A new dynamic operability index based on on-specification production for continuous pharmaceutical manufacturing under uncertainty

Operability analyses provide a general framework for assessing the process ability to satisfy its performance metrics under uncertain or disturbance conditions. The process operability is often quantified by the so-called operability index. However, most existing operability indexes assume steady-state operation, and thus, are suitable for high-volume processes running for extended periods such as those in the oil and gas industries. On the other hand, continuous manufacturing of fine chemicals such as pharmaceuticals are typically performed campaign-wise, which means the operation time is limited to a few weeks. Consequently, the process is mostly in transient, and steady state, if any, will occur for a short period only. This renders current steady-state operability indexes inapplicable for operability studies of such processes. A new operability index tailored for campaign continuous manufacturing is introduced in this paper, which unlike existing indexes, accounts for both transient and steady-state phases of the operation in a single formulation. Motivated by stringent product quality requirements in pharmaceutical industry, the index quantifies the process ability to maintain the desired amount of on-specification production over a range of process uncertainties. This is done by a special dynamic optimization problem that finds optimal process trajectories maximizing on-specification production for each uncertainty realization. The operability index is then defined as the ratio of the uncertainty realizations for which the maximum on-specification production is no less than the desired value to the entire uncertainty set. The new index is demonstrated by two examples including a campaign continuous aspirin crystallization process. The usefulness of the proposed index in screening different design alternatives and enhancing operability is also highlighted.