The increasing integration of Renewable Energy Sources (RES) in distribution networks causes a change in the operation of the grid which may affect the reliability of distribution transformers through mechanisms that extend beyond thermal stress induced by conventional loading alone. This paper proposes two statistical methodologies to investigate the potential impact of RES on distribution transformer failure rates, and applies them as example to the service area of a Dutch distribution system operator. First, the temporal analysis method reveals significant hourly correlations between failure rates and renewable generation profiles, although no seasonal trends are observed. However, the lack of a rising trend in these correlation values indicates that the increased capacity of RES has not yet impacted the failure rate. Second, a spatial analysis employs a Poisson Geographically Weighted Regression model to assess localized correlations between failures and different types of RES. While large-scale photovoltaic (PV) plants show no statistically significant spatial correlation with failures, the analysis reveals local positive correlations for residential PV and wind generation. Even though the analyses do not reveal increased failure rates due to increasing RES penetration, the findings suggest localized stress on assets and show the need for further research into long-term aging effects.