(104d) Identification of Critical Process Parameters from Observational Data, a Causal Inference Perspective

Critical process parameters (CPPs) are key variables affecting process product quality, and as a result, should be closely monitored or controlled. Additionally, research efforts can be prioritized on the CPPs so efficient improvements of the processes can be achieved. Therefore, the identification of CPPs is of great importance to improving process safety and productivity.

The physical intuition behind CPPs is usually causal instead of associative. The search for CPPs tries to infer the potential change of the outputs if external interventions, such as control, are exerted on certain process parameters. Through the act of intervention, the underlying data-generating process is modified. Therefore, the resulting distribution has been shifted, which cannot be inferred by associative models such as distribution functions.

Because of the causal intuition underlying CPPs, established methods of identifying CPPs are mainly based on the Design of Experiments (DOE), upon either physical systems [1] or computer simulations (such as flowsheet sensitivity analysis) [2,3]. Because process parameters were independently assigned during experiments, the identified CPPs can be confidently interpreted in a causal way. However, developing mechanistic models and conducting controlled experiments can be very expensive or even infeasible. As a result, taking advantage of the increasingly available process data is a promising alternative for identifying CPPs. Nevertheless, in real-world operations, process variables are commonly dependent on each other due to recipes, control loops, or corrective interventions. Therefore, naively applying statistical methods directly to observational data would lead to erroneous results [4].

Causal inference provides a systematic way to leverage observational process data and solve causal problems [5]. With additional causal assumptions that identify invariant relationships, causal inference goes beyond statistics and can infer probabilities under changing conditions. As a general framework, causal inference theories subsume the DOE methodologies [6].

This study proposes a new method using causal inference to identify CPPs from observational data. The qualitative knowledge of causality is integrated with observational process data using a Structure Causal Model, and the causal outcome of controlling certain process variables can be estimated. Additionally, this work formulated a new index named Potential Variance Reduction (PVR), which quantifies each variable's importance under the proposed causal framework. The derivation of PVR is non-parametric so that any statistical model (such as ANNs or Kriging) can be applied, allowing for good flexibility when dealing with relationships of different complexity.

The proposed approach will be illustrated through a case study based on the steady-state operation of the Van de Vusse reactor, which exhibits input multiplicity behavior [7]. The simulation results demonstrate that naively applying statistical methods (such as Morris or Sobol sensitivity analysis) on observational data will lead to erroneous results. On the other hand, based on prior knowledge of the causal relationships, the proposed framework can identify the CPPs correctly.

References

[1] J. Thiry, F. Krier, B. Evrard, A review of pharmaceutical extrusion: Critical process parameters and scaling-up, Int. J. Pharm. 479 (2015) 227–240.

[2] N. Metta, M. Ghijs, E. Schäfer, A. Kumar, P. Cappuyns, I. Van Assche, R. Singh, R. Ramachandran, T. De Beer, M. Ierapetritou, I. Nopens, Dynamic Flowsheet Model Development and Sensitivity Analysis of a Continuous Pharmaceutical Tablet Manufacturing Process Using the Wet Granulation Route, Processes. 7 (2019).

[3] A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, S. Tarantola, Global sensitivity analysis: the primer, John Wiley \& Sons, 2008.

[4] E.D. Wilson, Q. Clairon, R. Henderson, C.J. Taylor, Dealing with observational data in control, Annu. Rev. Control. 46 (2018) 94–106.

[5] J. Pearl, Causality, Cambridge University Press, Cambridge, 2009.

[6] J. Pearl, An introduction to causal inference., Int. J. Biostat. 6 (2010) Article 7.

[7] B.W. Bequette, Process control: modeling, design, and simulation, Prentice Hall Professional, Upper Saddle River, NJ, United States, 2003.