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We consider a life testing situation in which systems are subject to failure from independent competing risks. Following a failure, immediate (stage-1) procedures are used in an attempt to reach a definitive diagnosis. If these procedures fail to result in a diagnosis, this phenomenon is called masking. Stage-2 procedures, such as failure analysis or autopsy, provide definitive diagnosis for a sample of the masked cases. We show how stage-1 and stage-2 information can be combined to provide statistical inference about (a) survival functions of the individual risks, (b) the proportions of failures associated with individual risks and (c) probability, for a specified masked case, that each of the masked competing risks is responsible for the failure. Our development is based on parametric distributional assumptions and the special case for which the failure times for the competing risks have a Weibull distribution is discussed in detail.