The disclosure provides an inflator device for a passive restraint device, like an airbag. In certain aspects, a fuel-rich gas generant grain is located in actuating proximity to an initiator device. The grain has at least one flow channel through which a shock wave generated by the initiator device passes. The shock wave opens a burst disc between the inflator housing and downstream airbag to permit gases to flow into the airbag. A chamber storing pressurized gas (having at least one oxidant, e.g., O2) is also disposed within the inflator. Upon initiator actuation, the oxidant can react with combustion products of the initiator and the fuel-rich gas generant and flow into the airbag for rapid inflation. Methods of inflating airbags and improving airbag deployment reliability are provided. Such inflators are particularly suitable for large volume (greater than 60 liter) airbags.