Extended multi-fragment Markov models of programmable devices with controlled degradation considering hidden failures

Abstract

This paper presents an enhanced Markov modelling framework for evaluating the dependability and instantaneous availability of programmable devices (PDs) operating with controlled multi-level degradation in aggressive environments. Two advanced multi fragment models are introduced: MFM03, which generalises the topology to arbitrary trapezoidal/rectangular fragment arrangements using a uniform rectangular implementation, and MFM04, which additionally accounts for imperfect diagnostic coverage and hidden failures. The study describes the unified classification of the complete model family (SFM, MFM01, MFM02, MFM03, MFM04), state space generation, transition matrix construction, and fully parametric MATLAB simulation approach. Numerical results based on ATtiny13A failure rates show that the generalised topology of MFM03 yields a 1–1.5 % absolute long-term availability improvement over the original strict triangular MFM02 after 3×10⁶ hours. The MFM04 model, under realistic diagnostic coverage of 60–90 %, exhibits a crossover phenomenon whereby moderate diagnostic imperfection imposes a small medium-term penalty but can produce marginal ultra-long-term gain due to temporally distributed recovery actions. Overall, the extended model hierarchy achieves cumulative availability gains of 11–12 % compared to conventional binary single-fragment approaches, delivering practical, scalable tools for resilience optimisation of PDs in ultra-long-lifetime safety- and mission-critical systems including spacecraft onboard electronics, UAV control platforms, and so on.