Latent Activation Limited Failure Models, Stochastic Ordering and Identifiability

Abstract

Limited failure or cure rate models provide generalization of lifetime models which allow the possibility of subjects or units to be cured or be failure-free. While modeling and analysis of such models are extensively studied, we study the important question of identifiability of these models. We discuss the latent and hierarchical activation cure models and establish a series of results on stochastic ordering within these models. We also establish a series of results on identifiability of these models under various conditions. Further, we demonstrate multiple cases where there models are not identifiable and illustrate the potential difficulty with these models in a simulation study.