Batch-to-Batch Variation: A Key Component for Modeling Chemical Manufacturing Processes

For chemical manufacturing processes, the chemical kinetics literature contains virtually no mention of quantitative models that involve batch-to-batch variation. Models for chemical process manufacturing quality improvement are being more carefully considered, particularly by the pharmaceutical industry and its regulators. This is evidenced in part by the recent ICH Q11 regulatory guidance on drug substance manufacture and quality. Quality improvement has been defined as a reduction in variation about a target. Hence the modeling of process variation plays an important role in quantifying quality improvement. Given that batch-to-batch variation is often a dominant source of process variation (usually exceeding measurement error variation), it is important for process models to incorporate such variance components. In this paper, we show how chemical kinetic models can incorporate batch-to-batch variation as well as measurement error. In addition, we show that these models can be used to quantify the reliability of meeting process specifications using Bayesian statistical methods. We also compare some different Bayesian computational approaches and recommend some software packages to aid with the computations.