Variance stabilization procedures

The most important advantage of such an IDMS procedure is that it compensates in an ideal way both for losses during sample workup and for variations in mass spectrometric response. As demonstrated by Claeys et al. (1977), the use of a stable isotope-labeled internal standard, as opposed to the use of homologs, produces the lowest variance factors due to instrumental stability and sample manipulating errors. Moreover, IDMS can be used both with and without prior chromatographic separation, as for instance in... 

The Limit of Quantitation (LOQ) and the reportable limit for impurities also impact impurity test OOT procedures. It is common practice to report impurity peaks below the Limit of Quantitation as < LOQ, which is set to the reporting limit for that impurity per ICH Q3A(R2). Therefore, the purity result for peaks just below the LOQ cannot be used for trending although the analytical method variance may be satisfactory at that level. This reporting practice again decreases the information presented in the stability data tables, limits the QQT tools for impurities close to the... 

At the beginning of Section 11.3, the calculation of constant distributions from experimental data is an ill-posed problem that, if approached by classical solution schemes, leads to serious numerical problems and instabilities. To circumvent these difficulties, least squares minimization procedures are modified by the introduction of constrains, regularization, or both of them, to provide a substantial stabilization of the resulting distributions these approaches have been widely applied (Provencher 1982a Cernik, Borkovec, and Westall 1995 Borkovec et al. 1996 Rusch et al. 1997 Bersillon et al. 2001). In general terms, all modifications are applied over the common least squares problem, where the function to be minimized is the variance ... 

Figure 14.5. The functions and Gsd s) will have to be chosen with care because of potential difficulties with stability. Also, these two functions must be chosen with primary regard for material-balance control, not composition control. This point of view is at variance with that sometimes expressed dsewhete in the literature. Finally, it is probably apparent that conventional tuning procedures are essentially useless for a system of this complexity control functitxis must be correctly preselected, and control-loop parameters calculated ahead of plant operation.

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