This paper describes a new method, called Decision-Theoretic Horn Abduction (DTHA), for generating and focusing on the most important explanations. A procedure is given that can be used iteratively to generate a sequence of explanations from the most to the least important. The new method considers both the likelihood and utility of partial explanations and is applica ble to a wide range of tasks. This paper shows how it applies to an important engineering design task, namely Failure Modes and Effects Analysis (FMEA). A concrete example illustrates the advantages of the general approach in the context of FMEA.