Our results extending Kuhn's fault class hierarchy provide a justification for the focus of fault-based testing strategies on detecting particular faults and ignoring others. We develop a novel analytical technique that allows us to elegantly prove that the hierarchy applies to arbitrary expressions, not just those in disjunctive normal form. We also use the technique to extend the hierarchy to a wider range of fault classes. To demonstrate broad applicability, we compare faults in practical situations and analyze previous results. In particular, using our technique, we show that the basic meaningful impact strategy of Weyuker et al. tests for stuck-at faults, not just variable negation faults.