This article considers the situation in which a system consists ofkcomponents and a defect in any component causes a system malfunction. When a system malfunction occurs, test procedures restrict the cause to some subset of the Ic components. When that subset consists of more than one component, this phenomenon is termedmasking. Typically, masking introduces two types of problems. First, it is desirable to estimate the “diagnostic probability”—that is, the probability, given a specified malfunctioning subset, that each of the masked components is the defective one. Second, when a set of historical data contains masked information, one would like to use this information to estimate the defect probability of each individual component type. The article discusses these problems in detail and derives two-stage procedures for estimation and inference.