Working range/linearity

Preparation of standard samples always should be as accurate as possible Therefore gravimetric procedures should be preferred compared to volumetric ones and several dilutions should be avoided since each dilution step adds to the uncertainty. For a basic calibration we need 6 to 10 standard samples. They should be distributed equidistant over the whole working range. Linear regression requires equidistant distribution. Otherwise... 

Linearity Linear range = working range linearity limits... 

According to ISO/IEC 17025, validation is confirmation by the examination and provision of objective evidence that the particular requirements for a specific intended use are fulfilled. Performance parameters can be divided into two groups. The first group refers to the properties of the measurement procedure detection limit and determination limit, working range, linearity, and sensitivity. The second group covers the properties of the results obtained with this particular measurement procedure, that is, traceability and uncertainty (including recovery, robustness, precision, and accuracy).9... 

Sensor linearity may concern primary measurand (concentration of analyte) or refractive index and defines the extent to which the relationship between the measurand and sensor output is linear over the working range. Linearity is usually specified in terms of the maximum deviation from a hn-ear transfer function over the specified dynamic range, hi general, sensors with linear transfer functions are desirable as they require fewer calibration points to produce an accurate sensor calibration. However, response of SPR biosensors is usually a non-linear function of the analyte concentration and therefore calibration needs to be carefully considered. 

The thermosetting materials are said to be initially linear but are cross-linked by heating in air to a temperature of at least 345°C. It is claimed that they have a useful working range up to 315°C. The materials may be used in compression mouldings powders, as the binder resin in glass cloth laminates and as the polymer base in heat-resistant metal coatings. 

A calibration procedure has to be validated with regard to general and specific requirements under which the calibration model has been developed. For this purpose, it is important to test whether the conditions represented in Fig. 6.6 are fulfilled. On the other hand, it is to assure by experimental studies that certain performance features (accuracy, precision, sensitivity, selectivity, specificity, linearity, working range, limits of detection and of quantification, robustness, and ruggedness, see Chap. 7) fulfil the expected requirements. 

QL can be also determined as the lowest concentration of the analyte in which duplicate injections have RSD values less than or equal to 2%. For clinical applications, QL should be at least 10% of the minimum effective concentration [2], and it should always be within the linear working range [3]. 

Method validation is defined in the international standard, ISO/IEC 17025 as, the confirmation by examination and provision of objective evidence that the particular requirements for a specific intended use are fulfilled. This means that a validated method, if used correctly, will produce results that will be suitable for the person making decisions based on them. This requires a detailed understanding of why the results are required and the quality of the result needed, i.e. its uncertainty. This is what determines the values that have to be achieved for the performance parameters. Method validation is a planned set of experiments to determine these values. The method performance parameters that are typically studied during method validation are selectivity, precision, bias, linearity working range, limit of detection, limit of quantitation, calibration and ruggedness. The validation process is illustrated in Figure 4.2. 

A detailed treatment of linearity evaluation is beyond the scope of this present book but a few general points are made below. It is important to establish the homogeneity of the variance ( homoscedasticity ) of the method across the working range. This can be done by carrying out ten replicate measurements at the extreme ends of the range. The variance of each set is calculated and a statistical test (F test) carried out to check if these two variances are statistically significantly different [9]. 

This slide describes the steps we have to follow. We start with choosing the range we want to cover with our analysis. Than we measure some calibration standards in this range. We try to apply a linear regression, but we also eheek for the vahdity of this ehoiee. If we succeed, we calculate the performanee eharacteristics of our method and finally fix the working range. 

There also might be requirements on the uncertainty of the measurement, which might not be fulfilled at the lower end of the preliminary working range. If we want to use a linear calibration strategy we have to ensure that the variances are sufficiently homogeneous and that there is no significant deviation from linearity. 

A linear calibration curve can only be used if linearity overthe working range is ensured Coefficient r is a measure of correlation, not a measire of linearity... 

A dilution factor may be incorporated into this calculation if the sample is first extracted and then diluted in order to bring it into the working range of the instrument. This approach to quantitation does not address the linearity of the method but since the variation in the composition of formulations should be within 10% of the stated amount there is some justification for using it. The precision of the method is readily addressed by carrying out repeat preparations of sample and calibration solutions. 

Graphite furnace atomic absorption spectrophotometry (AAS) has been shown to be a versatile technique for the detection of low levels of tin, reproducibly over a wide linear working range and was the method of analysis used in this study (10,11). 

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