Batch-to-Batch Variation: A Key Component for Modeling Chemical Manufacturing Processes Linas Mockus,* ,† John J. Peterson, ‡ Jose Miguel Lainez, § and Gintaras V. Reklaitis † † Purdue University, West Lafayette, Indiana 47907, United States ‡ GlaxoSmithKline Pharmaceuticals, Collegeville, Pennsylvania 19426, United States § University of Buffalo, Amherst, New York 14260, United States ABSTRACT: 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. ■ INTRODUCTION For chemical processes, the laws of chemistry often allow engineers to construct mechanistic predictive models. While these models are typically meant to describe how a reaction profile changes over time, they tend to model the chemistry but not the entire process. The resulting chemical equation (or equations) are the backbone of the process model, but more is needed to describe the batch-to-batch variation that is observed each time a process is run. For example, slight perturbations in input material (and/or the ratio of input materials) that charge the reactor can induce some of the batch-to-batch variation that is observed. In some cases, uncontrolled variations in environmental conditions or manufacturing settings can also contribute to variations that are seen from one run to another. Fortunately, with the proper experimental design, data can be collected that will allow one to build an enhanced chemical kinetic prediction model that takes into account the effects of batch-to-batch variation as well as measurement error. For many chemical industries, particularly the pharmaceutical industry, quality improvement is an issue of growing importance among both producers and regulators. This is evidenced in part by the recent ICH Q11 regulatory guidance 1 on drug substance manufacture and quality. While the notion of quality in ICH Q11 is rather broadly defined, it is important to note that quality improvement has been defined by some noted authors as a reduction in variation about a target. 2 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 fact, ICH Q11 lists “identification of potential sources of process variability” as a key aspect of quality-by-design (QbD). Batch-to-batch variation is certainly one of those potential sources. 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. ■ ROLE OF BATCH-TO-BATCH VARIATION IN QbD Quality improvement can be thought of as the reduction in variation about a target. 2 In addition, the larger the process variation, the more likely it is for a process to fail to meet manufacturing specifications. In fact, reduced process variation can even lower cycle time in manufacturing. 3 As such, the ability to quantify and model variation is a key element in QbD. Unfortunately, many engineers tend to build models for their processes that do not properly include terms for batch-to-batch variation. In addition, experimental designs sometimes do not employ true replicates of the process under the same experimental conditions (e.g., same temperature, pressure, etc.). In such cases, information on batch-to-batch variation may be confounded with other experimental factors and not able to be modeled or directly observed. A recent review of experimental designs for chemical kinetic models does not appear to address the issue of batch-to-batch information. 4 Special Issue: Application of ICH Q11 Principles to Process Development Received: July 28, 2014 Article pubs.acs.org/OPRD © XXXX American Chemical Society A dx.doi.org/10.1021/op500244f | Org. Process Res. Dev. XXXX, XXX, XXX-XXX