Estimation of microbial growth using population measurements subject to a detection limit

In this paper we develop a maximum likelihood estimation procedure for determining the mean and variance in microbial population size from microbial population measurements subject to a detection limit. Existing estimation methods generally set non-detectable measurements equal to the detection limit and are highly biased. Because changes in the mean and variance in the microbial population size are typical in industrial processes we also outline statistical tests for detecting such changes when measurements are subject to a detection limit, which is critical for process control. In an industrial process there may also potentially be variability in the microbial growth rate due to variation in the microbial strain, environment, and food characteristics. Accordingly, we also present a maximum likelihood procedure for estimating microbial growth model parameters and their variance components from microbial population measurements subject to a detection limit. Such information can be used to generate the mean and variance through time of the microbial population size, which is vital for the application of predictive microbiological models to risk assessment and food product shelf-life estimation.