ARMA Processes and Reliability‐Based Design of Wastewater‐Treatment Facilities

Abstract

The applicability of univariate uncorrelated, univariate ARMA, and diagonalized vector autoregressive moving average (ARMA) processes was studied and compared to published procedures for reliability‐based design of wastewater‐treatment plants. Three applications are presented. In the first application, influent biological oxygen demand (BOD) mass loading was simulated using a univariate, weekly periodic autoregressive process to calculate sustained peak loading. In the second application, three water‐quality variables were simulated jointly using a diagonalized vector autoregressive process to calculate potential nutrient deficiencies in activated sludge processes. In the third application, effluent BOD concentrations were simulated using a univariate autoregressive process to calculate the reliability of meeting permit limits of various durations. It was found that by more completely modeling the statistical structure of available historical data, the ARMA modeling techniques were effective for reliability‐based design applications for which duration is important, as distinct from instantaneous peak loading.