Many papers have presented models for estimating proton single event upset (SEU) cross sections from heavy-ion test data, but all rigorous treatments to date are based on the sensitive volume (SV) model for charge collection. Computer simulations have already shown that, excluding devices utilizing physical boundaries for isolation, there is no well-defined SV. A more versatile description of charge collection, which includes the SV model as a special case, utilizes a charge-collection efficiency function that measures the effect that the location of ionization has on collected charge. This paper presents the first rigorous analysis that uses a generic charge-collection efficiency function to relate proton to heavy-ion cross sections. The most practical result is an upper bound for proton SEU or single event latchup (SEL) cross sections, which requires no information about the charge-collection efficiency function, except that it exists. In addition, some models previously presented by others are reproduced (or, in one case, extended) by applying the general theory to special cases. The similarities and differences between a variety of models become clear when the models are recognized to be special cases or variations of this general theory.