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<p>Failure to establish a majority among the processing modules in a triple modular redundant (TMR) system, called a TMR failure, is detected by using two voters and a disagreement detector. Assuming that no more than one module becomes permanently faulty during the execution of a task, Re-execution of the task on the Same HardWare (RSHW) upon detection of a TMR failure becomes a cost-effective recovery method, because 1) the TMR system can mask the effects of one faulty module while RSHW can recover from nonpermanent faults, and 2) system reconfiguration-Replace the faulty HardWare, reload, and Restart (RHWR)-is expensive both in time and hardware. We propose an adaptive recovery method for TMR failures by "optimally" choosing either RSHW or RHWR based on the estimation of the costs involved. We apply the Bayes theorem to update the likelihoods of all possible states in the TMR system with each voting result. Upon detection of a TMR failure, the expected cost of RSHW is derived with these likelihoods and then compared with that of RHWR. RSHW will continue either until it recovers from the TMR failure or until the expected cost of RSHW becomes larger than that of RHWR. As the number of unsuccessful RSHW's increases, the probability of permanent fault(s) having caused the TMR failure will increase, which will, in turn, increase the cost of RSHW. Our simulation results show that the proposed method outperforms the conventional reconfiguration method using only RHWR under various conditions.</p>
fault tolerant computing; redundancy; Bayes methods; digital simulation; time redundancy approach; TMR failures; fault-state likelihoods; processing modules; triple modular redundant system; voters; disagreement detector; system reconfiguration; adaptive recovery method; Bayes theorem; simulation results.

K. Shin and H. Kim, "A Time Redundancy Approach to TMR Failures Using Fault-State Likelihoods," in IEEE Transactions on Computers, vol. 43, no. , pp. 1151-1162, 1994.
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