Method performance criteria

Repeatability is a measure of the short-term variation in measurement results and is the precision that can be most easily determined. It is often used to establish compliance with method performance criteria. While repeatability is a... 

The reliability of a method can be determined by assessing certain method performance criteria including, specificity, accuracy, precision, limit of detection and quantitation, sensitivity, applicability, and practicability as appropriate (13). This very often requires that an extensive collaborative study be undertaken to obtain the necessary data. Methods that have successfully undergone this performance review testing have been considered to be validated for the purpose of the analysis (14). 

The overall process from concept to validated method is illustrated on Page 4 (Figure 1). Once an appropriate analytical principle has been selected and the method performance criteria defined, the actual method development process can begin. Usually, this phase is carried out using pure materials and limited samples that are known, or assumed, to be homogeneous. 

The overall process of method validation is illustrated in Figure I. However, the extent and scope of validation is governed by the applicability of the method. An in-house procedure requires a less exacting process than a method intended for multi-matrix and/or multi-laboratory use. For the latter methods, a full collaborative trial is necessary and is covered in Chapter 9. However, for many purposes validation is limited to either demonstrating that method performance criteria established during development are met under routine laboratory conditions and/or showing method equivalence (Figure 18). 

Based on expected sample matrix variability, analytical method performance criteria, and budgetary considerations, the gray region is specified at 20 percent of the action level and ranges from 0.8 to l.Ogg/kg. 

More stringent method performance criteria to control analytical error... 

Food methods validated by a collaborative trial study and those validated using the single-laboratory approach have been adopted as national and international standards by, e.g. CEN, International Organisation for Standardisation (ISO), AOAC International and by the Joint FAO/WHO Codex Alimentarius Food Standards Programme. A number of EN Standards developed by CEN relate to the organisation of controls. It is however important to keep in mind that, in addition to the method performance criteria, economical and prevention strategy... 

A nested design, which is sometimes referred to as a hierarchical design, is used for an experiment in which there is an interest in a set of treatments and the experimental units are subsampled (Fig. 9.4). It has become a practical design or an approach to study and to evaluate method performance criteria that include accuracy expressed as overall recovery, intermediate precision, and... 

Scheme 9.1 SAS output, detailed calculations of method performance criteria, and SAS program.

Other method performance criteria, such as precision, selectivity and sensitivity, compare very favourably with more common methods of niacin analysis in foods. 

SUMMA canisters are stainless-steel spheres that have a passivated stainless-steel interior that is inert to VOCs and allow for long-term storage of air. The canisters come in a variety of sizes the most common size is 6 L, and they have a needle valve that allows for sampling and removal of air. SUMMA canisters that are coated internally with fused silica have become available. USEPA methods TO-14A and TO-15 describe the determination of VOCs in air using the SUMMA canisters. TO-15 is a new version of the canister method and has an expanded target hst with a total of 97 VOCs that include some of the more polar and water-soluble VOCs. Method TO-15 establishes method performance criteria for acceptance of data that allows for the nse of alternate bnt equivalent sampling equipment. TO-15 inclusively uses GCMS and has enhanced quality assurance provisions. 

The ATP describes predefined method performance criteria that any analytical method must meet to be used for the described purpose. It is a prospective summary of the performance characteristics of a measurement system. The ATP is used to direct initial method development as well as any subsequent changes to the method over the lifecycle of the product or analyte. The ATP can be structured so that it is independent of the t52pe of analytical technique, and just as with traditional validation, a method must be shown to meet the ATP criteria before it can be used. 

These examples illustrate why total method variability (combined accuracy and precision) and risk should be considered when establishing method performance criteria. An example ATP statement follows that describes both risk influencing factors (accuracy and precision) and a maximum risk level for measurements that fall outside this criteria. 

In many cases, the methods used to solve identification problems are based on an iterative minimization of some performance criterion measuring the dissimilarity between the experimental and the synthetic data (generated by the current estimate of the direct model). In our case, direct quantitative comparison of two Bscan images at the pixels level is a very difficult task and involves the solution of a very difficult optimization problem, which can be also ill-behaved. Moreover, it would lead to a tremendous amount of computational burden. Segmented Bscan images may be used as concentrated representations of the useful... 

An alternative procedure is the dynamic programming method of Bellman (1957) which is based on the principle of optimality and the imbedding approach. The principle of optimality yields the Hamilton-Jacobi partial differential equation, whose solution results in an optimal control policy. Euler-Lagrange and Pontrya-gin s equations are applicable to systems with non-linear, time-varying state equations and non-quadratic, time varying performance criteria. The Hamilton-Jacobi equation is usually solved for the important and special case of the linear time-invariant plant with quadratic performance criterion (called the performance index), which takes the form of the matrix Riccati (1724) equation. This produces an optimal control law as a linear function of the state vector components which is always stable, providing the system is controllable. 

The most commonly used family of methods for cluster seeking uses optimization of a squared-error performance criterion in the form... 

These results show clearly the importance of the optimization criterion to clustering. The computationally simple Ward s method performs better than the simulated annealing approach with a simplistic criterion. However, a criterion that more correctly accounts for the hierarchy, by minimizing the sum of squared error at each level, performs much better. As with partitional clustering the application of simulated annealing to hierarchical clustering requires careful selection of the internal clustering criterion. 

Although the method is applicable to the analysis of DEHP in surface water and allows achievement of a sufficiently low LoQ to conduct compliance checking in principle, many laboratories have serious blank problems and are hence, not able to meet the LoQ performance criterion (LoQ < 30 % EQS). 

The VPA is a valuable tool to compare objective trade-offs among suppliers. In some cases, price of the product may dictate the chosen suppliers and in some other cases, the suppliers chosen may be dictated by lead time or quality. The output of the VPA can be used to determine trade-offs among different optimal solutions. For example, it can be seen from Figure 7.14 that preemptive GP solution does 1.6% better than non-preemptive GP on the lead time objective and 0.4% better on MtT but it does 0.3% worse on price and 3.8% worse on VaR objectives. Such comparisons can lead to the choice of an optimal solution that is acceptable to the management. VPA also allows assessing the sensitivity of optimal solutions with respect to each criterion. It can be seen from Figure 7.14 that all the GP methods perform very close with respect to the price objective hence the optimal supplier selection is very sensitive to the price criterion, which is the most important one. For the VaR objective, on the other hand, GP methods provide a scattered performance pattern, which indicates that the optimal solution is not very sensitive to the least important criterion. 

One convenient method is to combine the information available from either isochronous stress-strain curves or stress-time curves obtained on the same materials at different temperatures. For example, suppose the performance criterion for a particular application is that the total strain should not exceed 2% in 1000 hours. Using the 1000 hour isochronous stress-strain curve for each temperature, and erecting an ordinate at the 2% point on the strain axis, the individual working stresses for each temperature can be obtained. Alternatively, by erecting an ordinate at the 1000 hour point on the stress-time curve for 2% strain for each temperature investigated, the individual working stresses can be similarly obtained. From these interpolated results the stress-temperature curve can be drawn. 

The effects of including the triple excitations in coupled cluster linear response theory for evaluating the dynamic polarizabilities have been assessed for a set of closed-shell (Ne, HF, N2, CO) and open-shell (CN, CO, O2) systems, in view of exploring a new accuracy regime for molecular properties. The main conclusions include that i) for systems with little or no static correlation, CC3 is nearly identical to CCSDT, ii) CC3 and PS(T) [pole shifted technique where the CCSD-LR poles are corrected by adding a noniterative correction due to the triples] methods perform better than CCSD but their relative accuracy is not determined yet, iii) differences between CCSD and CC3 results as well as the errors with respect to CCSDT drop when the basis set is increased, and iv) ROHF-based CC-LR approaches should be favored over their UHF counterparts while the dilfer-ences between the ROHF and UHF appear as an appropriate criterion for determining whether higher-order UHF-based CC calculations can be used. 

The first two points are valid for open-loop process nonlinearity measures as well. The third point is new in control-relevant nonlinearity quantification. In a more general context, one has not only to consider the performance criterion but additionally mention the controller design method. Following the idea of Ref 24, optimal control theory with an integral performance criterion will be used here as it represents a benchmark for any achievable performance. Considering nonlinear internal model control with different filter time constants is also possible, see for example Ref 23. 

Figure 3 illustrates the relationship between the robustness function and the feasible domain of stmctural design to satisfy the performance criterion / < / for two-dimensional interval parameters. The robustness function a is derived as the worst case of the objective function, i.e., the upper bound of the objective function / in U X , (x). However, when the number of the combinations of uncertain parameters is extremely large, it may be hard to evaluate the worst case of the objective function reliably. For this reason, an efficient uncertainty analysis method is desired which can evaluate the upper bound of... 

In view of such limitations the trend is to evaluate the performance of the fibres by studying their behaviour under realistic conditions (i.e. in the real cementitious matrix) and relying on strength retention measurements as the performance criterion. Special methods have been developed for this purpose, most notably the strand in cement (SIC) test [15] which is shown schematically in Figure 8.4. Whether tested in solutions or in the cementitious matrix, the ageing effects are frequently accelerated by carrying out the tests at elevated temperatures, in the range of 40-60°C. 

The method of lines formulation for solving Equation (8.52) does not require that T aii be constant, but allows T aiiiz) to be an arbitrary function of axial position. A new value of T aii may be used at each step in the calculations, just as a new may be assigned at each step (subject to the stability criterion). The design engineer is thus free to pick a T au z) that optimizes reactor performance. 

Eq. 16 is an extremely useful criterion for examining the extent of dipolar interaction in a multispin system, and gives the relaxation method a major advantage over the n.O.e. method. The equivalent quantitative test for the n.O.e. experiment requires all but the receptor nucleus to be saturated and this is not readily performed in practice. 

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