Snapshot 2: estimate of the most probable number of probiotic bacterial cells from which

to

will remain viable upon reaching the gut

This Demonstration generates estimates of the most probable initial number of cells, customers, or units in general within the range

minimum to

maximum set by the user with sliders and a drop-down menu. The ranges of the

probability factors (

from 1 to 6) are specified by

minimum and

maximum and are also set by sliders. Monte Carlo simulations to determine the initial number can be done with or without a seed. Check the "seed repeatable random numbers" box to generate a repeatable random sequence from the seed selected using the "seed value" slider. The number of repeated trials is entered using the "random trials to generate" slider. The program generates a new dataset whenever the value of any control other than the clear button is altered. For a new random dataset at the current control settings, click "clear" followed by "generate". For scenarios involving fewer than all six

factors, set the unused factor's minimum and maximum values to 1. The panel shows the program controls at their current settings, a histogram of the estimates computed in the repeated trials, and the lognormal distribution having the same logarithmic mean and standard deviation as the generated estimates shown as a solid blue curve. The plot title text includes the analytic solution "best estimate" and the one derived from the lognormal distribution's mode. Estimates for

and

outside their sliders' allowed range of 1 to 1000 can be obtained by setting the "

multiplier" drop-down menu to the appropriate factor. Notice that if all seven factors' (i.e.,

and the six

's) minimum and maximum values are the same, the program will render the conventional Fermi solution plotted as a spike. Also, if all but one of the seven factors' minimum and maximum values are the same, then the program will generate random estimates with a uniform distribution. In that case, although the program still generates a corresponding lognormal distribution curve, it may no longer be representative.

The difference between this Demonstration and the Demonstration

Expanded Fermi Solution for Risk Assessment is that the initial number estimates are calculated by dividing the entered

's by the product of the corresponding six

's.

M. Peleg, M. D. Normand, J. Horowitz, and M. G. Corradini, "An Expanded Fermi Solution for Microbial Risk Assessment,"

*International Journal of Food Microbiology*,

**113**(1), 2007 pp. 92–101.