Generalising maintainability to state re-union maintainability for discrete-time homogeneous semi-Markov systems

The study of maintainability for Markov models is well documented, while maintainability for semi-Markov models was first introduced in Vassiliou et al. (1992). Yet, the concept of maintainability in semi-Markov models demands further investigation. In response, this paper examines maintainable population structures for discrete-time homogeneous semi-Markov models and introduces the novel concept of State Re-union maintainability (SR-maintainability). We demonstrate that under specific conditions, the seniority-based paths linked to SR-maintainable structures converge. This property enables the characterization of the convex set of SR-maintainable structures. For semi-Markov and Markov models estimated on a same data set, the connection between the SR-maintainable region and the maintainable region is investigated.