Plurality voting for enhancing reliability

Abstract

Due to the ubiquity of electronic systems, they are relied on now more than they ever have been in the past. Since technology trends suggest that the reliability of these systems will continue to be a serious concern, and due to their use in safety critical domains, they must be robust. Modelling the reliability of systems, electronic or otherwise, affords an understanding of how to design them to be more reliable. The perspective is taken that hardware is assumed to be abundant but faulty, and the question of how to combine unreliable components to produce a reliable system using redundancy is addressed. This leads to a model based on plurality voting, in which the mathematical properties of the model are explored in depth. Additionally, many properties of plurality voting itself are explored and proved. The model is deliberately made to be very general and does not assume the availability of much exploitable information. The parameter space is explored freely, allowing for high levels of redundancy and covering any number of states. These properties make plurality voting a more practical choice than other popular voting methods such as majority voting. Plurality voting is a more involved and lesser explored voting mechanism, particularly on the scale applied in this work. It is found that the rate at which the number of error states grows and the entropy of the error distribution are amongst the most important factors in the reliability. An interesting connection is found between Renyi entropy and plurality voting that provides a practical approximation for calculating the reliability of an arbitrary error distribution in the context of the model. A conjecture is made about this connection and it is proved for a special case. Finally, interesting and complex patterns are discovered when plurality voting is applied in a hierarchical structure. The interactions between the reliability and cost characteristics of the structures reveal that hierarchical structures can be optimal in reliability and cost for regions of high reliability, providing reliability boosts for free. A conjecture is made about the general behaviour of the optimal set of structures to this effect.

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Identifiers

ORCID for David, Thomas Vaughan: orcid.org/0000-0003-1126-5701

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