Stochastic Considerations on the Upper and Lower Limits of Colony Counts on Agar Plate for Microbial Count Calculation

The upper and lower limits of microbial colony count on agar plate are essential for microbial cell calculation of food samples. In the present study, the limits presented by the three standards of Ministry of Health, Labor, and Welfare of Japan, Food and Drug Administration of US (FDA), and Japanese Industrial Standards (JIS) were studied from the stochastic point of view. Here colony counts per plate were assumed to follow the Poisson distribution from our previous studies. The probability of acceptance of a pair of colony counts, P_A for cell calculation by each standard was then calculated for various values of the mean of the Poisson distribution theoretically and by simulation with random sampling numbers. The values of P_A at the lower and upper limits of the standards were low. For example, P_A at the mean of 25 which is the lower limit of the FDA standard was 0.278. The values of P_A of colony count pairs by the three standards were demonstrated in a wide range of the mean colony count. The largest range of the mean at P_A>0.5 was observed in the JIS standard among the three. A new method to determine the limits for colony counts was developed with the risk of not acceptance. These findings would be helpful to consider the limits of colony counts for cell calculation.