From iteration to system failure: Characterizing the fitness of periodic weakly-hard systems

Arpan Gujarati, Mitra Nasri, Rupak Majumdar, Björn B. Brandenburg

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Estimating metrics such as the Mean Time To Failure (MTTF) or its inverse, the Failures-In-Time (FIT), is a central problem in reliability estimation of safety-critical systems. To this end, prior work in the real-time and embedded systems community has focused on bounding the probability of failures in a single iteration of the control loop, resulting in, for example, the worst-case probability of a message transmission error due to electromagnetic interference, or an upper bound on the probability of a skipped or an incorrect actuation. However, periodic systems, which can be found at the core of most safety-critical real-time systems, are routinely designed to be robust to a single fault or to occasional failures (case in point, control applications are usually robust to a few skipped or misbehaving control loop iterations). Thus, obtaining long-run reliability metrics like MTTF and FIT from single iteration estimates by calculating the time to first fault can be quite pessimistic. Instead, overall system failures for such systems are better characterized using multi-state models such as weakly-hard constraints. In this paper, we describe and empirically evaluate three orthogonal approaches, PMC, Mart, and SAp, for the sound estimation of system's MTTF, starting from a periodic stochastic model characterizing the failure in a single iteration of a periodic system, and using weakly-hard constraints as a measure of system robustness. PMC and Mart are exact analyses based on Markov chain analysis and martingale theory, respectively, whereas SAp is a sound approximation based on numerical analysis. We evaluate these techniques empirically in terms of their accuracy and numerical precision, their expressiveness for different definitions of weakly-hard constraints, and their space and time complexities, which affect their scalability and applicability in different regions of the space of weakly-hard constraints.

Original languageEnglish
Title of host publication31st Euromicro Conference on Real-Time Systems, ECRTS 2019
EditorsSophie Quinton
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Number of pages23
ISBN (Electronic)9783959771108
Publication statusPublished - 2019
Event31st Euromicro Conference on Real-Time Systems, ECRTS 2019 - Stuttgart, Germany
Duration: 9 Jul 201912 Jul 2019


Conference31st Euromicro Conference on Real-Time Systems, ECRTS 2019


  • MTTF/FIT analysis
  • Reliability analysis
  • Weakly-hard constraints

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