Statistical functional approach for interlaboratory studies with thermal data

A new statistical functional data analysis (FDA) approach to perform interlaboratory tests is proposed and successfully applied to thermogravimetry (TG) and differential scanning calorimetry (DSC). This functional approach prevents the typical losses of information associated to the dimension reduction processes. It allows the location and variability of the thermal curves obtained by the application of a particular test procedure. The intra- and inter-laboratory variability and location have been estimated using a FDA approach as well as the traditional reproducibility and repeatability studies. To evaluate the new approach, 105 TG curves and 90 calorimetric curves were obtained from calcium oxalate monohydrate. The obtained curves correspond to seven simulated laboratories, 15 curves per laboratory. Functional mean and variance were estimated. From a functional point of view, these descriptive statistics consider each datum as a curve or function of infinite dimension. Confidence bands were computed using smooth bootstrap resampling. A laboratory consistency study is performed in a functional context. The functional depth approach based on bootstrap resampling is a useful tool to identify outliers among the laboratories. The new FDA approach permits to identify as outliers the thermal curves obtained with old or wrong calibrations. Functional analysis of variance test based on random projections and the false discovery rate procedure (FDR) provides which laboratories obtain significant different thermal curves. This approach can be applied to perform interlaboratory test programs where the response of the test result is functional, as, for example, DSC and TG tests, without having to assume that data follow a Gaussian distribution.