Failure is inevitable in scientific computing. As scientific applications and facilities increase their scales over the last decades, finding the root cause of a failure can be very complex or at times nearly impossible. Different scientific computing customers have varying availability demands as well as a diverse willingness to pay for availability. In contrast to existing solutions that try to provide higher and higher availability in scientific grids, we propose a model called Task Replication for User-defined Availability (Trua). Trua provides flexible, user-defined, availability in scientific grids, allowing customers to express their desire for availability to computational providers. Trua differs from existing task replication approaches in two folds. First, it relies on the historic failure information collected from the virtual layer of the scientific grids. The reliability model for the failures can be represented with a bimodal Johnson distribution which is different from any existing distributions. Second, it adopts an anomaly detector to filter out anomalous failures; it additionally adopts novel selection algorithms to mitigate the effects of temporary and spatial correlations of the failures without knowing the root cause of the failures. We apply the Trua on real-world traces collected from the Open Science Grid (OSG). Our results show that the Trua can successfully meet user-defined availability demands.