Fault trees (FTs) and their extensions are diagrammatic formalisms that are commonly used for reliability assessment and that represent the structure function of systems. The structure function determines tie sets and cut sets, and minimal tie sets are instrumental for assessing systems reliability. In a previous paper, we used satisfiability (SAT) techniques to compute tie sets from the structure function. In this paper we define minimal tie sets with sequences (MTSSs) as an extension of minimal tie sets for analyzing dynamic fault trees (DFTs), and we extend our previous techniques for computing MTSSs. We illustrate our approach using a standard case study and assess its performance over several industrial-size benchmarks