Partial Ordering and Metrology Analyzing Analytical Performance

Abstract

Classical measurements of performances are typically based on linear scales. However, in analytical chemistry one scale may be not sufficient to measure items appropriately. However, explorative statistics provide more factors, which all tell their own story about the analytical performance. Partial order methodology offers a possibility to evaluate analytical performance based on data provided, e.g., through method development and thus method optimization. Without presumptions or pretreatment of the data, the performance can be evaluated taking into account all indicators simultaneously and thus elucidating a “distance” from a reference, i.e., a result that is considered as the “best” or “optimal” possibly based on a certified value. In the present study, we elucidate the mutual ranking of the single analytical approaches, i.e., results from different analytical procedures. Initially, a simple approach for evaluating analytical performance is presented followed by more elaborate analyses. The analyses are based on various partial order tools and lead to (1) a partial ordering of the different analytical approaches (2) the “distance” to the reference value and (3) a classification due to the concept of “peculiar points” pin-pointing certain methods that do not fall into the “main-stream”. Additionally, information on the relative importance of the single indicator for the overall performance and a ranking without assuming weights for any single indicator can be obtained. In multi-rule systems incomparabilities appear, i.e., not every analytical result can be compared with another one. Even minor differences in indicator values may lead to incomparabilities. To elucidate these factors a detailed study of incomparabilities based on scanning analyses, tripartite graphs and fuzzy partial orders are presented in order to better understand strengths and weaknesses of the different analytical approaches. Thus, the analyses may lead to detailed recommendations for subsequent improvement. Eventually, the possible use of weight intervals for the single indicators is discussed.