| چکیده انگلیسی مقاله |
In recent years, powerful and widely used MCR techniques have been extensively used to study chemical systems in various scientific fields. In most cases, the main goal in all these fields is to extract quantitative information from the systems under consideration, which is basically possible using calibration methods that use second-order and higher-order multivariate calibrations as a more suitable alternative to univariate calibrations. As with any calibration, reporting the analytical figures of merit (AFOMs) is a requirement, but computation and extracting multivariate figures of merit (MFOMs) for this type of calibration is not simple and evident. But in the last decade, MFOMs have been reported completely and one by one for different analytical methods in multivariate calibrations [1 and 2]. When MCR is used to analyze complex systems, area feasible solutions (AFS) are found that result from the rotational ambiguity associated with the bilinear decomposition of the data matrix, in which case a unique solution is not possible even with applied appropriate constraints. Therefore, instead of having specific MFOMs (such as sensitivity, selectivity, LOD, LOQ and etc.), there should be an MFOM for each possible solution within the AFS, resulting in a range of MFOMs. In this report, we present that there is a range of FOMs due to rotational ambiguity, and we also show that the values of FOMs in the AFS range have variations with a fixed movement for each of the MFOMs that can be fully interpreted, and in this way, it can be predicted which MFOMs will have maximum or minimum values in which range of the feasible band, or even what kind of incremental or decremental changes will occur. Due to the rotational ambiguity in the bilinear solutions, the systematic grid search method was used to compute all possible solutions and then to calculate the MFOMs inside the feasible band. We support our proposal on several simulations for two-component systems (one calibrated analyte and one uncalibrated interferent in test sample) and demonstrate its application on two experimental data aimed at the determination of drugs in water and human urine samples and generalized this to the three-component simulated system. In the feasible band for simulated noise-free two-component chromatographic data in the concentration space, the maximum sensitivity and selectivity in the inner boundary of the band have the values 0.3643 and 0.5006 respectively, and their minimum in the outer boundary with the values 0.1747 and 0.1863. |
