System-level diagnosis has become an important diagnosis method for multiprocessor systems. Among all system-level diagnosis measures, diagnosability is relatively small. The conditional diagnosability constraint that each vertex has at least one good neighbor is relatively conservative when the dimension is far greater than 1, and g-good-neighbor conditional diagnosability does not consider this restriction on faulty vertices. Therefore, a thorough study of diagnosability under the condition that each vertex has at least g good neighbors is an appealing subject. Motivated by R g vertex connectivity, in this paper, we introduce a novel generalized system-level diagnosis measure named R g conditional diagnosability, which assumes that every processor has at least g good neighbors. The popular conditional diagnosability is a special case of R g conditional diagnosability when g = 1. Then, we determine that the R g conditional diagnosability of n -dimensional hypercube Q n under the Preparata Metze Chien (PMC) model is 2 2 g ( n − 2 g ) + 2 2 g − 1 − 1.