Selection for uniformity in birth weight (BW) could lead to a more ethical and efficient livestock production because it results in more robust animals, which are easier to manage, more feed-efficient and are more likely to survive to weaning. This study aimed to estimate the genetic component of residual variance for BW and its relationship with piglet survival in a Swiss experimental farm. The data set comprised 43,135 records of BW from 3,163 litters of 986 sows, and pedigree data for 45,737 individuals. A heteroscedastic model was used, including fixed effects such as sex, month-year, litter size, and parity, and the litter effect was added as a random effect in addition to the genetic effect. The data was assigned to the mother, and the same effects were fitted for mean BW and its variability. A threshold homoscedastic model was performed for the probability of stillbirth (SB). A multivariate analysis was performed for BW and SB including the additive genetic effect and the maternal genetic effect using a Markov Chain Monte Carlo software (GSEVM) for the heteroscedastic model and TM software for the homoscedastic one. The genetic coefficient of variation was 0.29, and the genetic correlation between the mean BW and its variability was 0.24 (SE=0.09). The individual and maternal h2 were 0.04 (0.01) and 0.23 (0.03) and 0.00 (0.00) and 0.05 (0.01), for BW and SB, respectively. The direct genetic correlation between BW and SB was 0.14 (0.31) and the maternal one 0.01 (0.11). In conclusion, our results show that there is potential for selection for the reduction of environmental BW variability, and the correlation between maternal breeding values indicates that it will not negatively affect the survival of piglets.