A novel method of analysing serial production lines has been developed. This method lets one compute the throughput rate of lines composed of dissimilar stations, as well as for a large class of distributions of station service times. Several distribution-free models of 3-station lines are presented. These models are used to compute the throughput rate of unbalanced lines in which the sum of the mean service times is constant. Results are shown as contour plots of constant throughput rate. The bowl phenomenon is reviewed in the light of this capacity to model with a greater degree of freedom.