prediction of the reliability of a system with multiple redundant elements

The present paper focuses on the problem of active redundancy in the general case where several participating elements are kept on standby. this study assumes that the failure distribution of all redundant elements, as well as the switch and the failure detector, all follow the exponential law characterized by a constant failure rate. the analysis of the different success modes of the system considered, first in the specific case of a system with a single element on standby, then with two, and finally with three elements on standby, this analysis has allowed us to establish a recurrence relation that provides the analytical expression of the reliability of an active redundancy system in the general case where several elements are kept on standby.