New mathematical concepts hold promise for augmenting sterility assurance in ionizing irradiation of single-use medical devices. Of particular significance are those that address risks posed by natural, uncontrolled (stochastic) fluctuations in equipment and process. The emerging probabilistic Fr 13 (Friday 13^th) risk assessment is illustrated as a new quantitative tool to augment sterility assurance in sterilizing surgical gloves by gamma ionizing irradiation. A computer model to simulate irradiation is synthesized and solved using the Fr 13 risk framework. A major advantage is that this quantitatively accounts for the impact of natural, random fluctuations in equipment and contaminants. Contamination with Cl. botulinum Type A viable spores is postulated. The new computational results are compared with traditional ones and differences that could be used to improve sterility assurance are established. Two (unexpected) failures in sterilization each calendar year are illustrated, averaged over an extended period of operation, because of naturally occurring, random fluctuation in irradiation intensity of the cobalt-60 source. These failures cannot be attributed to operator error or to faulty fittings. It cannot be assumed that these will be spaced equally in time. It is determined that natural variability in irradiation intensity significantly affects sterility, and that iterative application of the Fr 13 risk assessment can be used to augment confidence in sterility in cobalt-60 irradiation treatment of surgical gloves through optimized control of exposure time. Because the risk concept appears generalizable it is concluded that it is applicable to a range of pathogens, products, machine-types and locations.