Characterization and propagation of RTD uncertainty for continuous powder blending processes

Residence time distribution (RTD) is a probability density function that describes the time materials spend inside a system. It is a promising tool for mixing behavior characterization, material traceability, and real-time quality control in pharmaceutical manufacturing. However, RTD measurements are accompanied with some degree of uncertainties because of process fluctuation and variation, measurement error, and experimental variation among different replicates. Due to the strict quality control requirements of drug manufacturing, it is essential to consider RTD uncertainty and characterize its effects on RTD-based predictions and applications. Towards this end, two approaches were developed in this work, namely model-based and data-based approaches. The model-based approach characterizes the RTD uncertainty via RTD model parameters and uses Monte Carlo sampling to propagate and analyze the effects on downstream processes. To avoid bias and possible reduction of uncertainty during model fitting, the data-based approach characterizes RTD uncertainty using the raw experimental data and utilizes interval arithmetic for uncertainty propagation. A constrained optimization approach was also proposed to overcome the drawback of interval arithmetic in the data-based approach. Results depict probability intervals around the upstream disturbance tracking profile and the funnel plot, facilitating better decision-making for quality control under uncertainty.