Abstract
Estimating metrics such as the Mean Time To Failure (MTTF) or its inverse, the FailuresInTime (FIT), is a central problem in reliability estimation of safetycritical systems. To this end, prior work in the realtime 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 worstcase 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 safetycritical realtime 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 longrun 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 multistate models such as weaklyhard 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 weaklyhard 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 weaklyhard constraints, and their space and time complexities, which affect their scalability and applicability in different regions of the space of weaklyhard constraints.
BibTeX  Entry
@InProceedings{gujarati_et_al:LIPIcs:2019:10746,
author = {Arpan Gujarati and Mitra Nasri and Rupak Majumdar and Bj{\"o}rn B. Brandenburg},
title = {{From Iteration to System Failure: Characterizing the FITness of Periodic WeaklyHard Systems}},
booktitle = {31st Euromicro Conference on RealTime Systems (ECRTS 2019)},
pages = {9:19:23},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771108},
ISSN = {18688969},
year = {2019},
volume = {133},
editor = {Sophie Quinton},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10746},
URN = {urn:nbn:de:0030drops107468},
doi = {10.4230/LIPIcs.ECRTS.2019.9},
annote = {Keywords: reliability analysis, MTTF/FIT analysis, weaklyhard constraints}
}
Keywords: 

reliability analysis, MTTF/FIT analysis, weaklyhard constraints 
Seminar: 

31st Euromicro Conference on RealTime Systems (ECRTS 2019) 
Issue Date: 

2019 
Date of publication: 

08.07.2019 