Event-driven evaluation of state-dependent maintenance policies for degraded repairable systems using piecewise deterministic Markov processes

This paper develops an event-driven piecewise deterministic Markov process (PDMP) framework for evaluating state-dependent impulse maintenance policies in degraded repairable k -out-of- \((M+S)\) systems with warm standby redundancy, retrial repair access, imperfect interventions, general residual times, and limited shared maintenance capacity. Degradation-dependent failures are modeled as stochastic interior jumps, whereas residual-time completions and threshold hits are treated as marked boundary events at which at most one admissible impulse action may be taken. This construction yields consistent occupation measures, event fluxes, availability, reliability, congestion, action frequencies, and long-run costs. The event-driven simulator is validated against an exact CTMC benchmark, an analytical degradation-dependent failure clock, and ten executable event-kernel tests. A common reproducible protocol is then used for paired finite-grid screening and fresh post-selection comparison of corrective-only, orbit-retrieval-only, pure threshold preventive-maintenance, periodic-inspection threshold-gated preventive-maintenance, and hybrid policies. In the baseline regime, screening selects a retrieval-dominant hybrid whose fresh stationary outputs coincide with retrieval-only control on the evaluated seed block. At \(θ =0.20\) , materially active preventive maintenance increases the penalized cost by \(12.30± 0.82\) relative to retrieval-only control. Across fifteen re-screened scenarios, no fresh paired hybrid–retrieval-only \(95% \) cost interval excludes zero. The results therefore support the framework as a reproducible policy-evaluation tool, while showing that preventive-maintenance effects are regime- and capacity-dependent and do not establish general hybrid-policy superiority.