Estimation of parameters in the Weibull model from microbial survival data obtained under constant conditions with come-up times

The Weibull model is frequently used to describe non-linear microbial survival due to its simplicity and flexibility. An essential part of developing a predictive microbiological approach is to accurately estimate survival parameters. In this study, an explicit integral representation of the Weibull model was derived from its original differential form. Calculated microbial survival curves under the same conditions were identical when both forms of the equation were used. The integral equation was able to be simplified into an explicit algebraic equation under specific processing conditions that consisted of a come-up time (CUT) followed by a lethal agent having a constant magnitude. These conditions are found in microbial survival tests in which currently used methods ignore or incorporate CUT using an empirical approach to estimate microbial survival parameters. Using the proposed method, microbial survival parameters were accurately estimated by fitting the obtained explicit algebraic equation to microbial survival data, whereas the conventional method resulted in inaccurate parameter estimation.