Evaluation of variation in dynamic processes via online spectrometers Jarno Kohonen*, Hannu Alatalo and Satu-Pia Reinikainen Theory of sampling offers powerful tools for process optimization. An adequate sampling interval can be determined for spectral measurements when utilizing a multivariate extension of variography by applying score vectors as independent sources of uncertainty. The traditional way is to apply variographic analyses into single process variables independently. In the multivariate extension, those process variables are replaced with score vectors of principal component analysis. The combined uncertainty found this way depends not only on the variance in the spectra, but also, for example, on the number of utilized score vectors and the preprocessing method. This approach is illustrated with a crystallization process continuously followed with an attenuated total reflectance Fourier transform infrared instrument. The results show that the approach is highly applicable but should only be utilized as an indicative tool. Copyright © 2012 John Wiley & Sons, Ltd. Keywords: variography; theory of sampling; PCA; IR 1. INTRODUCTION Novel fast, easy and automated methods often involve spectral instruments. They have been found as powerful, nondestruc- tive and easily automated method, which can be applied in determination of several parameters simultaneously. As easily automated methods, they—along with other well-established automated instruments—have gained reputation in monitor- ing of dynamic processes with very short sampling interval, sometimes only a few seconds. Because of that efficiency, it has been found difficult to determine correct or adequate sampling interval, and quite often excessive amounts of data are collected yet poorly utilized. A steady-state process could sometimes be followed with enough accuracy also with longer sampling intervals. For spectral data and complex processes, the sampling interval is often quite difficult to determine. Different phenomena affect different parts of a spectrum, and thus, univariate approaches would inevitably disregard infor- mation. This issue has recently been discussed in [1], where dynamic sampling step optimization is suggested to avoid missing process features due to sparse sampling. With multi- variate extension of univariate uncertainty determination, the sampling interval can be determined on the basis of score vectors. Despite the fact that multivariate methods have been found highly suitable in handling of spectral data and univariate sampling optimization is well founded [2,3], multivariate optimiza- tion of sampling frequency is only rarely carried out [4]. 2. THEORY 2.1. Combined uncertainty Modern process monitoring and controlling involves quantifica- tion of measurand uncertainties on a wide range. In general, uncertainty of a measurement comprises many components, which can be characterized by standard deviations on the basis of experience or experimental data. In metrological terminology, uncertainty of a measurement is defined as a parameter, associ- ated with the result of a measurement, which characterizes the dispersion of the values that could reasonably be attributed to the measurand. This ‘parameter’ may be, for example, a range, a standard deviation, an interval (a confidence interval, for instance) or other measure of dispersion such as a relative standard deviation [5]. In practice, the uncertainty of the result may arise from many possible sources, which may be incomplete definition, sampling, matrix effects and interferences, environmental conditions, uncertainties of equipment, reference values, approximations and assumptions incorporated in the measurement method and procedure, and random variation. Analytical uncertainty of an instrument is often one of the smallest uncertainty sources, and it can be easily determined or checked [6]. Each of the separate contributions (source of uncertainty) is referred as an uncertainty component. When the uncertainty components are expressed as standard deviations, they are known as standard uncertainties [5]. If there is correlation between the uncertainty components, it has to be taken into account by determining their covariance. However, it is often possible to evaluate the combined effect of several components, thus reducing the overall effort involved in the evaluation of the contribution of correlated uncertainty components [7,8]. Combined uncertainty is calculated using the law of propagation of uncertainty (Equation (1)). When combining uncertainty components. they are summed as variances (squared standard deviations), and the square root of this sum is called combined uncertainty. It should be noted that the uncertainty components * Correspondence to: Jarno Kohonen, Lappeenranta University of Technology, PO Box 20, FI-53851 Lappeenranta, Finland. E-mail: jarno.kohonen@lut.fi J. Kohonen, H. Alatalo, S.-P. Reinikainen Lappeenranta University of Technology, LUT Chemistry, Lappeenranta, Finland Special Issue Article Received: 9 December 2011, Revised: 5 April 2012, Accepted: 6 April 2012, Published online in Wiley Online Library: 22 May 2012 (wileyonlinelibrary.com) DOI: 10.1002/cem.2451 J. Chemometrics 2012; 26: 333–339 Copyright © 2012 John Wiley & Sons, Ltd. 333