Identifiability of degradation severities from condition-monitoring records: exact residual ambiguity under partial intervention labels

In many engineering systems, several degradation mechanisms can be active at the same time. These mechanisms may change the monitored signals in similar ways. The same measurements can then be explained by more than one combination of mechanisms. The required maintenance action, however, depends on which mechanism is present. This paper determines which mechanisms can be distinguished from the monitoring and intervention record when controlled interventions (seeded fault tests) label only some of them. Six acquisition conditions are assumed: (i) a healthy reference segment in every session; (ii) healthy data that separate operating-condition, session and noise effects from degradation; (iii) linearly independent mechanism signatures that remain constant with operating condition; (iv) verified health of every nontarget mechanism during each intervention; (v) at least one positive measured severity for each labelled mechanism; and (vi) sufficiently independent variation during passive operation. Under these conditions, Theorem 1 gives the complete set of mechanism decompositions that the record cannot distinguish. For three mechanisms, successive labels reduce the ambiguity dimension from nine to seven, five and three. When unlabelled mechanisms occur together, separate pairwise intensity bounds can be too restrictive or too permissive. In a two-mechanism example, cooler fouling is labelled and filter clogging remains unlabelled. The clogging trend is recoverable. The cooler inspection decision stays ambiguous until independent sensor calibration is added. A decision about a specific mechanism is justified when every explanation consistent with the record leads to the same outcome. An intensity trend for an unlabelled mechanism is guaranteed only when no other mechanism is unlabelled.