In this paper, we analysed individual cell growth images obtained by flow chamber microscopy system. We used replicate flow chamber experiment data as reported by [Elfwing, A., Le Marc, Y., Baranyi, J., Ballagi, A., 2004. Observing the growth and division of large number of individual bacteria using image analysis. Applied and Environmental Microbiology 70, 675-678] involving both unstressed and heat shocked Listeria innocua cells. After observing the kinetics of a large number of cells, we propose a new stochastic model for their individual growth. By comparing our model with other existing models in the literature, we demonstrate that ours can accurately describe the growth of both stressed and unstressed cells. Our results indicate that the lag period, in terms of cell division, coincides dominantly with a lag period in terms of cell size. We also reveal various connections between cell length, lag time and cell division models. Finally, we present the results of our investigation on the effect of the duration of sublethal heat shock on the found growth properties.