Total active disc area and the number of RBC stages are optimized for the deterministic case, and are then incorporated into a risk-based method of assigning per-stage active disc areas. The risk of the final stage SBOD exceeding a fixed effluent standard is evaluated by taking into account the variable nature of the influent flowrate and SBOD concentration. Bivariate normal, lognormal and shifted lognormal distributions are considered as models for the input random variables. The effluent SBOD probability density function is obtained according to the method of transformation of random variables. Illustrative examples are presented.