspection and traffic enforcement violations during a traffic enforcement. The model applies a multiplier for each additional violation identified during an intervention, by the same logic, correcting both roadside inspection and traffic enforcement violations during one intervention will increase the chances of preventing a crash when compared to interventions that uncover only roadside inspection violations or only traffic enforcement violations. Examples Intervention B The following example illustrates the Traffic Enforcement Program breakdown methodology through Intervention B. Intervention A will not be used to illustrate this portion of the model, as it represents a roadside intervention with only roadside inspection violations and does not apply in this example. First, initial crash risk reduction is calculated. This value is calculated separately for roadside inspection activities and traffic enforcement activities, respectively, using Equation [6] and Equation [7]: Risk Category Higher Bound Calculation 1 2 . Risk Category Higher Bound Calculation 1 2 Next, Equation [8] and Equation [9] calculate the final crashes avoided for each risk category within roadside inspection activities and traffic enforcement activities, respectively, and Equation [10] and Equation [11] calculate the totals for Intervention B, notated by : and . Risk Category Higher Bound Calculation 1 2 Total Risk Category Higher Bound Calculation 1 2 Total Calculating Equation [12] and Equation [13] determines the total number of crashes avoided across all interventions in this example, evaluating roadside inspection activity and traffic enforcement activity independently, such that =0.0525 and =0.07 (note that and are equal to and since this example only uses one intervention). As previously calculated on page 8, =0.27 when evaluating the Traffic Enforcement Program as a whole. Note: because is a roadside intervention and hence has no traffic enforcement activities. Finally, Equation [15] yields , where expresses the combined effect of uncovering and correcting both roadside inspection and traffic enforcement violations during traffic enforcement interventions. Indirect-Effect Approach The fundamental premise of the indirect-effect approach is that once motor carriers have been exposed to roadside inspection and traffic enforcement actions, a change in their behavior will be manifested by a reduction in crashes. This section presents a summary of the methods used in the model to arrive at the programs' indirect effects. Figure 3 provides a view of the processes involved in assessing the indirect effects of the model. Figure 3. Indirect Effect Approach Indirect effects require means other than direct measurement to reveal their presence. For that reason, the model uses changes in the number of violations recorded during inspections to identify and evaluate the indirect effects. Specifically, the model's algorithm employs two successive years of inspection data to undertake this process. To conduct a year-to-year comparison, it is necessary to identify and link the carriers who were inspected with the inspections each received during the two-year span. Only in this way can a cross-year evaluation discern the indirect influence (i.e., behavior modification) that causes a reduction in crashes. In contrast, this inspection-carrier link is not needed in the direct-effect approach. Modified Approach The method of computing indirect effects has been modified. For the years 1998 to 2000, the Intervention Model used the methodology described in the September 2002 report “Intervention Model: Roadside Inspection and Traffic Enforcement Effectiveness Assessment.” This methodology has been modified so that the results of a program’s effectiveness can be computed in the year following the program’s execution rather than two years after. This section will discuss the modified approach to computing the indirect effects. According to the modified approach, for each program, an unweighted average of the indirect benefits’ contribution to the total is computed using the results from the previous two years. For example, to calculate the estimated indirect benefits as a percentage of total for 2006, the actual indirect benefits as a percentage of the total benefits for 2005 and 2004 are averaged. See the most recent Intervention Model Executive Summary for more details. Since the estimated indirect benefits are measured as a percentage of the total benefits, which are also composed of the indirect benefits, it is necessary to manipulate basic equations in order to express the indirect benefits as a function of the direct benefits. [16] [17] Where is the indirect effect percent of roadside inspection total benefits. Solving Equation [17] for the Total Crashes Avoided (TCA) and substituting that expression into Equation [16] yields the desired result. [18] Similarly for the Traffic Enforcement Program: [19] The indirect effect percentages are not intended to be constants. In fact, they will be continually updated as the second year’s worth of data becomes available and the full version of the indirect model can be run. To continue with the example for 2006, once the 2007 data become available the indirect benefits for 2006 will be replaced with the actual benefits instead of the estimated numbers. Examples Continuing with Intervention A and Intervention B yields the following results for the program level indirect benefits. An example of the indirect effect percentages for both programs is given below in Table 8, for the most recent indirect effect percentages please refer to the most recent Executive Summary document. Table 8. Indirect Benefits as Percentage of Total Program Percentage 20.00% 15.00% Substituting these percentages into Equation [18] and Equation [19] yields the indirect effect benefits for Intervention A ()and Intervention B (). Program Benefits Crash severity varies. Some crashes may result in no more than minor property damage, while others may result in bodily harm or loss of life. Of the many gradations possible, two classifications of crashes suffice for calculating program benefits, fatal crashes and injury crashes. Any commercial vehicle crash that results in at least one fatality is a fatal crash. A fatal crash may also involve injuries, but the fatality governs the crash's classification. Any motor carrier crash that results in at least one injury requiring transport for immediate medical attention but no fatalities, is an injury crash. Statistics of fatal and injury crashes supply the basis for creating lives saved and injuries avoided figures. Fatal crashes avoided translate to lives saved and injuries avoided, while injury crashes avoided translate to injuries avoided. Figure 4 shows the process used to calculate program benefits. Figure 4. Program Benefits Determination Obtaining program benefits from estimated crashes-avoided figures requires two prior determinations, the first being a proportional identification of crashes by severity and the second being the average numbers of fatalities and injuries per crash. State-reported crash data in the Motor Carrier Management Information System (MCMIS) are used to determine the shares of fatal, injury, and tow away crashes. In order to smooth out yearly fluctuations, the Intervention Model uses a two-year average in partitioning the crashes avoided into fatal and injury crashes. The share of fatal, injury, and tow away crashes is also referred to as the probability of a fatal, injury, or tow away crash given a crash. In the second step in the determination of program benefits, the expected number of fatalities and injuries per crash type are used to compute the lives saved and injuries avoided. State-reported crash data in the MCMIS were used to compute the average number of fatalities in fatal crashes. The number of injuries per crash are found in both fatal and injury crashes, since fatal crashes can also result in injuries. The average number of injuries in fatal and injury crashes in a given year are derived from the state-reported crash data in MCMIS. These values are recomputed each year and used in the program benefits calculations. In order to be consistent with the Compliance Review Effectiveness Model and to smooth yearly fluctuations, a two-year average is used by the Intervention Model to estimate the lives saved and injuries avoided. The input to the program benefits portion of the model requires the union of crashes avoided attributable to direct effects and indirect effects. The program benefits calculations use the output of Equation [20] and Equation [21]. The calculations entail the development of estimated totals of crashes by severity as well as the final tally of lives saved and injuries avoided. [20] [21] where TCA is the Total Crashes Avoided for each of the programs (Roadside Inspection and Traffic Enforcement). Fatal and Injury Crashes Avoided The model breaks out program crashes-avoided figures into the numbers of program crashes avoided by severity. The expected number of fatal crashes avoided are computed as follows: [22] [23] where FCA is the Fatal Crashes Avoided for each of the programs (Roadside Inspection and Traffic Enforcement) and is the probability of a fatal crash given a crash. The expected number of injury crashes avoided are computed as follows: [24] [25] where ICA is the Injury Crashes Avoided for each of the programs (Roadside Inspection and Traffic Enforcement) and is the probability of a injury crash given a crash. Lives Saved To calculate the number of lives saved, the number of fatal crashes avoided is multiplied by the average number of fatalities per fatal crash. [26] [27] where LS is the Lives Saved for each of the programs and is the average number of fatalities per fatal crash. Injuries Avoided To calculate the number of injuries avoided, the number of fatal crashes avoided is multiplied by the average number of injuries per fatal crash, and the number of injury crashes avoided is multiplied by the average number of injuries per injury crash. The two products are then added to obtain the total number of injuries avoided. [28] [29] where IA is the Injuries Avoided for each of the programs, is the average number of injuries per fatal crash, and is the average number of injuries per injury crash. Examples Continuing with the example interventions, the program benefits are estimated using the following two year averages of crash severity proportions and fatalities and injuries given in Tables 9 and 10. For actual crash severity statistics, see the most recent Executive Summary document. Table 9. Two Year Average of Crash Severity Proportions Crash Severity Percentage Fatal 5% Injury 45% Tow Away 50% Table 10. Two Year Average of Fatalities and Injuries Two-Year Average Fatalities Per Fatal Crash 1.2 Injuries Per Fatal Crash 1.1 Injuries Per Injury Crash 1.5 The first step is to apply Equation [20] and Equation [21] to determine the total crashes avoided for each program. Now that the total number of crashes avoided has been computed, these crashes can be partitioned into the expected number of injury and fatality accidents according to Equation [22] through Equation [25]. Fatal Crashes Avoided Injury Crashes Avoided The second step in the computation of the overall program benefits is to apply Equation [26] through Equation [29] to determine the number of lives saved and the number of injuries avoided. Lives Saved Injuries Avoided Table 11 summarizes the program benefits from the two example interventions. Table 11. Example Program Benefits Crashes Avoided Lives Saved Injuries Avoided Roadside Inspection 0.11719 0.00703 0.08555 Traffic Enforcement 0.31765 0.0191 0.18122 Intervention Model Total 0.43484 0.02613 0.26677 June 2007 Intervention Model Technical Documentation Prepared for: Federal Motor Carrier Safety Administration Office of Information Management Analysis Division 400 Seventh Street, SW Washington, DC 20590 Prepared by: John A. Volpe National Transportation Systems Center Office of System and Economic Assessment Motor Carrier Safety Assessment Division, RTV-3E Kendall Square 55 Broadway Cambridge, MA 02142 Document Number: FMCSA-RRA-07-016