The study of the lifetimes of contrails from a satellite perspective benefits from the extended coverage and close temporal monitoring. However, the initial stages of the contrail development are not observed from a satellite platform due to the sub-pixel size of the forming cloud. The final stages may be unobserved as well when the contrails get spatially diluted and when they lose contrast with their background. In this paper we apply a Weibull distribution model to describe the survival rate of contrails during their observed life-span and adjust its two defining parameters (λ$\lambda$ and k$k$) to fit a dataset of over 2300 contrails. Using the Weibull distribution, it is possible to estimate the expected further lifetime of the contrails after satellite observation ceased. Depending on the actually observed lifetime, the expected extension can range from about 1 to 4 h, but the overall mean of this duration is about 1.3 h. The time elapsed between contrail formation and first satellite observation is estimated from the initial width distribution of the contrails. Under the assumption of a 5 km/h spreading rate, the average age of contrails at the time of their first satellite detection is 1.5±0.4$1.5\pm0.4$ h. Using a Monte Carlo simulation, we are able to compute the cumulative distribution of the complete (i.e. initial spreading, tracking, and after-tracking periods) lifetime of persistent contrails. This complete lifetime has a mean value of 3.7±2.8$3.7\pm2.8$ h. The Weibull distribution (k<1$k<\nobreak 1$) shows that the probability to survive increases with contrail age, which corresponds to the actual decay rate of contrails in nature. Additionally, we analyse lifetime differences between daytime and nighttime contrails. We find that nighttime contrails have slightly shorter lifetimes than daytime contrails. Although this difference is statistically significant, it remains to be shown whether this has important physical consequences.