Background Duration of fertility (DF) is an important economic trait in poultry production because it has a strong effect on chick output. Various criteria or traits to assess DF on individual hens have been reported but they are affected by many nongenetic factors. Thus, a reliable definition and associated genetic parameters are needed. Because egg production is also vital in chicken breeding, knowledge of the relationship between DF and laying performance is needed for designing selection programs. Methods We used five traits that consider both fertility and embryonic livability to delineate DF. Phenotypic and genetic analyses were completed for 2094 hens, with measurements of DF at 35 and 60 weeks of age and hatching egg production at 400 days of age (HEP400). The selection differentials for DF and HEP400 were evaluated. Results DF is largely independent of the number of oviposited eggs in the peak laying period but both egg production and DF naturally decline with age. The heritability of the five DF traits ranged from 0.11 to 0.13 at 35 weeks of age and increased slightly in the later laying period, ranging from 0.14 to 0.17 (except for efficient duration, time between insemination and the first unhatched egg). Estimates of the genetic correlation for a given trait measured at the two ages were moderate (0.37–0.44), except for efficient duration. However, number of viable embryos depends strongly on egg production. Estimates of genetic correlations of fertility duration day (FDD) at both ages with HEP were weak. Selection for FDD improved DF but without a significant change in laying performance. Selection for increased HEP400 did not contribute to DF improvement. Conclusions Although estimates of heritability of the five traits related to DF were low, selection to improve DF based on any one of them is possible. Among these, FDD is an effective selection criterion when the eggs are collected for approximately two weeks after insemination. The best selection procedure for DF improvement would involve multiple measurements at various ages. FDD is independent of laying performance and can be incorporated into a breeding program with egg production to improve reproductive efficiency.