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Fault trees are a major model for the analysis of system reliability. In particular, Boolean difference methods applied to fault trees provide a widely used measure of subsystem criticality. This paper generalizes the fault-tree model to time-varying systems and uses timedependent Boolean differences to analyze such systems. In particular, suitable partial Boolean differences provide maximal and minimal solution sets for sensitization conditions. A method of common-cause failure analysis based on partial time-dependent Boolean differences allows the study of failures due to repeated occurrences, at different times, of the same phenomenon. Such methods generalize to systems with repair, and under certain assumptions of independence, steady-state distributions can be used for the analysis of system faults. These methods are generally useful in reliability and sensitivity analysis.