Thermionic devices, particularly those operating in collective plasma physics modes, exhibit complex nonlinear dynamics including hysteresis in current-voltage characteristics and chaotic instabilities, which impact long-term reliability. This study develops a semi-Markov process (SMP) framework to model time-to-failure in such systems, incorporating path-dependent behaviors from experimental observations in a dc argon glow discharge plasma. Drawing from historical thermionics evolution and modern applications, the SMP accounts for non-memoryless holding times and asymmetric transitions, validated against qualitative hysteresis sketches and chaos metrics (e.g., information dimension 2.75, positive Lyapunov exponents). A 3-level full factorial design of experiments (DOE) simulates modulation effects on chaos suppression, with ANOVA revealing significant interactions between discharge voltage, modulation amplitude, and frequency. Computational results align with experimental trends, predicting reduced mean time to failure (30%) on backward hysteretic paths due to stairstep instabilities. The model enhances predictive maintenance for thermionic converters in space and energy sectors, with implications for chaos control via small perturbations.