(417a) Nested Sampling Algorithm for Probabilistic Design Space Definition with Recourse Action

The increasing pressure to continually improve pharmaceutical manufacturing practices has promoted the use of process systems engineering techniques to support pharmaceutical process development. Of particular interest is the use of model-centric approaches to defining a design space in pharmaceutical quality-by-design (QbD) [1]. But such mathematical models carry uncertainty, typically in the form of uncertain parameters. Accounting for this uncertainty is of paramount importance to prevent false positives, in agreement with the ICH quality guideline Q8 (R2) [2]. This leads to the concept of probabilistic design space [3], which is akin to stochastic flexibility analysis [4,5] in the process systems engineering literature.

As a consequence of these developments, interest in numerical tools capable of characterising a probabilistic design space has grown significantly. Existing algorithms either approximate the design space with a set of samples [6,7] or seek to inscribe a given shape inside the design space of interest [8,9]. As the use of process analytical technology and advanced process controls are becoming commonplace in modern pharmaceutical manufacturing, the ability to consider recourse system variables during design space definition is paramount [10]. There is, therefore, a need for algorithms which rigorously account for model uncertainty and recourse actions, whilst simultaneously remain general and tractable for solving a wide range of practical problems.

This talk presents an extension to the nested sampling algorithm for probabilistic design space definition [6] that enables processes with recourse variables. The main idea entails the combination of adaptive sampling of the critical process parameter (CCP) space, with a recourse optimization problem that maximizes the feasibility probability for each CPP realization. The former is based on the nested sampling algorithm implemented in the Python package DEUS [6]. The latter approximates the chance constraints via Monte Carlo sampling of the uncertain model parameters, and it considers either a mixed-integer programming formulation or its continuous relaxation for computational tractability [5], both implemented in Pyomo. The approach is illustrated for several steady-state design space problems, where the recourse action is essentially acting as a perfect control. Comparisons are also made with the counterpart design space problems without recourse action to demonstrate the potential benefits (see Figure).

References

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