The completeness fraction as a function of input flux density at 250, 350 and 500 μm for the three different types of source catalogues (top: SXT; middle: SF; bottom: SF250). The horizontal dashed line marks the 90 per cent completeness level. The left-hand column corresponds to the simulated unclustered COSMOS field and the right-hand column corresponds to the simulated unclustered Lockman SWIRE field. The curves are the best-fitting generalized logistic functions to describe the completeness ratio as a function of input flux density. Simulations with clustered input sources produce similar completeness curves.