The FRED score answers one question for every property motor carrier registered with FMCSA: how many recordable crashes is this motor carrier likely to generate per power-unit-year over the coming twelve months, and how does that compare with a motor carrier of its class? The answer is built entirely from public FMCSA records and refreshed weekly across the whole property universe — for-hire, private and exempt, interstate and intrastate — about 1.84 million motor carriers, of which the 109,449 with ten or more power units form the ranked underwriting book.
The engine is the product of the Safety Core Study, a stand-alone study of motor carrier crash-risk modelling on public data in which FMCSA's own measures appear only as benchmarks. Its prediction is the product of three named factors: a class rate \(\mu_{\text{class}}\) per power-unit-year from a Poisson regression on the motor carrier's size, class, tenure, filing recency, how much of its filed fleet the roadside record sees, and road activity (§4); a violation relativity \(V\) from three credibility-shrunk ratios — driver behaviour, and out-of-service and violation ratios standardised for where the motor carrier was inspected (§5); and a crash-experience term \(\bar\theta\), the Gamma–Poisson posterior mean of the motor carrier's own recordable crashes over 36 months, decayed on a linear ramp, against the crashes the first two factors predict (§6). Their product gives the relativity to class \(\bar R = V\bar\theta\) and the forward expectation \(\mu_{\text{class}}\bar R\) per power-unit-year (§7).
The grade is a band from fitted cuts on \(\bar R\), then screens: the top tiers require proof (60% of the posterior below the cut, a driver-behaviour relativity no worse than class, no fatal crash, enough inspections, a plausible fleet), the bottom tiers require observed events and the same 60% posterior test in the other direction, so a wide posterior falls back toward the class rate whichever way it points (§8); a Satisfactory whose 80% range still runs from Excellent to Poor territory is shown as Not enough record, with no score (§8). Every weekly change is attributed to one of six causes and improvements are ramped one band per run (§9); nineteen acceptance checks run before anything is written (§10). Out of sample the engine explains 28.2% of forward crash deviance with an exposure-weighted normalized Gini of 0.653, 0.021 behind a gradient-boosted ceiling while remaining fully decomposable; out of time, in the latest run's gate year, its grades realize 0.50, 0.68, 0.94, 1.25, 1.68 and 3.08 times the class expectation, Excellent to Critical, in order (§8, §11).
For motor carrier \(i\) at a cutoff date \(C\), the target is the number of federally recordable crashes the motor carrier generates in the twelve months after \(C\), per power-unit-year of exposure. Writing \(y_i\) for the realized count and \(E_i\) for forward exposure, the engine estimates the rate \(\lambda_i\) with \(y_i \sim \text{Poisson}(\lambda_i E_i)\):
$$ \lambda_i \;=\; \mu_{\text{class}}(x_i)\cdot V_i\cdot\bar\theta_i, \qquad \bar R_i \;=\; V_i\,\bar\theta_i \;=\; \frac{\lambda_i}{\mu_{\text{class}}(x_i)}. $$\(\mu_{\text{class}}\) is what a motor carrier with this one's attributes is expected to do; \(\bar R\) is how far this motor carrier's own record moves it from that expectation. \(\bar R = 1\) means “typical for a motor carrier of this class”; 0.5 means half the crashes, 2 means twice. The grade reads \(\bar R\); the motor carrier page also shows the absolute expectation \(\lambda_i\cdot\text{PU}_i\) as expected crashes over the next twelve months.
The target is frequency, not a severity-weighted burden. The study's variable-importance work found severity weights in the frequency model to be noise, and a frequency target is what the Gamma–Poisson experience term is exact for. Severity is modelled separately for display and loss-cost work (§12).
Five properties were fixed in the study charter before any model was fit, and the design below is the attempt to satisfy them: (1) a thin or unreliable record sits near its class rate; (2) the top tier requires proof; (3) the bottom tier requires observed adverse events, never attributes alone; (4) events decay smoothly to zero weight; (5) no grade jumps upward without a cause that can be named.
All inputs are FMCSA files published on data.transportation.gov, downloaded weekly and archived point-in-time: the company census (power units, class, operation type, hazmat, domicile, registration date, MCS-150 filing date and mileage, safety rating), the MCMIS crash file (full history, with the date FMCSA added each record), the MCMIS inspection file (36 months) and its inspection-violation detail, SMS inspection units (vehicle VINs), the licensing and insurance history and out-of-service orders (exits), and the SMS violation lookup that maps each violation code to its BASIC. FMCSA BASIC percentiles are never read: the public SMS carries none for property motor carriers, and they would leak the outcome into the inputs.
The universe is every property motor carrier — for-hire, private and exempt; interstate and intrastate — with at least one power unit; operation type is a class-rate feature, not an exclusion. Passenger strata (buses, coaches, school buses, vans, limousines) are held out for their own class models. A motor carrier under an out-of-service order at the cutoff is excluded from grading, as is one whose operating authority was revoked with no roadside inspection or crash recorded since and no active authority on the current FMCSA file (activity or a reinstatement cancels the exit). A motor carrier registered on or after \(C\) has no exposure inside a window yet, a census record outside the population at the cutoff (inactive, no power units or no forward exposure) has nothing to grade, a filing of 1,000 or more power units that its own drivers and the roadside record contradict is not credible, and a fleet of more than 5,000 power units is not graded yet (§3); each is shown with the reason instead of a grade. The 2026-11-07 run graded 1,835,687 property motor carriers. The reasons are written for the motor carriers of the site's searchable census, a list that differs from the graded universe (a graded motor carrier outside the census is not searchable), and 144,337 census motor carriers were shown with a reason instead of a grade: 101,175 operating authority revoked, no roadside activity since; 29,757 passenger operation — outside the model for motor carriers of property; 8,017 registered after the scoring cutoff; 4,620 under a federal out-of-service order; 697 filed fleet not credible: the drivers and the roadside record contradict the filed power units; 44 outside the scoring population at the cutoff; 21 very large fleet (5,000+ power units), size confirmed roadside: not graded yet; 6 5,000+ power units on file, not confirmed by the roadside record.
Each weekly run at run date \(R\) uses two cutoffs. \(C\) is the first of the month containing the knowledge date \(\min(R,\ \text{data-as-of} + 1\text{ day})\), so the run reads whole months the FMCSA files cover. Inspections, violations, the census facts and the VIN count are read through \(C\); crashes stop one month earlier, at \(C_{\text{crash}} = C - 1\text{ month}\), because crash reports reach FMCSA weeks late. The run reads the records on FMCSA's file at the data date and places each by the date it happened — a crash by its report date, an inspection by its inspection date — so a record that reaches the file late enters the window at its own date in the next weekly run; the validation replays of Appendix B read the add dates instead, to reproduce what each run could have known. The 2026-11-07 run used \(C\) = 2026-10-01 and \(C_{\text{crash}}\) = 2026-09-01 with data as of 2026-10-29. The windows are half-open and in calendar months:
$$ \underbrace{[\,C_{\text{crash}}-36\text{ m},\ C_{\text{crash}}\,)}_{\text{crash window (36-month ramp)}}\qquad \underbrace{[\,C-24\text{ m},\ C\,)}_{\text{inspection, violation and VIN window}}\qquad \underbrace{[\,C,\ C+12\text{ m}\,)}_{\text{forward outcome (validation only)}} $$Why this timing: nationally 85% of crashes are known to FMCSA within 60 days (67.7% within 30, 92.5% within 90) and completeness is strongly state-dependent — Colorado reached only 25% at 60 days in the study's measurement — while inspection records arrive within days to weeks. The reporting-hold study (Appendix B) replayed 13 historical monthly runs, each with only the records it would have had, and judged five timings on the crashes motor carriers had afterwards. Every timing that counted more recent events beat holding everything back two months on all 13. Counting crashes right up to the run date gained most in normal months but drifted generous when FMCSA's crash reporting stalled in mid-2025; holding crashes one month kept the longer hold's calibration and grade mix. A state-specific completeness factor fitted from the weekly archive is the planned refinement.
| Symbol | Meaning |
|---|---|
| \(C,\ C_{\text{crash}}\) | Cutoffs: \(C\) = first of the month containing \(\min(R,\ \text{data-as-of} + 1\text{ d})\); inspections, violations, census and VINs through \(C\). Crashes through \(C_{\text{crash}} = C - 1\) month |
| \(\text{PU}_{\text{floor}}\) | Exposure power units: max(filed power units, power-unit VINs observed in 24 months) (§3) |
| \(c\) | Fleet-size cohort of the motor carrier: one of nine (§3) |
| \(\mu_{\text{class}}(x)\) | Class rate: expected recordable crashes per power-unit-year from the frozen Poisson GLM (§4) |
| \(\tilde r_s,\ V\) | Shrunk relativity of violation signal \(s\); violation relativity \(V = \prod_s \tilde r_s^{\gamma_s}\) (§5) |
| \(N,\ \Lambda\) | Decayed recordable crashes in 36 months; decayed class-and-violation-expected crashes (§6) |
| \(a,\ \bar\theta,\ Z\) | Credibility prior \(a(c,\Lambda)\) for the cohort and the record's expected crashes; experience relativity \((a+N)/(a+\Lambda)\); credibility \(\Lambda/(a+\Lambda)\) (§6) |
| \(\bar R\) | Relativity to class \(V\bar\theta\): the graded statistic, the posterior mean (§7) |
| \(q_{10},\ q_{90}\) | 10th and 90th percentiles of the posterior for \(R\) (§7) |
Crash risk is rated per power-unit-year, and the filed power-unit count alone is a poor measure of it. Counting distinct power-unit VINs seen at inspections and crashes in the trailing 24 months (trailers excluded — the second unit of an inspection is usually a trailer), the study measured realized ÷ predicted crashes under a cohort-rate model:
| Group | Motor carriers | Realized ÷ predicted |
|---|---|---|
| Observed fleet consistent with filing | 54,720 | 1.08 |
| More power units observed than filed | 47,544 | 1.71 |
| Fewer than a fifth observed (large fleets — inspections sample a big fleet) | 894 | 0.97 |
| Never seen in 24 months | 358,638 | 0.50 |
Hence the exposure floor \(\text{PU}_{\text{floor}} = \max(\text{filed PU},\ \text{observed power-unit VINs})\): a “one-truck” motor carrier seen with seven tractors is not a one-truck exposure. The never-seen population is not excluded — its dormancy is carried into the class rate through activity, filing recency and tenure (§4), and the VIN count is only ever a floor. Every filing of 1,000 or more power units is checked against the roadside record before grading: when at most 13 different trucks of the motor carrier were inspected in 24 months and the filing lists under one driver per 50 filed units (or the filing is above 5,000 units), the filed fleet is not credible and the motor carrier is not graded. Above 5,000 power units no motor carrier is graded yet: where the roadside confirms the size (at least 500 different trucks inspected in 12 months, and either a third of the filed fleet seen or a driver count in line with honest filers of 50–500 units), these fleets crash about 1.4 times the rate of a 5,000-unit fleet and their forecast holds, but the grade moved between bands too often from month to month to publish. Truck leasing and rental fleets and unconfirmed filings are shown with their own reasons. Exposure months are weighted by the same ramp as crashes, with tenure measured from the registration date, so a steady fleet contributes about 1.54 decayed power-unit-years per power unit over the 36-month window. FMCSA sometimes re-dates the registration of a motor carrier that has been operating for years; when a motor carrier has crashes or inspections on record in the two years before its registration date, tenure runs from its first crash or inspection on record instead, so the crashes it is charged with are always set against the time it was on the road. A motor carrier with no activity in those two years keeps its registration date.
Every motor carrier belongs to one of nine fleet-size cohorts. The cohort indexes the credibility prior (§6) and the reference rate for the driver-behaviour relativity (§5), and carries an indicator in the class rate (§4). The six cohorts of ten or more power units are the ranked book; the three below ten are graded but advisory, searchable and shown with their grade but outside the ranked book and the default charts.
| Cohort | Power units | Scope | Cohort prior \(a\) |
|---|---|---|---|
pu1 | 1 | Advisory; capped at Strong | 0.79 |
pu2_5 | 2–5 | Advisory | 1.58 |
pu6_9 | 6–9 | Advisory | 1.88 |
pu10_19 | 10–19 | Ranked | 2.23 |
pu20_49 | 20–49 | Ranked | 1.88 |
pu50_99 | 50–99 | Ranked | 2.23 |
pu100_199 | 100–199 | Ranked | 1.88 |
pu200_499 | 200–499 | Ranked | 1.88 |
pu500p | 500+ | Ranked | 1.88 (pooled) |
In the 2026-11-07 run the ranked book held 109,449 motor carriers; the advisory cohorts together hold 1.73 million of the 1.84 million graded.
The class rate is a Poisson regression with a log link and the decayed power-unit-years as offset, fitted once on the study's fit split (8.11 million motor-carrier-origin rows, 540,090 forward crashes) and frozen. Its 60 design columns are:
| Block | Columns | Reference level |
|---|---|---|
| Size | \(\log \text{PU}\), \(\log^2 \text{PU}\), eight cohort indicators | cohort pu10_19 |
| Class | for-hire flag; intrastate-only; hazmat; government; motor carrier class private / mixed | for-hire freight |
| Tenure | registered < 1 y, 1–2 y, 2–5 y, 10 y+ | 5–10 years |
| MCS-150 age (as of \(C\)) | 1–2 y, 2–3 y, 3–5 y, 5 y+, unknown (latest filing postdates \(C\)) | under 1 year |
| MCS-150 miles per power unit | < 1k, 1–10k, 10–30k, 60–100k, 100–300k, > 300k, unknown / implausible | 30–60k |
| Roadside fleet evidence | share of the filed fleet seen roadside in 24 months: never, ≤ 0.1, 0.1–0.25, 0.25–0.5, > 1; each band also interacted with a filing of 50+ power units and with \(\log(1 + \text{inspections per filed unit})\) | 0.5–1 of filed PU seen |
| Country | Canada, Mexico, other | United States |
| Inspection regime of the domicile state | low tertile, high tertile | middle tertile |
| Activity, 24 months | \(\log(1 + \text{traffic-enforcement inspections}/\text{PU})\), roadside, fixed-facility — each ratio capped at 4 per PU | — |
| Violation relativities (§5) | \(\log \tilde r\) for driver behaviour, OOS ratio, violation ratio | — |
The engine is chunked iteratively-reweighted least squares with a count-scale ridge of one expected crash (it pins rare dummies and leaves populated terms untouched) and motor-carrier-cluster standard errors. The domicile state is deliberately absent: it would add about 0.75 points of deviance explained, but the study showed it is confounded with how completely each state reports crashes, so it waits for the completeness factor.
The study's Poisson gradient-boosting model on the full feature library explained 31.4% of forward-crash deviance on the select split. Exposure and activity alone explained 20.4% and ranked motor carriers almost as well as the full model; inspections alone and violations alone each explained 14.0% — the same 14%, two measurements of one thing. Crash history alone explained 5.3% but almost all of it was unique: it is the one family that is not a proxy for activity, and it is the experience term of §6.
The inspection-selection analysis then settled how activity enters. Between inspection regimes the count means almost nothing (tertile effects of −5%), within regimes a great deal; type matters more than count — a traffic-enforcement stop is an observation of driving (relative risk about 2.4 per log unit of stops per truck), a weigh-station pull-in an observation of being on the road (about 1.15), and motor carriers inspected mostly at scales realized 0.69 of the activity model; among 308,800 rows with inspections and no violation at all, the slope of inspections on crashes is zero and realized ÷ expected falls with the count. The count's predictive power is activity plus what the inspections find. Above about four inspections per power unit the realized curve flattens, so the activity terms are capped there — an audit of the Excellent list found a 61-truck motor carrier whose 1,219 inspections had extrapolated its class rate to 15× and hidden a crash rate above the book average.
The roadside record is the only independent check on a filed fleet, and the class rate reads it in two dimensions: how much of the filed fleet the road actually sees, and how actively the motor carrier is inspected. A single “observed fleet” band was tested and rejected: it puts a 200-unit filing seen with 18 units and a 12-unit fleet seen with 5 in the same cell, and under it the clean, thinly seen large filings realized 1.5–2.4× their forecast and graded in inverted order. With six seen-share bands, each interacted with a 50-plus filing and with inspections per filed unit, that slice realizes 0.99 of its forecast and 0.94 / 1.09 / 1.02 by tercile of \(\bar R\). Replacing the filed fleet by a roadside capture–recapture estimate of the true fleet as the exposure was also built and rejected: it lost deviance in a model-free test and, refitted, changed no cohort's Gini.
| Filing, activity | never seen | ≤ 0.1 | 0.1–0.25 | 0.25–0.5 | > 1 |
|---|---|---|---|---|---|
| Under 50 PU, 0.25 inspections per unit / 24 m | 0.34 | 0.43 | 0.61 | 0.82 | 1.64 |
| Under 50 PU, 2 inspections per unit | 0.91 | 1.56 | 0.90 | 0.89 | 1.16 |
| 50+ PU, 0.25 inspections per unit | 0.06 | 0.36 | 0.62 | 0.81 | 2.21 |
| 50+ PU, 2 inspections per unit | 0.16 | 1.31 | 0.92 | 0.88 | 1.57 |
| Input | Rate ratio |
|---|---|
| Last MCS-150 filing 1–2 y / 2–3 y / 3–5 y / 5 y+ old (vs. under 1 y) | 0.83 / 0.72 / 0.64 / 0.40 |
| Latest filing postdates the cutoff (an active filer) | 1.76 |
| Registered under 1 y / 1–2 y / 2–5 y / 10 y+ (vs. 5–10 y) | 1.58 / 1.17 / 1.10 / 0.93 |
| Share of the filed fleet seen roadside | Table 4.3 |
| Traffic-enforcement / roadside / fixed-facility inspections per PU (per log unit, before the seen-share interaction) | 1.61 / 1.40 / 0.86 |
| MCS-150 mileage unknown or implausible (vs. 30–60k miles per truck) | 0.60 |
| Intrastate-only operation | 0.77 |
| Domiciled in Canada / Mexico / elsewhere (vs. United States) | 0.66 / 0.12 / 0.29 |
| Low / high inspection-regime tertile (vs. middle) | 0.99 / 0.97 |
Each ratio holds the other inputs fixed; the for-hire flag and the motor-carrier-class indicators interact and are not read singly, and the cohort indicators are small (0.93–1.21) once the size terms are present. The model-free counterpart of the filing-recency effect in the study was starker: motor carriers whose last MCS-150 was more than five years old realized 0.18× a cohort-rate prediction — most are dormant registrations that still carry power units.
The GLM was fitted on origins 2024-11 to 2025-08, when the VIN sightings behind the seen-share terms covered 1–10 of their 24 months (they begin 2024-10) and the inspection file 12–21. Live origins see full windows, so the same coefficients place motor carriers in higher-rated seen-share and activity bands than the fit ever did; a back-cast (realized crashes over the 12 months ending four months before the origin, divided by the class expectation, live against the backtest) put the live class level at 0.74 for the ranked book. Until the GLM is refitted on window-consistent features, the class rate is multiplied by $$ k \;=\; 1 + w(\Lambda_0)\,\big(f_g(m) - 1\big), \qquad w(\Lambda_0) = \operatorname{clip}\!\left(\frac{\ln(\Lambda_0/0.02)}{\ln 10},\,0,\,1\right), $$ where \(m\) is the months of VIN sightings inside the 24 months before the origin (counted from the first full month the run's sightings cover), \(f_g\) a piecewise-linear factor per size group \(g\) fitted on the fit split to be neutral over the training coverage and to match the live back-cast at \(m = 24\) (1–5 PU 0.77, 6–9 0.838, 10–19 0.856, 20–49 0.847, 50+ 0.728), and \(\Lambda_0\) the unadjusted 36-month expectation. The out-of-time gate frame, scored at an older origin, gets the factor its own coverage calls for; at the 2026-11-01 run its aggregate calibration went from 0.945 to 1.000 and the worst evidence bucket from 0.102 to 0.050, with the per-cohort Ginis unchanged.
Three violation signals over the trailing 24 months enter the class-rate GLM as \(\log \tilde r_s\), each a credibility-shrunk ratio of observed to expected. The shrinkage is Bühlmann's linear form, and the credibility constant \(K_s\) and the exponents \(\gamma_s\) were chosen on the select split by out-of-sample forward-crash deviance:
$$ \tilde r_s \;=\; Z_s\cdot\frac{\text{observed}_s}{\text{expected}_s} \;+\; (1 - Z_s), \qquad V \;=\; \prod_s \tilde r_s^{\,\gamma_s}. $$| Signal | Observed | Expected | Credibility \(Z_s\) | \(\gamma_s\) |
|---|---|---|---|---|
| Driver behaviour | Unsafe Driving + Hours-of-Service violations | driver-level inspections × the cohort's rate per inspection | \(n/(n+10)\), \(n\) = driver-level inspections | 0.112 |
| Out-of-service ratio | inspections with an OOS result | Σ over the motor carrier's inspections of the OOS rate for that inspection's state × level cell | \(e/(e+1)\), \(e\) = expected OOS inspections | 0.083 |
| Violation ratio | all violations | Σ over inspections of the violation rate for that state × level cell | \(e/(e+3)\), \(e\) = expected violations | 0.077 |
The two ratios are indirectly standardised for where and how the motor carrier was inspected: the expected count is built from the state × inspection-level mix of the motor carrier's own inspections (an inspection by a federal inspector is filed under a federal code rather than a state, so it is compared with federal inspections of the same level wherever they took place). In the study the standardised ratio beat the raw per-inspection rate every time, decisively for out-of-service results — once the standardised OOS ratio is in the model the raw OOS rate takes a negative sign. Model-free, a standardised violation ratio below 0.5 of expected realized 0.87–0.95 of the activity model and above 2× realized 1.10–1.18, monotone in every regime tertile; real, consistent, and modest beside the exposure and activity effects, which is why the \(\gamma\) are small.
| Cohort | pu1 | pu2_5 | pu6_9 | pu10_19 | pu20_49 | pu50_99 | pu100_199 | pu200_499 | pu500p |
|---|---|---|---|---|---|---|---|---|---|
| Rate | 0.322 | 0.318 | 0.286 | 0.266 | 0.245 | 0.219 | 0.195 | 0.189 | 0.148 |
Which violations earn a place. With activity and regime controlled, the forward-predictive BASICs are Unsafe Driving (relative risk 1.87 per log unit of violations per inspection), Hours-of-Service (1.21) and Vehicle Maintenance (1.16) — the same three UMTRI found in 2011 — and the maintenance signal is carried by the OOS ratio. Driver Fitness (0.66) and Hazardous Materials (0.64) are negative and get no term of their own — their violations count only inside the all-violations ratio: licence and medical-card violations mark administrative motor carriers, not dangerous ones. At the violation-group level the top of the table is driver behaviour, in order — speeding, seat belt, phone, texting, reckless driving, relative risks 1.15–1.24 — which is the content of the two BASICs in the driver-behaviour signal. Violation detail adds little to frequency once inspection and OOS counts are present; its role in the rating is face validity and the Excellent screen (§8).
A motor carrier's own crash history is the one family of information that is not a proxy for activity, and it enters as classical Gamma–Poisson credibility. Let the motor carrier's true relativity to its class-and-violation expectation be \(\theta \sim \text{Gamma}(a, a)\) — mean 1, variance \(1/a\) — and let its decayed crash count be Poisson given \(\theta\) and the decayed expectation \(\Lambda\). Conjugacy gives the posterior and its mean in closed form:
$$ \theta \mid \text{data} \;\sim\; \text{Gamma}(a + N,\ a + \Lambda), \qquad \boxed{\;\bar\theta \;=\; \frac{a + N}{a + \Lambda}\;}, \qquad Z \;=\; \frac{\Lambda}{a + \Lambda}, $$so \(\bar\theta = Z\cdot(N/\Lambda) + (1-Z)\cdot 1\): the motor carrier's own ratio weighted by its credibility \(Z\), the class expectation by the rest. Here
$$ N \;=\; \sum_{\text{recordable crashes}} w(\text{age}), \qquad \Lambda \;=\; \mu_{\text{class}}\cdot V\cdot\sum_{\text{months}} \text{PU}_{\text{floor}}\cdot\tfrac{\text{days}}{365}\cdot w(\text{age}), \qquad w(\text{age}) \;=\; 1 - \frac{\text{age in months}}{36}. $$Because \(\Lambda\) includes \(V\), \(\bar\theta\) is the residual after class and violations have spoken.
Events and exposure share the weight \(w\): a crash loses one thirty-sixth of its weight each month and is gone at 36 months, with no step anywhere. The shape was chosen by the out-of-time negative-binomial predictive likelihood of the next twelve months' crashes over 13.3 million motor-carrier-origin rows, jointly with the credibility prior. On a like-for-like comparison every 36-month shape beat every 24-month shape; among 36-month shapes the step-free linear ramp sat 1,257 log-likelihood units (0.19%) behind an unconstrained exponential that keeps a quarter of an event's weight at month 36 and would therefore step when it leaves the window, and 3,597 units ahead of equal weights. Fred's decision (2026-10-22): a crash signal on 36 months with a linear ramp to zero; the inspection and violation signals stay on 24 months, since the inspection file carries only 36 months of history.
The prior strength \(a\) is fitted after the class model by the same forward negative-binomial likelihood on the fit split, per cohort and per band of the record's expected crashes \(\Lambda\) (< 0.1, 0.1–0.3, 0.3–1, 1–3, 3–10, 10+), and interpolated linearly in \(\log a\) over \(\log \Lambda\) between band midpoints so that a motor carrier crossing a band edge does not jump:
$$\bar\theta = \frac{a(c,\Lambda) + N}{a(c,\Lambda) + \Lambda}, \qquad Z = \frac{\Lambda}{a(c,\Lambda) + \Lambda}.$$A single constant per cohort, the textbook choice, was tested and rejected: right on average, it was wrong in both directions by record. A crash on a ranked record expecting under 0.1 crashes was followed by 3.6× the class rate against 1.26× credited, and clean records expecting one to three crashes had 21% more crashes than credited (0.60 of class against 0.49). The fitted table gives a thin record a diffuse prior — one crash moves it a long way — and a record with a few expected crashes a narrow one.
| Cohort | \(\Lambda\) < 0.1 | 0.1–0.3 | 0.3–1 | 1–3 | 3–10 |
|---|---|---|---|---|---|
| pu1 | 0.79 | 0.94 | |||
| pu2_5 | 0.67 | 1.88 | 2.65 | ||
| pu6_9 | 0.33 | 1.12 | 2.65 | ||
| pu10_19 | 0.24 | 0.94 | 2.23 | 3.75 | |
| pu20_49 | 0.10 | 0.40 | 1.12 | 3.75 | |
| pu50_99 | 0.14 | 0.40 | 0.94 | 1.58 | 7.48 |
| pu100_199 | 1.12 | 5.30 | |||
| pu200_499, pu500p |
\(Z = \Lambda/(a + \Lambda)\) is shown on the motor carrier page as a credibility tier — High (≥ 0.60), Moderate (≥ 0.30),
Low (≥ 0.10), Prior-only (below 0.10, marked provisional). The tier is descriptive; the grade uses the full posterior. The
displayed \(Z\) is scaled by an exposure corroboration factor \(c = \min\{1, \max(s/0.5,\; i/0.5)\}\), where \(s\) is the
share of filed power units seen roadside in 24 months and \(i\) the inspections per filed unit-year: a filed fleet the roadside
record never sees cannot carry High confidence, whatever \(\Lambda\) says. From 10 filed units, \(c < 0.5\) raises the
EXPOSURE_UNVERIFIED flag and, as an interim rule, holds an Excellent or Strong grade one band lower (Table 8.2).
The relativity and forecast are not scaled by \(c\); exposure trust enters them through the roadside-fleet terms of the class
rate (§4) and the record-dependent prior above. The cap exists because those terms were fitted when the roadside VIN record
covered only part of each 24-month window (it begins in late 2024), so for a filing the road rarely sees the class rate's
discount is not yet tested on a full window; it is lifted once an origin with full roadside coverage has a mature outcome
year that shows the favourable grades hold.
A 10–19 power-unit fleet whose class rate and exposure give \(\Lambda = 0.3\) expected crashes over the decayed 36-month window, with none observed and a clean violation record (\(V = 1\)): the prior there is \(a = 1.42\), so \(\bar\theta = 1.42 / 1.72 = 0.83\). A modest discount — Satisfactory, not a clean sheet (the Strong cut is 0.756). A single truck with one recent crash (\(N \approx 0.9\) after decay) and \(\Lambda = 0.04\) has \(a = 0.79\) and \(\bar R \approx 2.0\), in the Poor band; but only about half of its wide posterior lies above the Poor cut, so the downside screen grades it Marginal. A fleet with tens of expected crashes and none observed drives \(\bar\theta\) toward zero and passes the Excellent screen on its own evidence.
The graded statistic is the posterior mean relativity to class — never the median, which on thin Gamma posteriors sits far below the mean:
$$ \boxed{\;\bar R \;=\; V\cdot\bar\theta\;}, \qquad \mathbb{E}[\text{crashes}_{12\text{ mo}}] \;=\; \mu_{\text{class}}\cdot\bar R\cdot\text{PU}_{\text{floor}}, \qquad \mathbb{E}[\text{crashes}_{12\text{ mo}}\mid\text{class only}] \;=\; \mu_{\text{class}}\cdot\text{PU}_{\text{floor}}. $$The posterior for the motor carrier's relativity is the Gamma of §6 scaled by \(V\); its tail probabilities are the screens of §8. The reported range \(q_{10}, q_{90}\) is that posterior widened by a variance floor: a Gamma with mean \(\bar R\) and \(\mathrm{CV}^2 = 1/(a+N) + 0.01\), because among fleets with steady activity the realized spread of the best-measured records was about ±15% against the posterior's ±11% (range study, 2026-11-01). The likely next-12-month crash count is the 10th–90th percentile of a negative binomial with mean \(\mu_{\text{class}}\bar R\,\text{PU}_{\text{floor}}\) and \(\mathrm{CV}^2 = 1.8/(a+N) + 0.012\), which covered about 80% of realized counts in every fleet-size cohort on the select split. Neither width enters a grade, a score or a gate; the screens use the posterior itself:
$$ P(R \lt c) \;=\; F_{\text{Gamma}(a+N,\ a+\Lambda)}\!\left(\frac{c}{V}\right). $$On the study's select split the posterior was neither too narrow nor too wide: among rows with at least 0.5 expected crashes, 86% realized at or below the posterior 80th percentile (0.80–0.90 is the calibrated range once integer counts are allowed for). The 0–100 FRED Score interpolates \(\bar R\) linearly within its band between the anchors 100 / 90 / 75 / 50 / 30 / 10 / 0 at the band edges, reaching 0 at twice the Critical cut, so score and grade never disagree.
Bands come from cuts on \(\bar R\). The four lower cuts were fitted on the fit split: the isotonic (pool-adjacent-violators) fit of realized ÷ class-expected crashes on \(\bar R\), weighted by class-expected counts rescaled so that every cohort carries equal total weight (an exposure-weighted fit would let the largest fleets set the small fleets' cuts), is crossed at the nominal boundaries 0.80 / 1.10 / 1.40 / 1.90. The fitted values are 0.756 / 1.057 / 1.570 / 2.109: the two lower ones within 6% of nominal, which is the check that \(\bar R\) is calibrated through the middle; the two upper ones above nominal, because motor carriers with high posterior relativities realize somewhat less than \(\bar R\) says and the fitted cuts absorb it. The Excellent cut is set at 0.60 by decision — half the crashes of a comparable fleet — with the rate-based proof screens below carrying the burden of selectivity; count-based screens punish size.
| Grade | Relativity to class \(\bar R\) | Score | Realized ÷ class-expected |
|---|---|---|---|
| Excellent | \(\bar R \lt 0.60\) | 90–100 | 0.50 |
| Strong | \(0.60 \le \bar R \lt 0.756\) | 75–90 | 0.68 |
| Satisfactory | \(0.756 \le \bar R \lt 1.057\) | 50–75 | 0.94 |
| Marginal | \(1.057 \le \bar R \lt 1.570\) | 30–50 | 1.25 |
| Poor | \(1.570 \le \bar R \lt 2.109\) | 10–30 | 1.68 |
| Critical | \(\bar R \ge 2.109\) | 0–10 | 3.08 |
The band says where the posterior mean falls; the screens ask whether the record supports it. They are applied in order — the downside posterior test first, then the upside tests, then the event requirements — and each is one-directional.
| Rule | Condition | Otherwise |
|---|---|---|
| Downside posterior (Critical, Poor, Marginal in turn) | \(P(R \gt \text{band's lower cut}) \ge 0.6\) | one band toward Satisfactory, then tested as that band — a wide posterior can fall more than one band |
| Excellent | band Excellent and \(P(R \lt 0.60) \ge 0.6\) and at least 0.3 expected crashes over the window (\(\Lambda \ge 0.3\)) and driver-behaviour relativity \(\tilde r \le 1.0\) and no fatal crash in the window and ≥ 3 inspections and ≥ 0.1 inspections per filed power unit (24 months) and more than one power unit | Strong, then tested as Strong |
| Strong | band Strong or demoted from Excellent, and \(P(R \lt 0.756) \ge 0.6\) and ≥ 0.1 inspections per filed power unit | Satisfactory |
| Critical | band Critical and (a fatal crash, or ≥ 2 recordable crashes in the window, or \(P(p_{\text{oos}} \gt 2\mu_{\text{oos}}) \ge 0.8\)) | Poor, then tested as Poor |
| Poor | band Poor or demoted from Critical, and (≥ 1 recordable crash in the window, or \(P(p_{\text{oos}} \gt 1.5\mu_{\text{oos}}) \ge 0.8\)) | Marginal |
| Exposure cap (interim) | from 10 filed power units, exposure corroboration \(c \lt 0.5\) (§6): under a quarter of the filed units seen roadside in 24 months and under 0.25 inspections per filed unit-year | Excellent → Strong, Strong → Satisfactory |
| Adverse rating | a current FMCSA Unsatisfactory or Conditional safety rating | capped at Marginal |
| Evidence for Satisfactory (display) | grade Satisfactory and not (\(q_{10} \lt 0.60\) and \(q_{90} \ge 1.57\)) | shown as Not enough record: no grade, no score; forecasts unchanged |
Not enough record. Every other grade passes a 60% posterior test against its cut; Satisfactory is what remains when none passes, which mixes a record that supports the class rate with a record that supports nothing. When the 80% range spans both the Excellent cut and the Poor cut, the record cannot separate a best-in-class fleet from a poor one, and the motor carrier is displayed as Not enough record and sorted after graded motor carriers; the engine's grade, gates, history and forecasts are untouched. On the select split (ten monthly origins, 2024-11 to 2025-08, realized 12-month crashes), ranked-book motor carriers under this rule realized 1.00 of their class expectation and 1.01 of their forecast, the same as Satisfactory motor carriers whose range supports the grade; the difference is the dispersion of the true rate around the forecast, estimated from \(E[(y - \hat\mu)^2 - y] = \phi\hat\mu^2\): \(\phi = 0.46\) (±68%) against 0.07 (±26%) for a range inside 0.60–1.57, and the posterior's share at Poor-level rates (17%) matched the realized spread (18%).
The out-of-service posterior is a Beta: with \(k\) OOS inspections of \(n\), \(\mu_{\text{oos}}\) the motor carrier's own regime-expected OOS rate (its expected OOS count over its inspections; the cohort mean when it has none) and prior strength \(K = 1/\mu_{\text{oos}}\) inspections (one expected OOS event),
$$ p_{\text{oos}} \sim \text{Beta}\big(k + K\mu_{\text{oos}},\ n - k + K(1-\mu_{\text{oos}})\big), \qquad \text{test } P(p_{\text{oos}} \gt m\,\mu_{\text{oos}}) \ge 0.8,\ m \in \{2,\ 1.5\}. $$Why 0.6. The bands are already cut on the posterior mean, so the quantile screen is a safeguard, not the main event: in the study's sweep 0.5 and 0.6 were nearly identical, while 0.8 left 0.2% of the book in Strong and 299 rows in Excellent. The evidence floor \(\Lambda \ge 0.3\) exists because a diffuse prior on a thin record (Table 6.1) can pass the posterior test on almost no evidence. The binding upside screens in that sweep were exposure plausibility (13,629 band-Excellent/Strong rows with fewer than 0.1 inspections per filed power unit — one filer of 4,150 trucks had three inspections), the driver-behaviour screen (7,979 rows) and the crash-event screen (1,759); the posterior quantile blocked 292. The sweep ran the driver-behaviour and crash screens in count-based forms (any Unsafe Driving or Hours-of-Service violation; any injury or fatal crash), which were rejected because they punished size — a large fleet always has some violation and some injury crash — in favour of the rate-based relativity and fatal-only rules of Table 8.2.
The size skew — “bigger the better, all else equal.” Between two motor carriers at the same point estimate, the larger fleet's relativity is known and the smaller fleet's is a wide guess. The posterior encodes exactly that, so the principled implementation is to leave Satisfactory in either direction only when 60% of the posterior lies beyond the cut. On the select split the downside screen took the 10+ book from 21.2% Marginal and 4.4% Poor to 9.2% and 1.9%, concentrated in fleets with evidence (50+ PU kept 15% Marginal and 5% Poor; 10–19 PU fell to 6.7% and 0.7%); a single truck is Poor only 0.2% of the time — one crash on one truck is not enough on its own — and the tiers that remain are purer (Marginal realizes 1.39 of class instead of 1.26, Poor 1.82 instead of 1.70). Going to 0.7 on both sides would have cut Strong from 15% to 6% of the book for little added purity.
The charter requires a published table of the minimum clean exposure at which Excellent is reachable. For each cohort, \(\Lambda_{\min}\) is the decayed expected count at which a clean record with \(V = 1\) first satisfies both the band (\(\bar\theta \lt 0.60\)) and the posterior screen \(P(\theta \lt 0.60 \mid N = 0) \ge 0.6\), from the evidence floor upward, and the steady fleet size that produces it (about 1.54 decayed power-unit-years per power unit) at two class rates, each measured on its own population: the cohort's median over every graded motor-carrier-origin of the study's select split (§11), dormant and never-seen registrations included, and its median over the fleets the road sees in a live run of the engine (graded motor carriers with exposure corroboration \(c \ge 0.5\), §6), which is higher by a factor of 2.2 to 2.8 in the cohorts from 6 to 499 power units, 3.4 at 500 or more and 5.2 at 2–5.
| Cohort | \(\Lambda_{\min}\) (expected crashes) | \(a\) there | Median class rate / PU-yr, all filings | Steady fleet for \(\Lambda_{\min}\) | Median class rate / PU-yr, fleets seen roadside | Steady fleet, seen roadside |
|---|---|---|---|---|---|---|
| pu2_5 | 1.24 | 1.84 | 0.0059 | 136 | 0.0304 | 26 |
| pu6_9 | 1.39 | 2.01 | 0.0117 | 77 | 0.0328 | 27 |
| pu10_19 | 2.38 | 3.25 | 0.0138 | 112 | 0.0346 | 45 |
| pu20_49 | 2.31 | 3.16 | 0.0148 | 101 | 0.0348 | 43 |
| pu50_99 | 0.71 | 1.06 | 0.0178 | 26 | 0.0413 | 11 |
| pu100_199 | 0.97 | 1.45 | 0.0185 | 34 | 0.0414 | 15 |
| pu200_499 | 1.27 | 1.88 | 0.0171 | 48 | 0.0398 | 21 |
| pu500p | 1.27 | 1.88 | 0.0105 | 78 | 0.0357 | 23 |
At the class rate of a fleet the road sees, a clean record alone earns Excellent from the mid-40s of power units upward (every 50+ cohort reaches \(\Lambda_{\min}\) at any size in its range); at the median over every filing it takes about 50. Below that it takes a clean record and a violation record better than class (\(V \lt 1\)), which is how the Excellent motor carriers in the 10–49 cohorts get there; the exposure cap of Table 8.2 then holds the grade at Strong while the filed fleet is uncorroborated. A single-power-unit motor carrier is capped at Strong by rule: nothing is proven on one unit, and 682 heavily inspected single trucks reached Excellent through the rate-based screens in a study dry run without it. Excellent is deliberately rare even among large fleets: 2.0% of the ranked book in the 2026-11-07 run.
Against the previous run, the change in a motor carrier's log relativity decomposes exactly. Writing primes for the previous run and \(\Lambda_{\text{class}} = \Lambda / V\) for the expectation at the class rate alone,
$$ \Delta\log\bar R \;=\; \underbrace{\big[\log(a+N) - \log(a'+N')\big]}_{\text{new event, decay roll-off or data correction}} \;+\; \underbrace{\Delta\log V + \big[\Delta(-\log(a+\Lambda)) - \Delta(-\log(a+\Lambda_{\text{class}}))\big]}_{\text{violations}} \;+\; \underbrace{\Delta\big(-\log(a+\Lambda_{\text{class}})\big)}_{\text{exposure \& class}} \;+\; \underbrace{\text{residual}}_{\text{recalibration}}. $$The numerator term is labelled new event when the decayed or raw crash count rose, decay roll-off when it fell by no more than one month of the ramp can explain (\(N'/36\)), and data correction when the raw window count fell and the decayed count fell by more than that — a crash removed from the FMCSA file. The recalibration term is non-zero only in a methodology run — one whose artifact checksum, cutoff rule, tenure rule or exposure-cap rule differs from the previous run's: there the decay, violation and exposure components are folded into it, so everything but a new event or a data correction is credited to the scoring update. A grade moved by a screen alone, with no component of \(\bar R\) moving, is credited to exposure & class (the screens read fleet size and activity), or to the recalibration in a methodology run. The dominant component with the sign of the move names the cause on the motor carrier page; a motor carrier whose relativity did not move is unchanged, one absent from the previous run is new.
The upside governor. An improvement whose dominant cause is not decay roll-off, a data correction or a recalibration is ramped one band per run: displayed = max(model grade, previous displayed − 1), and the model grade is kept as the pending grade until the display reaches it. The downside is never governed — a worse model grade shows at once. In the engine's monthly simulation on the selection split the largest upward moves were all exposure moves (a single-truck motor carrier observed with a second power unit, a burst of inspections raising its activity term, halving \(\bar R\) in a month without a new crash); they are real information about exposure, and the governor is right to let them arrive gradually with the attribution saying “exposure & class.” With every parameter frozen, 0.66–0.80% of motor carriers moved at least one band per 30 days, 0.02–0.03% two bands, 0.38–0.49% upward and 0.27–0.31% downward; the governor touched 0.15–0.24% per month and left the realized gradient of the displayed grades within a hundredth of the model grades'. The live run's churn is reported in §11. No motor carrier ever improved because of a new event — that is also a hard gate (§10).
Every run grades, on the same artifact, the population as it stood at the latest month-start origin whose twelve-month outcome year ended at least 120 days before the data date, and judges it on the crashes realized in that year — the wait is so that the year is nearly fully reported (the add-date completeness curve reaches 92.5% at 90 days, 94.7% at 120 and 98.5% at a year). Hard gates abort the write; soft gates are reported in the weekly run report, which lists every gate with its value and bound, the grade mix for the universe and the ranked book, churn with its causes, and the ten largest moves each way.
| Gate | Bound | Kind | Latest run (2026-11-07) |
|---|---|---|---|
| Out-of-time Gini, ranked cohorts with enough outcomes to judge (10–19 / 20–49 / 50–99 PU) | ≥ 0.55 each | hard | 0.597 / 0.649 / 0.724 |
| Grade monotonicity (realized ÷ class-expected by grade) | No inversion > 2 standard errors | hard | Monotone |
| Aggregate calibration (realized ÷ predicted) | 0.90 – 1.10 | hard | 0.999 |
| Calibration by evidence bucket (expected crashes), worst bucket | Within ±10% soft, ±20% hard | soft / hard | 1.05 / 0.98 / 0.99 / 0.98 / 1.03 / 1.02 / 0.99 → 0.051 |
| Posterior coverage (share realized at or below the 80th percentile) | 0.78 – 0.92 | soft | 0.858 |
| Moves of two or more bands | ≤ 0.5% of motor carriers | hard | 0.000% |
| Moves of one or more bands; governed share | ≤ 3%; ≤ 0.5% | soft | 0.00%; 0.00% |
| Upward moves caused by a new event | 0 | hard | 0 |
| Rows graded; ranked rows | ≥ 900,000; ≥ 80,000 | hard | 1,835,687; 109,449 |
| Single-power-unit Excellent | 0 | hard | 0 |
| Scores in range; all six grades present | 0 – 100; yes | hard | 0 – 96.7; yes |
| Pooled Gini; dead-signal share | Reported | info | 0.626; 0.515 |
Verdict of the 2026-11-07 run: all nineteen checks ran, every one inside its bound, with no hard or soft failure. The evidence buckets realize 1.05 / 0.98 / 0.99 / 0.98 / 1.03 / 1.02 / 0.99 of forecast from under 0.05 to 5+ expected crashes; a shortfall in the buckets between 0.05 and one expected crash is the class rate's known soft spot, where the log-linear class rate slightly over-predicts quiet, lightly inspected motor carriers (§11).
Ten monthly origins, 2024-11 through 2025-08, each with features as of the origin (by add date) and a mature 12-month forward outcome; all property motor carriers with filed power units ≤ 5,000, not under an exit at the origin, forward exposure > 0 (VIN-floored power units × the fraction of the year before any exit). Motor carriers were split by DOT number — odd: fit; divisible by four: select (model choice, \(K\), \(a\)); remainder two: eval, locked and read once after the candidate was frozen. Rows of one motor carrier stay in one split, so every out-of-sample figure is also out-of-motor-carrier. The ten origins overlap eleven-twelfths in outcomes and are one independent outcome year; confidence intervals come from the motor-carrier-cluster bootstrap. Metrics: Poisson deviance explained against a single-rate null, exposure-weighted normalized Gini (pooled and per cohort), Σ realized ÷ Σ predicted overall, by cohort and by decile, top-5% exposure lift, and the posterior 80th-percentile coverage.
| Model | Deviance explained | Normalized Gini |
|---|---|---|
| PU-cohort rate (the size-only baseline) | 1.1% | 0.13 |
| The FRED engine (class rate × violation relativities × crash experience) | 28.2% | 0.653 |
| Gradient-boosting ceiling (same rows, same inputs, no leak) | 30.5% | 0.674 |
The engine sits 0.021 Gini and 2.3 points of deviance behind the gradient-boosted ceiling. That gap is the price of linearity among busy motor carriers: the tree ranks better pooled and, in the study's bake-off, inside every cohort — its advantage is nonlinear structure among active, inspected motor carriers — and it cannot decompose or be governed. Per cohort the engine's select-split Gini is 0.605 / 0.668 / 0.735 / 0.792 for pu10_19 / pu20_49 / pu50_99 / pu100_199. In the study the experience term was the single largest step (+3.4 points of deviance and +0.035 Gini on top of the class rate) and kept aggregate calibration at 1.00; neither an isotonic recalibration of the class rate nor activity band dummies paid (each gained 0.3–0.4 points of deviance and moved the Gini by at most 0.004). Normalized Gini throughout is the exposure-weighted Lorenz integral.
Calibration holds where it matters for underwriting. By decile of predicted rate, realized ÷ predicted runs from 0.90 at the lowest decile to 1.19 in the busy upper middle and 0.95 at the highest — a mild U-shape: the log-linear class rate slightly over-predicts quiet, rarely inspected motor carriers and under-predicts the busy upper middle. Thin ranked records (\(\Lambda \lt 0.3\)) realize 0.89 of their forecast when clean and 1.11 after a crash, and the clean, thinly seen large filings of §4 realize 0.99.
The locked split (4.03M rows, DOT mod 4 = 2, 268,454 forward crashes) was read once, at the bake-off, and has not been reopened. On it the three-factor structure explained 27.4% of deviance with Gini 0.647 and calibration 1.003, against the ceiling's 30.6%, 0.674 and 1.014 on the same rows — the same picture as select. Per cohort the Gini ran 0.59–0.83 with realized ÷ predicted 0.98–1.08 in every cohort. The engine's own figures (Table 11.1) are select-split figures.
Every run grades the population as it stood at a mature origin before its cutoff and checks the grades against the crashes that followed (§10). In the 2026-11-07 run's gate year the grades realize 0.50 / 0.68 / 0.94 / 1.25 / 1.68 / 3.08 of the class expectation from Excellent to Critical (Table 8.1), monotone by the 2-SE rule. The charter's tier criteria are met: Excellent realizes below 0.6, Critical above 1.9, no upside without the screens and no downside without events. In the engine's monthly simulation on the selection split, with every parameter frozen, 0.66–0.80% of motor carriers moved at least one band per 30 days, 0.02–0.03% two bands, and the governor touched 0.15–0.24%. In the live engine, between the 2026-11-07 and 2026-11-07 runs, 0.00% of the 1,835,687 motor carriers graded in both moved at least one band (0.00% per 30 days), 0.000% two bands (0.000% per 30 days), and the governor held 0.000%; 0 motor carriers moved up and 0 down, none up because of a new event.
On November 7, 2026 (inspections, violations and census facts through September 30, 2026, crashes through August 31, 2026, data as of October 29, 2026) the engine graded 1,835,687 property motor carriers, 109,449 of them in the ranked book. Every hard gate passed: per-cohort Gini 0.597 / 0.649 / 0.724, aggregate calibration 0.999, posterior coverage 0.858, 0 single-power-unit Excellent. The ranked-book grade mix in the live table (the governed grade of §9 after the adverse-rating cap of Table 8.2, before the Not-enough-record display rule of §8) was Excellent 2,182 (2.0%) · Strong 11,382 (10.4%) · Satisfactory 84,905 (77.6%) · Marginal 8,693 (7.9%) · Poor 1,624 (1.5%) · Critical 663 (0.6%) of 109,449; across the whole universe, in the live table, 2,202 · 18,878 · 1,775,035 · 34,541 · 3,817 · 1,214. The exposure cap of Table 8.2 held 5,245 Excellent or Strong model grades one band lower, and of the Satisfactory motor carriers 1,752,621 (95.5% of all graded; 67,928, 62.1%, in the ranked book) are shown as Not enough record (§8), leaving 22,414 (16,977 ranked) whose record supports the grade.
The graded quantity is recordable-crash frequency. For display and the later cargo and auto loss-cost layers, the motor carrier page also shows an expected severity mix — property-damage, injury and fatal crashes, and the probability of at least one fatal crash — computed as the frequency expectation times the cohort's observed severity mix. A separate severity model (a multinomial on class attributes and crash configuration) is a planned follow-up; severity never enters the frequency model.
| Not an input | Reason |
|---|---|
| Self-reported MCS-150 mileage | Blank, stale or implausible too often to be exposure; enters only as a coarse miles-per-truck band in the class rate |
| FMCSA BASIC percentiles, ISS | Outcome-dependent (would leak the target); the public SMS carries no percentiles for property motor carriers |
| Machine-learned models | The gradient-boosted model is a ceiling in the bake-off only; the engine must decompose and must not spike |
| Domicile state | Confounded with crash-reporting completeness (25% to over 90% known within 60 days by state); revisited with the completeness factor |
| Driver Fitness and Hazardous Materials violations as signals of their own; raw OOS and violation rates; driver-OOS rate | Negative or null once activity and the standardised ratios are present (the violations still count in the all-violations ratio) |
| A pending out-of-service order or revocation dated inside the outcome window | Forward-looking (a leak found in the study); exits are used only for censoring and the at-cutoff exclusion |
| Crash severity in the frequency model | Noise for frequency; modelled separately |
| Anything driver-level (CDLIS/PSP, Clearinghouse, ELD), IRP/IFTA, DataQs and enforcement-case detail | Not public |
Three illustrative motor carriers, computed with the production constants.
Inputs. 88 power units (cohort pu50_99), 120 inspections in 24 months, two recordable crashes in
36 months (1.32 after decay).
Factors. The class rate and violation relativity together expect \(\Lambda = 2.3\) decayed crashes for this fleet's exposure; its violation relativity is \(V = 0.66\) — fewer driver-behaviour violations and out-of-service results than its inspection regime expects. At \(\Lambda = 2.3\) the prior is \(a = 2.32\), so \(\bar\theta = (2.32 + 1.32)/(2.32 + 2.3) = 0.79\).
Grade. \(\bar R = 0.66 \times 0.79 = 0.52\): band Excellent. The screens: 67% of the posterior lies below 0.60, \(\Lambda\) is above the 0.3 floor, 120 inspections on 88 filed units is about 1.4 per unit, driver behaviour is better than class and there is no fatal crash — Excellent.
Inputs. 5 power units (pu2_5), two inspections, no crash; \(\Lambda = 0.04\) expected crashes over
the window and \(V = 0.90\).
Grade. The prior at \(\Lambda = 0.04\) is \(a = 0.67\), so \(\bar\theta = 0.67/0.71 = 0.94\) and \(\bar R = 0.85\): the record is too thin to move the motor carrier from its class rate — Satisfactory, advisory (under 10 power units). A clean sheet on two inspections is the absence of evidence, and the posterior says so; with \(\Lambda\) below 0.3 it could not be Excellent in any case.
Inputs. 40 power units (pu20_49), 70 inspections, twelve recordable crashes in 36 months, most of
them recent (7.5 after decay), against \(\Lambda = 3.1\) expected; \(V = 1.10\).
Grade. The prior is \(a = 2.64\), so \(\bar\theta = (2.64 + 7.5)/(2.64 + 3.1) = 1.77\) and \(\bar R = 1.94\): band Poor, below the Critical cut of 2.109. The posterior is narrow enough that 71% of it sits above the Poor cut (the downside screen holds), and twelve window crashes satisfy the event requirement many times over — Poor, score about 16. The engine does not round a bad record up to Critical: that tier begins at 2.109, the fitted point where realized crashes cross 1.9× the class expectation.
| Constant | Value | Section |
|---|---|---|
| Cutoffs \(C\), \(C_{\text{crash}}\) | first of the month after the last full month on file; crashes one month earlier | §2, §B |
| Crash window and decay | 36 months, \(w = 1 - \text{age}/36\) | §6 |
| Inspection, violation and VIN window | 24 months | §2, §5 |
| Exposure | \(\text{PU}_{\text{floor}} = \max(\text{filed}, \text{observed power-unit VINs})\), decayed PU-years | §3 |
| Fitted size range (not graded above it) | ≤ 5,000 filed power units | §2, §3 |
| Fleet-size check (1,000+ filed power units) | not credible: ≤ 13 different trucks inspected in 24 months and < 0.02 drivers per filed unit, or any filing above 5,000 with ≤ 13, or a well-repeated roadside record whose fleet estimate is under a tenth of the filing | §3 |
| Fleet-size cohorts | 9; ranked book = 10+ PU (6 cohorts) | §3 |
| Class-rate design | 60 columns; six seen-share bands × (≥ 50 filed PU) × log(1 + inspections per PU); ridge 1.0 expected crash; activity cap 4 inspections per PU | §4 |
| Driver-behaviour credibility \(K\) | 10 driver-level inspections | §5 |
| Standardised-ratio credibility \(K\) | 1 expected OOS event; 3 expected violations | §5 |
| Violation exponents \(\gamma\) (driver / OOS / violations) | 0.112 / 0.083 / 0.077 | §5 |
| Credibility prior \(a\) | per cohort × \(\Lambda\) band, interpolated in \(\log\Lambda\) (Table 6.1); cohort values 0.79 / 1.58 / 1.88 / 2.23 / 1.88 / 2.23 / 1.88 / 1.88 / pooled 1.88 | §6 |
| Credibility tiers on \(Z = \Lambda/(a+\Lambda)\) | High ≥ 0.60; Moderate ≥ 0.30; Low ≥ 0.10; Prior-only (provisional) below | §6 |
| Exposure corroboration (display credibility) | \(c = \min\{1, \max(s/0.5, i/0.5)\}\); displayed \(Z \times c\); flag below 0.5 from 10 filed PU, and Excellent/Strong held one band lower (interim) | §6, §8 |
| Grade cuts on \(\bar R\) | 0.60 (decision) / 0.756 / 1.057 / 1.570 / 2.109 (fitted at nominal 0.80 / 1.10 / 1.40 / 1.90) | §8 |
| Score anchors at band edges | 100 / 90 / 75 / 50 / 30 / 10 / 0 (0 at 2 × the Critical cut) | §7 |
| Posterior screens \(p_{\text{top}}\), \(p_{\text{down}}\), \(p_{\text{bottom}}\) | 0.6, 0.6, 0.8 | §8 |
| Excellent screens | \(\Lambda \ge 0.3\); driver-behaviour \(\tilde r \le 1.0\); no fatal crash; ≥ 3 inspections; ≥ 0.1 inspections per filed PU; > 1 PU | §8 |
| Strong screens | posterior; ≥ 0.1 inspections per filed PU | §8 |
| Critical / Poor event tests | fatal or ≥ 2 crashes or \(P(p_{\text{oos}} \gt 2\mu) \ge 0.8\); ≥ 1 crash or \(P(p_{\text{oos}} \gt 1.5\mu) \ge 0.8\) | §8 |
| Current FMCSA Unsatisfactory / Conditional | capped at Marginal | §8 |
| Governor | upward moves ramp 1 band per run unless decay, data correction or a model recalibration; downside ungoverned | §9 |
| Gate bounds | Gini ≥ 0.55 per ranked cohort with enough outcomes to judge (≥ 5,000 rows and 100 realized crashes in the gate year: 10–19, 20–49, 50–99 PU); monotone (2 SE); aggregate 0.9–1.1; evidence ±10% / ±20%; coverage 0.78–0.92; ≥ 2-band ≤ 0.5%; ≥ 1-band ≤ 3% (recalibration moves excluded and reported); governed ≤ 0.5%; rows ≥ 900k; ranked ≥ 80k; OOT year ≥ 120 d mature | §10 |
Nothing is refit week to week. The artifact's sha256 and the cutoff, tenure and exposure-cap rules are recorded in every run's metrics; a recalibration is a new artifact with its own checksum or a change of one of those rules, and its moves are attributed to recalibration on every motor carrier page and shown at once.
A grade computed today uses only the records FMCSA has published today; a validation computed on history can accidentally use records that arrived later. The reporting-hold study therefore replayed historical first-of-month run dates \(R\) with only the records each run could have seen — crashes by FMCSA add date, inspections and violations by their MCMIS add date — and scored every timing with the frozen model on the same outcome: the recordable crashes each motor carrier had after \(R\). Population, class columns, forward exposure and the inspection-window length were held fixed so only the newest events differed, and the replay reproduced the engine's own frame builder exactly before any timing was compared. Eight run dates (2025-01 to 2025-08) were judged on twelve months of outcome; five later ones (2025-10 to 2026-02), whose inspection windows are full production length, on six. Select split, about 400,000 motor carriers per run date. The decision rule was fixed in code before the run: a timing is better only if its gain in deviance explained over the two-month hold has a 90% bootstrap interval above zero on at least 75% of run dates, the ranked book's and each cohort's Gini do not fall by more than 0.005, grades stay monotone and the slow-reporting states' calibration stays within ±0.05.
| Timing | Crashes through | Inspections through | Better on | Δ deviance explained | Δ Gini, 10+ PU book (median) | Calibration shift, 10+ PU book |
|---|---|---|---|---|---|---|
| Two-month hold (reference) | \(R - 2\) m | \(R - 2\) m | — | — | — | — |
| One-month hold | \(R - 1\) m | \(R - 1\) m | 13 / 13 | +0.002 to +0.004 | +0.002 / +0.003 | < 1%; 2.5% in the 2025 stall |
| No hold | \(R\) | \(R\) | 13 / 13 | +0.003 to +0.007 | +0.003 / +0.005 | 1–2% kinder; 3–6% in the 2025 stall |
| Inspections now, crashes two months | \(R - 2\) m | \(R\) | 13 / 13 | +0.002 to +0.004 | +0.001 / +0.002 | < 1% |
| Inspections now, crashes one month (production) | \(R - 1\) m | \(R\) | 13 / 13 | +0.003 to +0.006 | +0.002 / +0.004 | < 1%; 2.4% in the 2025 stall |
Gini medians are for the six-month / twelve-month runs. Fresh inspections help on every run date. Fresh crash counts help while reporting is normal — a run knew 66–70% of the crashes dated in the two held months — but not when FMCSA's crash reporting stalled in mid-2025: a run on 2025-08-01 knew 7% of the June and July crashes, and counting crashes up to the run date left the ranked book 5.6% too kind. Holding crashes one month keeps most of the gain without that drift. A motor carrier with a crash or out-of-service inspection in the newest months is predicted markedly better (deviance explained 0.33–0.35 under the two-month hold, 0.35–0.37 under the production timing).
| Wait before grading | Kinder at the time | Kinder by 2+ bands | Harsher |
|---|---|---|---|
| None | 0.22–0.34% (0.58% in the 2025 stall) | 0.02–0.05% | 0.01–0.02% |
| 30 days | 0.09–0.17% (0.33% in the stall) | ≤ 0.03% | ≤ 0.01% |
| 60 days | 0.07–0.16% (0.33% in the stall) | ≤ 0.03% | ≤ 0.01% |
On the motor carrier page, an inspection dated after \(C\) or a crash dated after \(C_{\text{crash}}\) is shown as not yet scored; it enters the grade as the window moves forward each month.
This document specifies the production FRED scoring engine. Every formula, constant and threshold is taken from the frozen model artifact and the engine code; study figures are from the Safety Core Study and live figures from the latest weekly run (November 7, 2026). The engine re-scores the full property universe weekly with every parameter frozen between scheduled recalibrations.