Using a molecular model introduced previously, we study the effects of chain-end segregation on the relationship between strength (sigma) and diameter (d) in polymeric fibers. For segregated structures with a monodisperse molecular weight distribution, our results show a scaling law sigma approximately d(-alpha), with alpha in the range [0.4-0.5], in agreement with experimental observation. A weaker dependence is found for polydisperse systems. Further investigation also reveals that macroscopic cracks have little influence on the fiber strength/diameter relationship, unless the crack width shows a faster than linear increase with fiber diameter. Finally, our model results also indicate a very weak dependence of fiber strength on its length, in good agreement with experimental observation.