Tamar Gadrich

The occupancy problem is generalized to the case where instead of throwing one ball at a time, a fixed size group of indistinguishable balls are distributed sequentially into cells. Bose-Einstein statistics is used for analyzing the distribution of the waiting time until each cell is occupied by at least one ball. Each trial is classified according to its jump size, i.e. the number of newly occupied cells. We propose an approach to decompose the occupancy and filling processes in terms of the jumps sizes using a multi-dimensional representation. A set of recursive equations is built in order to obtain the joint generating probability function of a series of random variables, each of which denotes the number of trials for a given jump size that occurred during the filling process. As a special case, the joint probability function of these random variables is obtained.

Although some measurements can be made on any scale (including a continual scale), cost and speed considerations sometimes tip the scales toward using ordinal measurements. This paper presents 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. The only legitimate measurement operations among ordinal variables are limited to equal or greater than/less than, the usual assessment measures such as average, standard deviation cannot be applied. Consequently, in order to receive reliable results and draw valid conclusions from ordinal measurements it is essential to develop and use only the appropriate methods.

The usage of ordinal scales (sometimes called ‘semi-quantitative’ scales) for performing measurements in the area of applied chemical metrology and quality assurance is widespread. This paper presents a method for handling actions such as calibration, measuring systems’ capabilities comparison and reproducibility evaluation as a comparison between two measuring systems (MSs) referring to a known/unknown reference standard. The strength of the agreement between these MSs is evaluated through two known versions of Cohen’s kappa statistics (the traditional one and the modified one). The effectiveness of these statistics from the metrological point of view is examined, and the preferability of the modified kappa statistics is demonstrated via an example.