Masked Causes of Failure in Series Systems: A Likelihood Framework

We develop a distribution-agnostic likelihood framework for estimating component reliability from series system data with masked failure causes. Under three sufficient conditions on the masking mechanism (C1: candidate set contains the true cause, C2: symmetric masking, C3: masking independent of lifetime parameters), the unknown masking distribution is eliminated from the likelihood. The resulting likelihood is expressed entirely in terms of component hazard and reliability functions, covering exact, right-censored, left-censored, and interval-censored observations. We establish formal identifiability conditions: a necessary condition showing that diagnostically confounded components cannot be separately identified, and a sufficient condition guaranteeing identifiability when the candidate-set structure has full column rank. We provide instantiations for five common parametric families.