Formal Dependability Modeling and Optimization of Scrubbed-Partitioned TMR for SRAM-based FPGAs
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SRAM-based FPGAs are popular in the aerospace industry for their field programmability and low cost. However, they suffer from cosmic radiation-induced Single Event Upsets (SEUs). Triple Modular Redundancy (TMR) is a well-known technique to mitigate SEUs in FPGAs that is often used with another SEU mitigation technique known as configuration scrubbing. Traditional TMR provides protection against a single fault at a time, while partitioned TMR provides improved reliability and availability. In this paper, we present a methodology to analyze TMR partitioning at early design stage using probabilistic model checking. The proposed formal model can capture both single and multiple-cell upset scenarios, regardless of any assumption of equal partition sizes. Starting with a high-level description of a design, a Markov model is constructed from the Data Flow Graph (DFG) using a specified number of partitions, a component characterization library and a user defined scrub rate. Such a model and exhaustive analysis captures all the considered failures and repairs possible in the system within the radiation environment. Various reliability and availability properties are then verified automatically using the PRISM model checker exploring the relationship between the scrub frequency and the number of TMR partitions required to meet the design requirements. Also, the reported results show that based on a known voter failure rate, it is possible to find an optimal number of partitions at early design stages using our proposed method.
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