Homogenization time 628 • INDEX

The time series shows a. stationary pattern until a homogeneously oscillating flow rate around a constant level. However, an additive outlier occurs at time index 128. To analyse the time dependency pattern of the Naphtha time series, the effect of the outlier has to be removed. Therefore, the outlier s effect (i.e. the raise beyond the mean level) is estimated by modelling a simple linear regression model and the corresponding value of the time series is corrected by this estimate. For the corrected Naphtha time series, ACF and PACF are calculated (Figure 2.13a and Figure 2.13b). 

We will restrict ourselves to time invariant Markov chains where the transition probabilities only depend on the states, not the time n. These are also called homogeneous Markov chains. In this case, we can leave out the time index and the transition probability matrix of the Markov chain is given by... 

A homogeneity index or significance coefficienf has been proposed to describe area or spatial homogeneity characteristics of solids based on data evaluation using chemometrical tools, such as analysis of variance, regression models, statistics of stochastic processes (time series analysis) and multivariate data analysis (Singer and... 

Homogeneous breakage kernels with positive homogeneity index (A>0) produce self-similar size distributions at long times... 

Because almost all materials used in the pharmaceutical industry have NIR spectra, the use of NIR for assuring blend homogeneity may prove to be a valuable application. Ciurczak [24,25] reported some of the first work on this subject. His work involved the use of a fiber probe to collect spectra from various locations in the mixer. Spectral matching and principal component analysis (PCA) were used to measure how similar the powder mix in a particular portion of the blender was to a predetermined good, or complete, mix. The match index or PCA scores were plotted versus time to assess the optimal blending time. 

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