In this paper, the reliability and MTTF (Mean Time to Failure) for multi-ring RPR (Resilient Packet Ring) are calculated
on the conditions of single-link failures, double-link failures and no failure, respectively. The parameters such as the total
number of stations <i>N</i>, the number of the sub-rings <i>R</i>, and the distribution of <i>N<sub>i</sub> </i>which represents the number of the
stations in the <i>i</i>-th sub-ring (1≤<i>i</i>≤R) are contained in the formulas. The relationship between the value of the
reliability/MTTF and the parameters <i>N</i>, <i>R</i> and <i>N<sub>i</sub></i> is analyzed. The result shows that reliability/MTTF of the RPR
multi-rings is increasing while the variance of <i>N<sub>i</sub></i> is decreasing. It is also proved that the value of the reliability/MTTF is
maximum when <i>N<sub>i</sub>=N<sub>j</sub></i> ( <i>i ≠j</i> and 1≤<i>i</i>, <i>j</i>≤<i>R</i>) by using Lagrange multipliers method, i.e. the condition of the optimal
reliability of multi-ring RPR is satisfied when var(<i>N<sub>i</sub></i>) =0.