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Determining an estimate of an equivalence relation for moderate and large sized sets

Klukowski L.

Operations Research and Decisions

2017

Vol. 27, No. 2

45--58

This paper presents two approaches to determining estimates of an equivalence relation on the basis of pairwise comparisons with random errors. Obtaining such an estimate requires the solution of a discrete programming problem which minimizes the sum of the differences between the form of the relation and the comparisons. The problem is NP hard and can be solved with the use of exact algorithms for sets of moderate size, i.e. about 50 elements. In the case of larger sets, i.e. at least 200 comparisons for each element, it is necessary to apply heuristic algorithms. The paper presents results (a statistical preprocessing), which enable us to determine the optimal or a near-optimal solution with acceptable computational cost. They include: the development of a statistical procedure producing comparisons with low probabilities of errors and a heuristic algorithm based on such comparisons. The proposed approach guarantees the applicability of such estimators for any size of set.

Walidacja i niepewność metod analitycznych w laboratorium badawczym.

Pietrzak A.

Barwniki, Środki Pomocnicze

2006

nr 1-2

43-58

Jednym z wymagań normy PN-EN ISO/IEC 17025 dotyczącej kompetencji laboratoriów badawczych jest walidacja wykorzystywanych metod badawczych oraz szacowanie niepewności pomiaru. W artykule przedstawiono sposób określania niepewności zgodnie z Eurachem Citac 2000.

One of reguirement of the norm PN-EN ISO/IEC 17025 for the competence of testing laboratories is validation methods of measuring and estimation uncertainty of measurement Measurement method of uncertainty estimation according to Eurachem Citac 2000 have been presented.