Multivariate analytical figures of merit as a metric for evaluation of quantitative measurements using comprehensive two-dimensional gas chromatography-mass spectrometry

The present contribution is devoted to develop multivariate analytical figures of merit (AFOMs) as a new metric for evaluation of quantitative measurements using comprehensive two-dimensional gas chromatography-mass spectrometry (GC × GC-MS). In this regard, new definition of sensitivity (SEN) is extended to GC × GC-MS data and then, other multivariate AFOMs including analytical SEN (γ), selectivity (SEL) and limit of detection (LOD) are calculated. Also, two frequently used second- and third-order calibration algorithms of multivariate curve resolution-alternating least squares (MCR-ALS) as representative of multi-set methods and parallel factor analysis (PARAFAC) as representative of multi-way methods are discussed to exploit pure component profiles and to calculate multivariate AFOMs. Different GC × GC-MS data sets with different number of components along with various levels of artifacts are simulated and analyzed. Noise, elution time shifts in both chromatographic dimensions, peak overlap and interferences are considered as the main artifacts in this work. Additionally, a new strategy is developed to estimate the noise level using variance-covariance matrix of residuals which is very important to calculate multivariate AFOMs. Finally, determination of polycyclic aromatic hydrocarbons (PAHs) in aromatic fraction of heavy fuel oil (HFO) analyzed by GC × GC-MS is considered as real case to confirm applicability of the proposed metric in real samples. It should be pointed out that the proposed strategy in this work can be used for other types of comprehensive two-dimensional chromatographic (CTDC) techniques like comprehensive two dimensional liquid chromatography (LC × LC).