This paper analyzes the effect of error correlation on the SISRE bounding for GPS and Galileo satellites. For a given period of data collection, it computes the effective number of independent samples contained in a dataset applying an estimation variance analyses. Results show that the time between effective independent samples is highly dependent on the constellation and onboard clock type. On one hand, GPS satellites equipped with Rubidium clocks exhibit longer error correlation that those with onboard Cesium clocks (50-60 hours versus 5-6 hours). On the other hand, Galileo satellites show a significantly shorter correlation among samples with less variability on a monthly basis (2.5- 3.5 hours for PHM-equipped satellites versus 4-5 hours for RAFS clocks). This paper also introduces a methodology to compute SISRE bounding accounting for the limited number of independent samples. Using a Bayesian approach, it computes the so-called inflation factor that a Gaussian overbound needs to be expanded with in order to account for the uncertainty within the observation data.