Analytical performance parameters Linearity

A number of experimental considerations must be addressed in order to use XRF as a quantitative tool, and these have been discussed at length [75,76]. The effects on the usual analytical performance parameters (accuracy, precision, linearity, limits of detection and quantitation, and ruggedness) associated with instrument are usually minimal. 

NIR spectroscopy became much more useful when the principle of multiple-wavelength spectroscopy was combined with the deconvolution methods of factor and principal component analysis. In typical applications, partial least squares regression is used to model the relation between composition and the NIR spectra of an appropriately chosen series of calibration samples, and an optimal model is ultimately chosen by a procedure of cross-testing. The performance of the optimal model is then evaluated using the normal analytical performance parameters of accuracy, precision, and linearity. Since its inception, NIR spectroscopy has been viewed primarily as a technique of quantitative analysis and has found major use in the determination of water in many pharmaceutical materials. 

The United States Pharmacopoeia (U.S.P.) [5] in a chapter on validation of compendial methods, defines analytical performance parameters (accuracy, precision, specificity, limit of detection, limit of quantitation, linearity and range, ruggedness, and robustness) that are to be used for validating analytical methods. A proposed United States Pharmacopeia (U.S.P.) general chapter on near-infrared spectrophotometry [6] addresses the suitability of instrumentation for use in a particular method through a discussion of operational qualifications and performance verifications. 

The following analytical performance parameters were included into the validation process selectivity stability during chromatograidiic development and in solution spot stability prior to the run and after development linearity and range precision reproducibility limit of quantitation limit of detection accuracy. The definitions used for the performance parameters the methods applied to determine them and the acceptance criteria were also described. Therefore, these papers can be recommended to be used by practicising chromatographers. 

For non-compendial procedures, the performance parameters that should be determined in validation studies include specificity/selectivity, linearity, accuracy, precision (repeatability and intermediate precision), detection limit (DL), quantitation limit (QL), range, ruggedness, and robustness [6]. Other method validation information, such as the stability of analytical sample preparations, degradation/ stress studies, legible reproductions of representative instrumental output, identification and characterization of possible impurities, should be included [7], The parameters that are required to be validated depend on the type of analyses, so therefore different test methods require different validation schemes. 

The purpose of an analytical method is the deliverance of a qualitative and/or quantitative result with an acceptable uncertainty level. Therefore, theoretically, validation boils down to measuring uncertainty . In practice, method validation is done by evaluating a series of method performance characteristics, such as precision, trueness, selectivity/specificity, linearity, operating range, recovery, LOD, limit of quantification (LOQ), sensitivity, ruggedness/robustness, and applicability. Calibration and traceability have been mentioned also as performance characteristics of a method [2, 4]. To these performance parameters, MU can be added, although MU is a key indicator for both fitness for purpose of a method and constant reliability of analytical results achieved in a laboratory (IQC). MU is a comprehensive parameter covering all sources of error and thus more than method validation alone. 

Extent of Validation Depends on Type of Method On the one hand, the extent of validation and the choice of performance parameters to be evaluated depend on the status and experience of the analytical method. On the other hand, the validation plan is determined by the analytical requirement(s) as defined on the basis of customer needs or as laid down in regulations. When the method has been fully validated according to an international protocol [63,68] before, the laboratory does not need to conduct extensive in-house validation studies. It must only verify that it can achieve the same performance characteristics as outlined in the collaborative study. As a minimum, precision, bias, linearity, and ruggedness studies should be undertaken. Similar limited vahdation is required in cases where it concerns a fully validated method which is apphed to a new matrix, a well-established but noncol-laboratively studied method, and a scientifically pubhshed method with characteristics given. More profound validation is needed for methods pubhshed as such in the literature, without any characteristic given, and for methods developed in-house [84]. 

The dynamic range of a mass spectrometer is defined as the range over which a linear response is observed for an analyte as a function of analyte concentration. It is a critical instrument performance parameter, particularly for quantitative applications, because it defines the concentration range over which analytes can be determined without sample dilution or preconcentration, which effects the accuracy and precision of an analytical method. Dynamic range is limited by physiochemical processes, such as sample preparation and ionization, and instrumental design, such as the type of mass analyzer used and the ion detection scheme. 

Another level involves an analytical procedure which almost matches the users requirements. Perhaps the analyte molecule has a slight structural difference from the stored procedure, requiring a change in the pH of the medium during the analysis. Such slight differences in structure or reaction conditions require that CHESS have the ability to reason. Parameter estimation and calculation can be performed using Linear Free Energy Relationships (LFERs) and other types of additive relationships to predict properties. 

Next we covered analysis of data. We used probability and random variables to model the irreproducibie part of the experiment. For models that are linear in the parameters, we can perform parameter estimation and construct exact confidence intervals analytically. For models that are nonlinear in the parameters, we compute para ter estimates and construct approximate confidence intervals using nonlinear optimization methods. 

For obtaining reliable analysis results, the (high-performance) thin-layer chromatographic (TLC) method should he validated before using it as a quality control tool. The validation parameters that should he evaluated are stability of the analyte, specificity/selectivity, linearity, accuracy, precision, range, detection limit, quantification limit, and robustness/ruggedness. 

The peak dispersion in chromatography is generally characterized by the theoretical plate height (H) and the number of theoretical plates (N). The treatment of the mass transfer processes and the distribution equilibrium between the mobile and stationary phase in a column lead to equations that link the theoretical plate height as the crucial column performance parameter to the properties of the chromatographic systems, such as the linear velocity of the mobile phase, the viscosity, the diflusion coefficient of analyte, the retention coefficient of analyte, column porosity, etc. 

The most economic way of using CRMs for calibration purposes is to validate a procedure for routine analysis. The analytical procedure is carried out with the CRMs analysed as samples. "IMth the results achieved, all relevant analytical parameters can be determined, e.g. uncertainty, recovery, reproducibility, selectivity, linearity, etc. The procedure is then well known for the specific sample type and the specific analytes for which it is validated and can be applied routinely for this analytical problem, with a few regular reviews of the analytical performance. CRMs in this case are not used for calibration but rather for validation of the procedure and regular review of the method performance. 

Standards used to constmct a cahbration curve must be prepared such that the matrix of the standard is identical to the sample s matrix because the values of the parameters k and b associated with a linear cahbration curve are matrix dependent. Many areas of chemical analysis are plagued by matrix effects, and it is often difficult to duphcate the sample matrix when preparing external standards. Because it is desirable to eliminate matrix effects, cahbration in the sample matrix itself can be performed. This approach is called the standard addition method (SAM) (14). In this method, the standards are added to the sample matrix and the response of the analyte plus the standard is monitored as a function of the added amount of the standard. The initial response is assumed to be Rq, and the relationship between the response and the concentration of the analyte is... 

It is an essential condition of biological assay methods that the tests on the standard preparation and on the sample whose potency is being determined should be carried out at the same time and, in all other respects, under strictly comparable conditions. The validation of microbiological assay method includes performance criteria (analytical parameters) such as linearity, range, accuracy, precision, specificity, etc. 

Another important test of the accuracy of the superposition approximation is the diffusion-controlled A + B — 0 reaction. For the first time it was computer-simulated by Toussaint and Wilczek [27]. They confirmed existence of new asymptotic reaction laws but did not test different approximations used in the diffusion-controlled theories. Their findings were used in [28] to discuss divergence in the linear and the superposition approximations. Since analytical calculations [28] were performed for other sets of parameters as used in [27], their comparison was only qualitative. It was Schnorer et al. [29] who first performed detailed study of the applicability of the superposition approximation. 

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