1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark
In this thesis the use of various statistical methods to address some of the problems related to assessment of the homogeneity of powder blends in tablet production is discussed. It is not straight forward to assess the homogeneity of a powder blend. The reason is partly that in bulk materials as powder blends there is no natural unit or amount to define a sample from the blend, and partly that current technology does not provide a method of universally collecting small representative samples from large static powder beds. In the thesis a number of methods to assess (in)homogeneity are presented. Some methods have a focus on exploratory analysis where the aim is to investigate the spatial distribution of drug content in the batch. Other methods presented focus on describing the overall (total) (in)homogeneity of the blend. The overall (in)homogeneity of the blend is relevant as it is closely related to the (in)homogeneity of the tablets and therefore critical for the end users of the product. Methods to evaluate external factors, that may have an influence on the content in blend samples, as e.g. sampling device, have been presented. However, the content in samples is also affected of internal factors to the blend e.g. the particle size distribution. The relation between particle size distribution and the variation in drug content in blend and tablet samples is discussed. A central problem is to develop acceptance criteria for blends and tablet batches to decide whether the blend or batch is sufficiently homogeneous (uniform) to meet the need of the end users. Such criteria are most often criteria regarding sample values rather than criteria for the quality (homogeneity) of the blend or tablet batch. This inherently leads to uncertainty regarding the true quality of a specific blend or batch. In the thesis it is shown how to link sampling result and acceptance criteria to the actual quality (homogeneity) of the blend or tablet batch. Also it is discussed how the assurance related to a specific acceptance criteria can be obtained from the corresponding OC-curve. Further, it is shown how to set up parametric acceptance criteria for the batch that gives a high confidence that future samples with a probability larger than a specified value will pass the USP threeclass criteria. Properties and robustness of proposed changes to the USP test for content uniformity are investigated by the use of simulations, and single sampling acceptance plans for inspection by variables that aim at matching the USP proposal have been suggested.