High-value aviation rotable parts require accurate demand forecasting because each failure simultaneously creates a replacement demand, a repair workload, and a potential aircraft on-ground (AOG) risk. This study develops a continuous-time Markov chain (CTMC) queuing framework for forecasting demand and optimizing target stock levels under realistic maintenance, repair, and overhaul (MRO) capacity constraints. Historical service-engineering records from B737 mechanical engine control (MEC) units are first benchmarked and filtered to retain inherent random failures during the useful-life phase. A Kolmogorov-Smirnov goodness-of-fit test is then used to verify the exponential time-between-failure assumption required by the Markov model. Based on this validated failure-pattern classification, the study derives steady-state probability models for both an ideal $M/M/\infty$ repair system and a finite-capacity $M/M/c$ repair system. The main contribution is not the isolated use of Weibull or exponential reliability models, Markov chains, or inventory optimization, which are established methods, but their auditable integration into an airline rotable-parts workflow that links failure-pattern screening, finite repair capacity, service-level constraints, and engineering validation. The empirical results show that repair bottlenecks shift probability mass toward higher numbers of failed units, create a fat-tailed backlog distribution, and double the required target stock from 6 to 12 MEC units under a 95% service-level requirement. Sensitivity experiments further show that repair turnaround time, fleet size, and MRO channel capacity jointly determine the inventory-capacity cost trade-off. The proposed framework provides an interpretable decision tool for airlines to align spare-part procurement with actual repair-system performance.