Estimation of the thermal coefficient in the decline of a bacterial population under heat stress

The "most probable number" (MPN) technique for estimating numbers of bacteria in suspensions is well known and has been used for decades by microbiologists, food researchers, and other laboratory scientists. A related procedure, involving an infinite number of serial dilutions at each of times ti, i = 0,1,...,n, is considered, and the joint probability law of the index numbers of the last tubes showing growth at these times is derived through use of probability-generating functions. Maximum likelihood estimates of the initial density lambda and the thermal death rate mu are computed. Another estimate, mu, of mu is given, using a simple weighting scheme. Finally, the thermal death time (TDT) is estimated by D = (1n 10)/mu.