Transfer Function Modeling of Processes with Dynamic Inputs

Abstract

Time series structures, which are common occurrences with data in many industrial processes, complicate a quality practitioner's efforts to accurately position control chart limits. ARIMA modeling and a variety of control charting methods have been recommended for monitoring process data with a time series structure. Estimates of ARIMA model parameters may not be reliable, however, if assignable causes of variation are present in the process data used to fit the time series model. Control limits may also be misplaced if the process inputs are dynamic and exhibiting a time series structure. Our purpose in this paper is to explore the ability of a transfer function model to identify assignable causes of variation and to model dynamic relationships between process inputs and outputs. A transfer function model is developed to monitor biochemical oxygen demand output from a wastewater treatment process, a process with dynamic inputs. This model is used to identify periods of disturbance to the wastewater process and to capture the relationship between the variable nature of the input to the process and the resulting output. Simulation results are included in this study to measure the sensitivity of transfer function models and to highlight conditions where transfer function modeling is critical.