Stochastic simulation is used to account for the variation in the manufacturing and assembling processes of the vehicle structure and occupant restraint system. An integrated full vehicle model with belted driver, 50th percentile male Hybrid III dummy, subjected to a 35 mph zero degree impact test, is used to present the scatter in the vehicle crash and occupant restraint performance.

Yield stress of a typical mild steel has scatter values between 10 to 20% and a coefficient of variation of 5% is derived for scaling the stress and strain curve. The thickness tolerance has scatter values specified between 5 to 10% and a coefficient of variation of 2% is used in the study. The material properties and thickness of major structural components for absorbing impact energies, such as the motor/occupant compartment rails and upper rails, bumper beam, cradle, and toe pan are the random input variables for the structure. Characteristics of a restraint system also vary among the same design and a coefficient of variation of 5% is adopted in this study. The restraint system for the occupant, such as steering column stroke force, seat belt retractor force, airbag mass flow rate, and airbag deployment time, are the random variables selected in this study.

Typical injury criteria (head injury criteria (HIC), chest G, chest deflection, neck loads, and femur loads) and structural performance (intrusions of toe pan, steering column, and A-pillar) are extracted. These values are then used to determine the effect of the structural and the restraint system variations on the occupant and vehicle crash behaviors. The cross relationships between the structural crash behavior and occupant injury numbers are also studied.