2. Build the Restraint System Function Tree and Requirements Traceability

Why a Function Tree Must Precede Failure Analysis

DFMEA asks a single disciplined question: how can this function fail? That question is unanswerable until the function itself is written down at the right granularity. In a restraint system, "protect the occupant" is not a function — it is a mission statement. A function tree decomposes that mission into verifiable sub-functions, each with a measurable performance parameter, and then traces every leaf back to a vehicle-level requirement and a regulatory or consumer-test target. The traceability chain is what makes later severity, occurrence, and detection ratings defensible: a failure mode inherits its severity from the requirement it violates, not from engineering intuition.

This case builds that tree for a driver airbag and seatbelt restraint system, using the boundary established in the prior boundary/interface work. The deliverable is a traceability matrix in which every leaf function carries an ID, a performance parameter, a vehicle-level requirement, and a test target — so that when failure modes are enumerated later, each one maps to exactly one defined function.

Decomposition Logic: Four Functional Branches

Restraint performance is conventionally decomposed along the occupant's kinematic timeline. Four branches cover the driver-side system without overlap:

  • F1 — Occupant positioning: hold the occupant in the design seating position before and during the crash pulse (belt geometry, buckle engagement, pretensioner take-up).
  • F2 — Energy absorption: dissipate kinetic energy through controlled deformation and belt/airbag interaction so that occupant deceleration stays within injury-tolerance corridors.
  • F3 — Load limiting: cap the force transmitted to the chest through the belt and to the head/neck through the airbag, trading ride-down distance against peak load.
  • F4 — Deployment timing: trigger and stage the airbag and pretensioner so that the restraint is fully presented at the correct instant relative to occupant motion.

Each branch decomposes into two or three leaves. The leaves are deliberately written as functions with parameters, not as components — a component list ("inflator", "retractor") belongs in the boundary document, not the function tree. This separation is what allows a single component to serve multiple functions (the retractor contributes to both F1 and F3) and a single function to be served by multiple components.

Function Tree and Traceability Structure

The diagram below shows the four branches, their leaf functions with performance parameters, and the traceability links to vehicle-level requirements and test targets. Note that F4's leaves carry timing parameters in milliseconds, while F2 and F3 carry force and displacement parameters — the parameter type is a direct consequence of what the function must deliver.

Driver Restraint Function Tree — Traceability to Requirements and Test Targets Occupant Restraint — Driver Mission: limit injury to FMVSS 208 / Euro NCAP thresholds F1 Occupant Positioning hold in design seating position F1.1 Belt fit & buckle engagement param: lap/shoulder gap ≤ 25 mm F1.2 Pretensioner take-up param: slack removal ≥ 60 mm F2 Energy Absorption dissipate KE within tolerance F2.1 Airbag cushion energy uptake param: vent flow / cushion pressure F2.2 Belt webbing ride-down param: chest deflection ≤ 50 mm F3 Load Limiting cap transmitted force F3.1 Torsion-bar force limit param: belt force plateau 3.5–4.5 kN F3.2 Airbag pressure relief param: peak head accel ≤ 80 g F4 Deployment Timing present restraint at correct instant F4.1 Crash sensing & trigger param: fire time 15–25 ms post-t0 F4.2 Staged inflator output param: stage-2 delay 5–15 ms Traceability links (leaf → vehicle requirement → test target) F1.1 VR-SAF-012: occupant retained in position for 0–50 ms FMVSS 208 belt geometry / NCAP slip check F1.2 VR-SAF-014: pretensioner take-up before occupant forward travel FMVSS 209 / sled take-up timing F2.1 VR-SAF-021: head HIC₁₅ ≤ 700 in 56 km/h ODB FMVSS 208 / Euro NCAP ODB F2.2 VR-SAF-022: chest deflection ≤ 50 mm (driver, 50th percentile) FMVSS 208 chest criterion F3.1 VR-SAF-025: belt force plateau within 3.5–4.5 kN band Sled force-plate measurement F3.2 VR-SAF-026: peak head acceleration ≤ 80 g FMVSS 208 head accel corridor F4.1 VR-SAF-030: airbag fire time 15–25 ms after t0 Sled timing / OOP deployment test F4.2 VR-SAF-031: stage-2 delay 5–15 ms for adaptive output NCAP adaptive restraint assessment

Writing Leaf Functions That Survive DFMEA

The most common failure in this step is a leaf function that is too vague to fail in a specific way. "Provide restraint" cannot generate a meaningful failure mode; "F3.1 Torsion-bar force limit — belt force plateau 3.5–4.5 kN" can, because the failure mode "force plateau exceeds 4.5 kN" is immediately testable and immediately traceable to a chest-deflection requirement. Three rules keep leaves DFMEA-ready:

  1. One verb, one parameter. Each leaf states what the function does and the parameter that proves it. If a leaf needs two parameters, it is probably two leaves.
  2. Parameter must be measurable on a test. "Adequate" and "sufficient" are not parameters. Use the unit and the band that the validation test will actually record.
  3. Trace to a requirement ID, not a document name. "FMVSS 208" is a regulation; "VR-SAF-021: HIC₁₅ ≤ 700 in 56 km/h ODB" is a requirement that a failure mode can violate. The requirement ID is what the severity rating will reference.

Building the Traceability Matrix

The matrix is the working artifact. For the driver system, populate it with the columns below. The example rows use the same IDs as the diagram so the two stay consistent.

Function IDFunction statementPerformance parameterVehicle requirementTest targetVerification method
F1.1Maintain belt fit and buckle engagementLap/shoulder gap ≤ 25 mmVR-SAF-012FMVSS 208 / NCAP slip checkStatic fit check + sled
F1.2Remove belt slack via pretensionerSlack removal ≥ 60 mmVR-SAF-014FMVSS 209 / sled take-upSled with belt-pull sensor
F2.1Absorb head energy in airbag cushionHIC₁₅ ≤ 700VR-SAF-021FMVSS 208 / Euro NCAP ODBSled + full-vehicle ODB
F2.2Provide belt ride-downChest deflection ≤ 50 mmVR-SAF-022FMVSS 208 chest criterionSled with chest potentiometer
F3.1Limit belt force via torsion barPlateau 3.5–4.5 kNVR-SAF-025Sled force-plateSled force-plate measurement
F3.2Relieve airbag pressurePeak head accel ≤ 80 gVR-SAF-026FMVSS 208 head corridorSled + head accelerometer
F4.1Sense crash and trigger deploymentFire time 15–25 ms post-t0VR-SAF-030Sled timing / OOPSled with current probe
F4.2Stage inflator outputStage-2 delay 5–15 msVR-SAF-031NCAP adaptive assessmentSled with dual-stage current trace
Before moving to failure-mode enumeration, run a completeness check: every leaf must have a non-empty requirement ID and a test target. A leaf with a blank requirement column is a function nobody asked for — either find its requirement or delete it. A requirement with no leaf is a gap in the tree that will surface later as an unrated failure mode.

Verification and Common Pitfalls

Verify the tree by walking it in both directions. Top-down: does every vehicle-level requirement in the restraint scope land on at least one leaf? Bottom-up: does every leaf trace to a requirement that a customer or regulator actually imposes? A tree that passes both directions is ready to feed DFMEA structure analysis.

Typical failure symptoms at this stage: (1) leaves named after components ("inflator function") rather than functions — this collapses the tree into a BOM and destroys the ability to rate severity against requirements; (2) parameters without units or bands — these produce failure modes like "insufficient force" that cannot be ranked; (3) traceability to a document rather than a requirement ID — severity ratings then become subjective; (4) missing the timing branch entirely, which is common when the team thinks of restraint as purely structural, and which leaves deployment-timing failure modes orphaned. If any of these appear, correct the tree before proceeding — the cost of a bad function tree is paid in every downstream severity and detection rating.