ENBIS-11 in Coimbra

4 – 8 September 2011 Abstract submission: 1 January – 25 June 2011

Some Metrological Aspects of Ordinal Quality Data Treatment

5 September 2011, 11:50 – 12:10


Submitted by
Emil Bashkansky
Dr. Emil Bashkansky Tamar Gadrich
ORT Braude College, Department of Industrial Engineering and Management, P.O.Box 78, Karmiel 21982, Israel, ebashkan@braude.ac.il, emilbas@gmail.com
Ordinal scales are widely employed in the area of industrial quality engineering (quality sorting, customer satisfaction, severity of failure and so on). Despite the popular use of ordinal variables for different aims, misunderstanding and misinterpretation of the measurement results still sometimes occur. Ordinal quantities should only be used in comparison relations, and must not be appended by either measurement units or quantity dimensions. Comparisons of greater/less than in addition to equal/unequal can be made between ordinal variables, but the concept of distance between two generic levels of the same ordinal scale is meaningless. Such operations as conventional addition, subtraction, multiplication or division are forbidden, thus, all statistical measures of random ordinal variables must be based on these limitations. This means, however, that many common metrological concepts and definitions such as error, uncertainty, R&R, accuracy, as well as other statistical properties of repeated measurement results, have to be seriously revised. In practice we also often need to compare between two ordinal measuring systems (MSs) in aim to analyze the comparability and equivalence of measurement results (calibration, MS capabilities comparison, reproducibility evaluation). Our lecture will present a way to evaluate classical metrological characteristics, such as error, uncertainty and precision of single and repeated measurements based on the legitimate basic operations for ordinal data. A method for handling actions such as calibration, measuring systems’ capabilities comparison and reproducibility evaluation, as well as a comparison between two measuring systems (MSs) referring to a known/unknown reference standard is also proposed.

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