Functional extensions of Mandel's h and k statistics for outlier detection in interlaboratory studies

Functional data analysis (FDA) alternatives, based on the classical Mandel h and k statistics, are proposed to identify the laboratories that supply inconsistent results in interlaboratory studies (ILS). ILS is the procedure performed by a number of laboratories to test the precision of an analytical method, to measure the proficiency of laboratories in implementing an analytical procedure, to certify reference materials, and to evaluate a new experimental standard. The use of outlier tests, such as h and k Mandel statistics proposed by the ASTM E691, is crucial to assess these aims, estimating inter- and intra-laboratory data position and variability from a univariate point of view. Considering that experimental results obtained in analytical sciences are often functional, the use of FDA techniques can prevent the loss of important data information. The FDA approaches of h and k statistics are presented and point-wise obtained to deal with functional experimental data. Both functional statistics are estimated for each laboratory, their functional critical limits are obtained by bootstrap resampling, and new FDA versions of h and k graphics are presented. Real and synthetic thermogravimetric data are utilized to assess the good performance of the proposed FDA h and k statistics and their advantages with respect to the univariate approach.