This report presents a mathematical analysis o1 the methods used for determining the effectiveness of radappertization (radiation stcrilizülion) of food. A general theory is developed which makes it clear that two interrelated distribution functions, the probability of organism death and the probability of can-sterilization, play important parts in the process. A critique is given of the Schmidt-Nank method for calculating the 12D dose and the implications of the experimental data are studied. Modifications in both experimental design and data analysis are proposed. These are evaluated by using them to analyze artifical data generated by a fairly realistic computer simulation model. The proposed methods give considerably more accurate results than the traditional one, and it is concluded that the new methods appear promising for future use. This report is concerned with the determination of safe sterilization processes for canned food, i.e. processes which insure that the food is free of dangerous organisms. Although ionizing radiation is the method of sterilization considered here, the mathematical procedures described are equally applicable to any method of killing microorganisms in food. We may summarize the present situation as follows. An expert committee of the United Nations Food and Agriculture, World Health Organization and the International Atomic Energy Agency has recommended a criterion of safety for radiation-sterilization (see [13]), which states that the probability must be no more than 1 x 10" 12 that a dangerous microorganism (usually Clostridium botulinum) will survive the processing. The processing consists of exposing sealed cans of food to a dose of radiation under specified conditions, and the dose needed to satisfy the above criterion is called the 12D dose or minimal radiation dose (MRD). The 12D dose depends on both the microorganism and conditions (temperature, salinity pH, etc.) in the food substrate and is a measure of the radiation resistance of the microorganisms. The presently accepted procedure for estimating the 12D dose follows the January 1971 recommendation of the National Academy of Science-National Research Council's Advisory Committee to Natick Laboratories on Microbiology of Food. The procedure consists of a set of experiments, collectively called an inoculated pack, and a computation based on the resulting data. The experiments consist of inoculating cans of food with spores of c. botulinum, sealing the cans and exposing them to doses of radiation. Typically, 10 7 spores are inoculated in each can, 100 replicate cans are exposed to each dose and the deses may range from 0 to 5 megarads in increments of .5 megarads. After irradiation all cans are incubated for six months at 30°C. The cans are examined for swelling weekly during the first month and monthly thereafter. At the end of incubation cans are tested for toxin presence, and all cans showing neither swelling nor toxin are subcultured for surviving spores. The computation takes the resulting partial spoilage data (usua...