Applications structured as Directed Acyclic Graphs (DAGs) of tasks occur in many domains, including popular scientific workflows. DAG scheduling has thus received an enormous amount of attention. Many of the popular DAG scheduling heuristics make scheduling decisions based on path lengths. At large scale compute platforms are subject to various types of failures with non-negligible probabilities of occurrence. Failures that have recently received increased attention are “silent errors,” which cause data corruption. Tolerating silent errors is done by checking the validity of computed results and possibly re-executing a task from scratch. The execution time of a task then becomes a random variable, and so do path lengths in a DAG. Unfortunately, computing the expected makespan of a DAG (and equivalently computing expected path lengths in a DAG) is a computationally difficult problem. Consequently, designing effective scheduling heuristics in this context is challenging. In this work, we propose an algorithm that computes a first order approximation of the expected makespan of a DAG when tasks are subject to silent errors. We find that our proposed approximation outperforms previously proposed approaches both in terms of approximation error and of speed.