Relaxed Candidate Set Models for Masked Data in Series Systems

We develop likelihood-based inference methods for series systems with masked failure data when the traditional conditions governing candidate set formation are relaxed. While existing methods require that masking be non-informative (Condition C2) and parameter-independent (Condition C3), practical diagnostic systems often violate these assumptions. We derive the likelihood under various relaxation scenarios, establish identifiability conditions, and compare Fisher information under standard versus relaxed models. Simulation studies quantify the bias from incorrectly assuming standard conditions when masking is informative or parameter-dependent, and extend the framework to Weibull series systems. We implement these methods in the mdrelax R package.