Finite-Horizon Reliability-Oriented Synthesis of Cumulative Up/Down-Counter Fault-Confirmation Monitors

Up/down counters are ubiquitous in the alarm and fault-confirmation logic of electro-mechanical systems. In aircraft, several electro-mechanical modules provide position feedback for flight control; the Linear Variable Differential Transformer (LVDT) is a representative one, converting mechanical displacement into an electrical signal whose reliable monitoring is critical to flight safety. As such counters are deployed in ever more complex systems and more uncertain environments, rising safety requirements render their heuristic tuning unreliable. To address this challenge, this paper proposes a quantitative, reliability-oriented procedure for counter-based monitors, which replaces heuristic parameter tuning. Both healthy and faulty signal distributions are estimated by Kernel Density Estimation (KDE), so the framework handles non-Gaussian noise and FMEA-weighted failure modes. The threshold-and-counter logic is modeled as a finite-horizon absorbing Discrete-Time Markov Chain (DTMC), which yields the false-confirmation probability, missed-detection probability, and detection delay over a bounded horizon instead of long-run rates. Thresholds and counter parameters are then synthesized offline, leaving a lightweight online monitor that needs only threshold comparison and integer counter updates. We evaluate the method on an LVDT sum-voltage monitor using real aircraft healthy measurements and Simulink-based fault injection with 45 detectable modes, assessing the synthesized monitor on 558,001 real measured samples and an FMEA-driven fault population. Results show that, among the compared confirmation logics, our workflow yields a counter that meets the 10-9 false-confirmation target and the 10-6 missed-detection target while attaining the lowest detection delay.