On the Reliability of Cascaded TMR Systems

Triple modular redundancy (TMR) is a well-known technique for building fault-tolerant systems. In TMR, a module unit is triplicated, and the outputs of these three units are compared by a voter. In this paper we consider systems that consist of multiple TMR units in series. Only recently has it been found that even such simple systems can be configured into various structures. We propose (i) a method of calculating the reliability of cascaded TMR systems and (ii) an algorithm for finding a structure that maximizes reliability. The algorithm uses the branch and bound search algorithm, where candidate solutions are evaluated by means of the proposed reliability calculation method. We also show that some new structures have optimal reliability within some ranges of voter and module reliability.