In¯uence of the variability of processing factors on the F-value distribution in batch retorts Szabolcs Varga a , Jorge C. Oliveira b, * , Fernanda A.R. Oliveira c a Escola Superior de Biotecnologia, Universidade Cat olica Portuguesa, Rua Dr Ant onio Bernardino de Almeida, 4200 Porto, Portugal b Department of Food Science and Technology, University College Cork, Cork, Ireland c Department of Food Engineering, University College Cork, Cork, Ireland Abstract The F-value distribution in a batch retort processing of in-pack conduction heating foods resulting from the variability of four processing factors (initial temperature, heating time, headspace and external heat transfer coecient) was determined by mathe- matical modelling. Three hundred combinations were generated from normally distributed values for each factor, following the Monte Carlo approach. The retort temperature was assumed the same for all containers and the F-value at the geometrical centre of containers of dierent dimensions was calculated by solving the governing heat transfer equations using ®nite elements. It was found that in the range tested the variability of the heating time and of the external heat transfer coecient had the biggest impact on the F-value distribution and that the head space variability had a negligible impact. It was also found that although each in¯uencing factor had a normal distribution, the F-value distribution was not normal, showing a signi®cant tailing, being well described by a gamma function. Keywords: Conduction heating; Finite elements; Monte Carlo simulation; In-pack sterilisation 1. Introduction The design and evaluation of batch retort processes are based on the application of the ``cold spot'' and ``worst case'' approach, that is, on the de®nition of the location in the retort where the least thermal process occurs and of the combination of other factors that would result in the lowest F-value in that location. However, this approach is questionable from a statisti- cal point of view: it would be better to determine the actual process variability and F-value distribution and thus de®ne critical values. A statistically based approach requires an extensive and solid knowledge based on the impact of the pro- cessing factors on the F-value distribution. The retort temperature distribution is a major factor to be analy- sed, as required by GMP and legislation (Adams & Hardt-English, 1990). This work is concerned only with other factors. In literature, experimentally assessed thermal vari- ability is mostly restricted to the measurement of the in¯uencing factors (Hicks, 1961; Lenz & Lund, 1977; Lund, 1978; P¯ug & Odlaug, 1978; Patino & Heil, 1985; McGinnis, 1986; Hayakawa, Massaguer & Trout, 1988; Lebowitz & Bhowmik, 1989, 1990; Adams & Hardt- English, 1990; Park, Cables & Collins, 1990; Tung, Britt & Ramaswamy, 1990; Ramaswamy & Tung, 1990), but the eect of such variability on the resulting lethality has not been often reported (Powers, Pratt, Carmon, Nomenclature F sterilisation value, min h heat transfer coecient, W/m 2 K H height of container, m k thermal conductivity, W/m K r radial coordinate, m R radius, m T temperature, °C t time, s V volume, m 3 z axial coordinate, m l mean r standard deviation Subscripts 0 initial h heating