On the Efficacy of R-on-M Redundancy

A redundant configuration consisting of m identical elements and r universal spare elements is postulated. Each of the spares in this ``r-on-m'' configuration can substitute for any one of the m elements required for the system to be operational. The system reliability attainable with this configuration is examined as a function of r and m, simple bounds are derived, and a method is presented for determining the optimum values for r and m as a function of the relative complexity of the associated switch. It is shown that an r-on-m configuration can provide an extremely efficient means for obtaining significant improvement in reliability, and is often nearly as effective as a parallel configuration involving m times as many spares.