The formulation of Type A uncertainty in the GUM does not include the necessary assumptions. The paper reviews the common set of four assumptions and, in particular, the replacing the identity of distributions (i. d.) by a more general assumption of equivalence of observations. This assumption shows several advantages including its more natural relation to the measurement conditions. Possibilities of validating the assumptions, by an analysis of experiment and using the statistical tests, are briefly discussed.
Nested designs are one of experimental designs to evaluate and/or determine precision of measurement results, statistically. Unbalanced designs have interesting statistical problems, one of which is that an unbiased estimator of variance components is not unique. In our study, a new estimator of a variance component for the top stage of two-stages unbalanced nested designs is proposed. The performance of our estimator outperforms conventional estimators from the aspect of estimation accuracy.
In consideration, methods for calculating the temperature values and temperature errors are proposed. These methods are used for development of the evaluation criteria state of temperature transducers. The reliability of methods and efficiency of criteria were evaluated by a computational experiment both for the series of model functions and for the experimental data. The computational results confirm the efficiency of the proposed method and indicate the advantages of our approach.
The exact (statistical) inference frequently require evaluation of the probability density function (PDF), the cumulative distribution function (CDF), and/or the quantile function (QF) of a random variable from its (known) characteristic function (CF), which is defined as a Fourier transform of its probability distribution function. Working with CFs provides an alternative (frequently more simple) route, than working directly with PDFs and/or CDFs. In particular, derivation of the CF of a weighted sum of independent random variable is a very simple and trivial task (given the CFs of the...
Numerical algorithms used in metrology can be validated based on test data and corresponding reference results in order to improve the reliability of measurement results. This paper describes an innovative online based validation service. The concept is named Traceability for Computationally-Intensive Metrology (TraCIM). It allows end users and developers to get their software packages certified at the point of use. The service will be operated by European national metrology institutes (NMIs).
Expansion of logarithm likelihood ratio in the stochastic series is used to find the sequential change-point detection of non-Gaussian sequences. The moment criteria of the minimum of upper limit error probabilities sum is used to find the expansion coefficients. The proposed method is a semi-parametric type of CUSUM (cumulative sum) algorithm which needs of higher-order statistics. The experimental results show that polynomial algorithms are more effective in comparison with similar non-parametric procedures.
The neural network inverse model of a sensor with the filtration of the sequentially recovered signal is considered. This model allows it to effectively correct the dynamic measurements error due to the deep mathematical processing of measurement data. The result of the experimental data processing of the dynamic temperature measurements validates the efficiency of the proposed model and the algorithm of the dynamic measurements error correction.
In 2013, the National Prototype of the Kilogram (NPK) No.2 belonging to Romania, together with stainless steel kilogram standard Ni81, received an updated mass value from BIPM. Therefore, the first task after their receiving from BIPM was to perform comparisons between NPK and reference kilograms stainless steel standards. In the paper are described mass standards, weighing scheme used for comparisons, calculations of mass and associated uncertainties, as the mass change for all weights involved. It is also presented a comparison between Romanian CMC(s) and other countries for this important...
The mathematical justification of the algorithm for numerical restoration of the signal distorted by inertia and resonances in measuring transducer is presented. The structure of this algorithm is described. As an example, the numerical restoration of the test signal is shown. One of the directions for development of this theory is mathematical justification of restoration of stochastic signals, in particular ”white noise”.
Precision evaluation in quantitative measurements is a thoroughly discussed topic and the established methods are in use. Many methods are proposed for qualitative data, but their effectiveness and statistical properties are not so clear. This paper examines their properties by applying some of the major methods and then by comparing the applied results. The comparisons are made to binary data and also to ordinal categorical data. Some of the similarities and the differences among the methods became clear after examining the results.