CUSUM graph of the process simulated from the Gaussian white noise model with a slight bias. EWMA graph of the process simulated from the Gaussian white noise model with a slight bias.
Test with 20-year period data
We have highlighted, through these simulated and real data sets, the limitation of control charts to deal with the assessment of long-term stability of metrology instruments. In this case, time series analysis can be used as the most appropriate tool to address this objective.
Introduction to time series analysis applied to a long-term measurement model
The Kalman filter
The posterior estimate of the state X^i∣i and the posterior covariance Pi∣i of the posterior distributionp X ijy1:i. Then the residual (innovation)ei before fitting the estimate and the Kalman profit of Kiara are calculated by.
The Rauch-Tung-Striebel smoother
The auto-tuning of the RTS smoother
The variance of the low-frequency dynamic noise is determined by an iterative procedure that minimizes Lð Þτ so that. A well-designed experiment can greatly facilitate reliable evaluations of uncertainty and is an important part of the art of measurement.”.
Application of time series analysis on simulated and real measurement data
The green dots are estimates of the low-frequency fluctuations (red noise) of the measurementx^i with error bars representing the standard deviationsð Þ. The green dots are estimates of the low frequency fluctuations (red noise) of the measurement^xime error bars representing the standard deviationð Þ.
Conclusion
The international reference system for pure beta-particle emitting radionuclides: an evaluation of the measurement uncertainties.
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Introduction
The measurement uncertainty policy is based on the Guide to Uncertainty in Measurement (GUM) [8–11] and retains the common understanding of the term calibration and measurement capabilities (CMCs) from the joint statement issued by the International Bureau. of Weights and Measures (BIPM) and ILAC [12]. This document provides guidance for the evaluation and reporting of measurement uncertainty in testing in accordance with the requirements of the International Standard ISO/IEC 17025 [14]. To perform ILC for CLs, it is necessary to take into account the relevant requirements of the international standards ISO/IEC and ISO/.
In addition, it is necessary to take into account the specific characteristics of the calibration laboratories (CLs) when evaluating the results of ILС. In particular, unsatisfactory ILC results for all participating CLs may be associated with a large time drift of the calibrated measuring instrument. The growing practical need for ILCs for CLs to ensure recognition of the results achieved at both national and international levels underlines the relevance of this research.
The national interlaboratory comparisons for calibration laboratories The main purpose of accredited CLs is to calibrate working standards and mea-
Such ILCs are performed to determine the competence of the CLs in calibrating various measuring instruments and working standards for various measured quantities [16-24]. In all presented ILCs, the assigned value (AV) with its uncertainty was taken as the value with its uncertainty of the RL. This was done because the RL had the best measurement capabilities among all CLs that participated in the comparisons.
CLs participating in the ILCs performed calibration of the measuring instruments (calibration object) supplied to the RL in accordance with their own methods according to the radial scheme [4]. RL determined the characteristics of the calibration object instability before and after its research in the CLs that participated in the ILC. The general algorithm for processing the received primary data from ILCs given in [34] was used.
The traditional data evaluation of interlaboratory comparisons The traditional assessment of ILC data for CLs is carried out in accordance with
RL also published the CMC for some electrical quantities in the BIPM key comparison database [36]. In the event that the laboratory or laboratories received inconsistent comparison results, RL suggested that they take the necessary corrective actions. Figures 1–3 show the traditional graphical interpretation of the results of three ILCs at one of the calibration points (ILC 2–1, Figure 1, ILC 4–2, Figure 2 and ILC 6–1, Figure 3).
The evaluation of primary data from all ILCs is performed by means of the specially developed software "Interlaboratory Comparisons". To prepare reports on ILCs, RL used specified software to calculate the Enand z-indexes and compile a graphical representation of the results. Only two labs (lab 4 and lab 6 for ILC 2–1) have failed two ILCs using the Enindex. Enindex more characterizes the reliability of measurement results from laboratories participating in the ILC, but is not always sufficient to ensure the accuracy of measurement results.
The additional data evaluation of interlaboratory comparisons The consistency evaluation of data using E n and z indicators is important not
The additional data evaluation of inter-laboratory comparisons The consistency evaluation of data using Enandz indicators is not important. Thezindex compares the measurement results of all laboratories and provides better information about the accuracy of measurements in the laboratory. The measurement accuracy is an important characteristic for CL, therefore this index is more suitable for evaluating ILC data for CLs.
Tables 2–8 show the calculated results of the Enandz indices at all calibration points for all ILCs. Enandz indices are equal to zero for RL. An unsatisfactory result is an excess of 1 value for Enindex, and 2 (does not require adaptation or response measures) or 3 (requires adaptation or response measures) for zindex [4, 15].
The summarized results of interlaboratory comparisons
At the same time, 3 results of ILC3 according to toz indices have inconsistencies (only for laboratory 2), 14 results of ILC4 according to toz indices have inconsistencies (for laboratories 2, 3 and 4), and 4 results of the ILC6 according to toz indices have inconsistencies (for laboratories 2, 3 and 4), including 3 of 4 are very large (z>3.0). At the same time, 3 results of the ILC7 according to toz indices have contradictions (also for laboratory 2). The summarized results of estimation of Enand z indices for all ILCs: a is absolute value, b is percentage value.
The results of the data consistency analysis show that all ILCs, considering both indices, have measurement points with unsatisfactory results. This measurement uncertainty can be affected by both the calibration results of the laboratory work. Taking these recommendations into account may improve the results of those laboratories' participation in other rounds of ILCs or new ILCs.
The influence of travelling standards instability
Analysis of the data taking into account Enindex shows that only three ILCs (ILC3, ILC4 and ILC6) have satisfactory results. At the same time, analysis of the data taking into account thezindex (z>2) shows that all ILCs have measurement points with unsatisfactory results. In this case, it can be found that the use of a more unstable travel standard can improve the consistency of the ILC data, which is not acceptable for CL.
An RL analysis of traveling standard instability for all ILC7 calibration points is given in [33]. The contribution of the uncertainty due to the long-term drift of the traveling standard to the AV standard uncertainty for the entire duration of ILC7 is from 5.3 to 8.3% for all calibration points. Such drift of the measuring instrument used as a calibration object is acceptable for ILC.
The improvement of the evaluation of interlaboratory comparison results
The same requirements can be extended for compliance (≤2.0) or inconsistency (>2.0) of the value of thezindex with the established requirements. In this case, the minimum standard measurement uncertainty that can be claimed as calibration capability for CL participating in ILC will be determined by formulas (10) and (11), respectively. If the standard uncertainty Xð AVÞof the AV is too large compared to the standard deviationσ of the ILC, there is a risk that some laboratories will receive action and warning signals due to inaccuracy in the determination of the AV, not due to any reason within laboratories.
This equation can be used when the AV is not calculated using the results reported by CLs participating in ILC.z0 index will be interpreted in the same way aszindex and with the same critical values of 2.0 and 3.0. Comparison of the equations forzandz0 indices shows thatz0 index for ILC will all be smaller than the corresponding zindex with a constant factor of. In this case, z0 index will be almost identical tozindex, and it can be concluded that the uncertainty of the AV is negligible.
Conclusions
To participate in ILC, when declaring its measurement uncertainty, CLs must perform a thorough analysis of the components of this uncertainty. The smallest standard measurement uncertainty that can be claimed as the calibration capability of a CL participating in an ILC can be determined in different ways depending on the value of the obtained Enindex orzindex. Proceedings of the XX IMEKO World Congress "Metrology for Green Growth"; 2012; Busan, Republic of Korea.
Results processing features and estimation of measurement uncertainty of interlaboratory comparison for calibration laboratories. Proceedings of the XXI World Congress of IMEKO "Measurement in Research and Industry"; 2015; Prague, Czech Republic. Some of the achievements of modern optical metrology are presented to the reader in this chapter.
Micro and nanostructures and metrology applications 1 Using of micro- and nanoparticles for metrology
- Biaxial crystals in the tasks of creating multifunctional traps for micro- and nano-objects
- Micro and nanoparticles as field probes
- Evanescent fields for micro-object manipulation
- Measurement of optical parameters for low-absorbing microparticles The next step of our paper is to demonstrate one of the solutions for measure-
- Surface nanostructure and optical measurements
- Optical refractive index measurement
- Biomedical application of 3D laser polarization metrology
Here, the reader can estimate field distributions at the biaxial crystal output near the optical axis O. The spin density of the total output field (background), the spin current map (cyan arrows), and the polarization distribution (gray ellipses) are described in Fig. 1b. A comparative view of the mechanical action of the optical forces associated with the internal energy of the spin and the orbit is shown in Figure 4.
Both the orbital and rotational motions stop when the polarization of the incident beam is linear. Hence rectilinear motion of the plate without its rotation is possible due to the effect of . The ratio of optical power in the longitudinal and transverse directions (Fz=Fy) with interpolation described the resultant force in the z direction (Fz) and the transverse diagonal polarization dependent force induced by the vertical spin momentum in the y direction (Fy), as a function of of the angle of incidenceγ.
The characteristics of this movement essentially depend on the optical constants of the studied micro- and nanoparticles. As a result, a rotation of the linear polarization azimuth in the interference plane is observed, which takes the value α.
Conclusions
18]Angelsky OV, Maksymyak PP, Zenkova CYu, Maksymyak AP, Hanson SG, Ivanskyi DI, Peculiarities of control of erythrocytes moving in an evanescent field. 19]Angelsky OV, Zenkova CYu, Ivanskyi DI, Mechanical action of the transverse torque of the evanescent wave on gold nanoparticles in the media of biological objects. 20]Angelsky OV, Zenkova CY, Maksymyak PP, Maksymyak AP, Ivanskyi DI, Tkachuk VM, Peculiarities of energy circulation in an evanescent field.
22]Angelsky OV, Hanson SG, Maksimyak PP, Maksimyak AP, Zenkova CYu, Polyanskii PV and Ivanskyi DI, Effect of apparent wave on birefringent microplates. 27]Angelsky OV, Bekshaev AYa, Maksimyak PP, Maksimyak AP and Hanson SG, Measurement of small light absorption in microparticles by optically induced rotation. 31]Angelsky OV, Maksymyak PP, Polyansky VK, Measurement of refractive index of light-scattering media (Avtorskoye svidelstvo).
