This study introduces new approaches for analyzing the performance degradation of large-scale systems composed of many homogeneous units that degrade independently across a finite number of states. The methodologies presented in this book chapter draw from our previous three research papers (Ko and Byon in IEEE Trans Reliab 64:420–434, 2015, [10]; IISE Trans 49:493–504, 2017, [11], Lee et al. in IEEE Trans Reliab 73:1393–1406, 2024, [13]). We employ limit theorems and phase-type approximations to make the analysis tractable. The system’s probabilistic evolution over time under non-Markovian state transitions is accurately approximated. This approach demonstrates that as the system’s size increases, its mean dynamics can be approximated by its fluid limit (Ko and Byon in IEEE Trans Reliab 64:420–434, 2015, [10]). Using the limit process, the maintenance optimization analytically derives the optimal threshold that minimizes the long-run average maintenance cost (Ko and Byon in IISE Trans 49:493–504, 2017, [11]). Furthermore, we extend the maintenance optimization scheme to consider selective maintenance that is more realistic for the maintenance operation of large-scale systems in which all the units cannot be maintained in a single trip. We show that even under selective maintenance, the system dynamics become asymptotically regenerative, which makes the analysis tractable (Lee et al. IEEE Trans Reliab 73:1393-1406, 2024, [13]). Our maintenance approach is shown to outperform the traditional periodic maintenance policy.