The preignition probability for a sigmoidal reactivity input in Nuclear Explosive Devices (NEDs) with a strong inherent neutron source strength (i.e. using reactor grade plutonium) is treated comprehensively. The cumulative preignition probability, its probability density as well as the most probable time for preignition during the compression phase are presented in a closed analytical form. This general formalism can be used to calculate the preignition probability for any metallic core composition (either Pu or U or hybrid) possessing an inherently strong or weak background of neutrons.

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