Determining the Probability of Achieving a Successful Quantitative Analysis for Gas Chromatography–Mass Spectrometry

A new approach is presented to determine the probability of achieving a successful quantitative analysis for gas chromatography coupled with mass spectrometry (GC–MS). The proposed theory is based upon a probabilistic description of peak overlap in GC–MS separations to determine the probability of obtaining a successful quantitative analysis, which has its lower limit of chromatographic resolution R_s at some minimum chemometric resolution, R_s*; that is to say, successful quantitative analysis can be achieved when R_s ≥ R_s*. The value of R_s* must be experimentally determined and is dependent on the chemometric method to be applied. The approach presented makes use of the assumption that analyte peaks are independent and randomly distributed across the separation space or are at least locally random, namely, that each analyte represents an independent Bernoulli random variable, which is then used to predict the binomial probability of successful quantitative analysis. The theoretical framework is based on the chromatographic-saturation factor and chemometric-enhanced peak capacity. For a given separation, the probability of quantitative success can be improved via two pathways, a chromatographic-efficiency pathway that reduces the saturation of the sample and a chemometric pathway that reduces R_s* and improves the chemometric-enhanced peak capacity. This theory is demonstrated through a simulation-based study to approximate the resolution limit, R_s*, of multivariate curve resolution-alternating least-squares (MCR-ALS). For this study, R_s* was determined to be ∼0.3, and depending on the analytical expectations for the quantitative bias and the obtained mass-spectral match value, a lower value of R_s* ∼ 0.2 may be achievable.