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The row of international standards and guides describe various statistical methods that apply for a management, control and improvement of processes with the purpose of realization of analysis of the technical measurement results. The analysis of international standards and guides on statistical methods estimation of the measurement results recommendations for those applications in laboratories is described. For realization of analysis of standards and guides the cause-and-effect Ishikawa diagrams concerting to application of statistical methods for estimation of the measurement results are constructed.

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Table 1. Factors of cause and effect Ishikawa diagram for application of statistical methods

Secondary factor Tertiary and other factors

1 – terminology 1.1 – statistics probability; 1.2 – metrology; 1.3 – design of experiments; 1.4 –

applied statistics

2 – describe 2.1 – prediction interval; 2.2 – median; 2.3 – difference of 2 median; 2.4 –mean;

2.5 – variance; 2.6 – proportion; 2.7 – tolerance interval; 2.8 – normal distribution

3 – compare 3.1 – variances; 3.2 – means; 3.3 – proportion; 3.4 – power of test

4 – explain 4.1 – design of experiments

5 – accept 5.1 – sampling (5.1.1 – guide); 5.2 – process performance

6 – follow in

time

6.1 – reliability (6.1.1 – maintainability; 6.1.2 – adjustment; 6.1.3 – estimation;

6.1.4 – sampling plan); 6.2 – evolution (6.2.1 – statistical process control, SPC);

6.2.2 – control charts; 6.2.3 – process capability)

7 – measurement

control

7.1 – accuracy; 7.2 – laboratory capability; 7.3 – measurement uncertainty; 7.4 –

reference materials

Table 2. Factors for application of statistical methods and international standards or guides

Tertiary and other factors International standards or guides

1.1 – statistics probability ISO 3534-1, 2

1.2 – metrology ISO 5725-1; ISO 11843-1

1.3 – design of experiments ISO 3534-3

1.4 – applied statistics ISO 3534-2

2.1 – prediction interval ISO 16269-8

2.2 – median ISO 16269-7

2.3 – difference of 2 median ISO 2854

2.4 – mean ISO 2854; ISO 2602

2.5 – variance ISO 2854

2.6 – proportion ISO 11453

2.7 – tolerance interval ISO 16269-6, ISO 3207

2.8 – normal distribution ISO 5479

3.1 – variances ISO 2854

3.2 – means ISO 2854; ISO 3301

3.3 – proportion ISO 11453

3.4 – power of test ISO 3301; ISO 3494

4.1 – design of experiments ISO 3534-3

5.1 – sampling

ISO 2859-0…5, 10; ISO 3951-1…5; ISO 8422; ISO 8423;

ISO/TR 8550-1…3; ISO 10725; ISO 11648-1, 2; ISO 13448-

1, 2; ISO 14560; ISO 18414; ISO 21247

5.2 – process performance ISO 21747

6.1.1 – maintainability IEC 60706-2, 3, 5

6.1.2 – adjustment IEC 60605-6; IEC 61649

6.1.3 – estimation IEC 61073-1; IEC 60605-4

6.1.4 – sampling plan IEC 60410; IEC 61123; IEC 61070

6.2.1 – statistical process control ISO 11462-1, 2

6.2.2 – control charts ISO 7870-1, 3, 4; ISO/FDIS 7870-2, 5; ISO 8258; ISO 7873

6.2.3 – process capability ISO 21747; ISO 22514-1…4, 6…8

7.1 – accuracy ISO 5725-1…6; І SO 15725-1, 2; ISO/TR 22971

7.2 – laboratory capability ISO/IEC 17043; ISO 13528

7.3 – measurement uncertainty ISO/IEC Guide 98-1, 3, 4; ISO/IEC Guide 99; ISO TS 17503;

ISO/TR 21748; ISO/TS 21749

7.4 – reference materials ISO 11095; ISO Guide 31, 33, 35, ISO 10576-1, ISO 11843-

1…5; ISO 11843-6

IMEKO IOP Publishing

Journal of Physics: Conference Series 588 (2015) 012017 doi:10.1088/1742-6596/588/1/012017

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The most essential international standards for measurement control in laboratories are standards ISO

5725 with the group name "Accuracy (trueness and precision) of measurement methods and results" (6

parts) [5–10].

The international standard ISO/TR 22971 [11] provides users with practical guidance to the use of ISO

5725-2 [6] and presents simplified step-by-step procedures for the design, implementation, and

statistical analysis of inter-laboratory studies for assessing the variability of a standard measurement

method and on the determination of repeatability and reproducibility of data obtained in inter-

laboratory testing.

The standard ISO/ІЕС 17043 [12] specifies general requirements for the competence of providers of

proficiency testing schemes and for the development and operation of proficiency testing schemes.

These requirements are intended to be general for all types of proficiency testing schemes, and they

can be used as a basis for specific technical requirements for particular fields of application.

International standard ISO 13528 [3] contains the detailed descriptions of statistical methods, that use

for data analysis, which got by means of charts of qualification verification, and gives to

recommendation concerning using by the participants of such charts and authorized persons. It is

appointed as adding to the standard ISO/ІЕС 17043 concerning verification of abilities by means of

interlaboratory comparisons.

The International standard ISO 21748 [13] gives guidance for evaluation of measurement uncertainties

using data obtained from studies conducted in accordance with standard ISO 5725-2 and comparison

of collaborative study results with measurement uncertainty obtained using formal principles of

uncertainty propagation. This standard is applicable in all measurement and test fields where an

uncertainty associated with a result has to be determined. It does not describe the application of

repeatability data in the absence of reproducibility data.

The standard ISO 21748 assumes that recognized, non-negligible systematic effects are corrected,

either by applying a numerical correction as part of the method of measurement, or by investigation

and removal of the cause of the effect. The recommendations in this standard are primarily for

guidance. It is recognized that while the recommendations presented do form a valid approach to the

evaluation of uncertainty for many purposes, it is also possible to adopt other suitable approaches. In

general, references to measurement results, methods and processes in this standard are normally

understood to apply also to testing results, methods and processes.

The International standard ISO 21749 [14] follows the approach taken in the GUM and establishes the

basic structure for stating and combining components of uncertainty. To this basic structure, it adds a

statistical framework using the analysis of variance (ANOVA) for estimating individual components,

particularly those classified as Type A evaluations of uncertainty, i.e. based on the use of statistical

methods. A short description of Type B evaluations of uncertainty (non-statistical) is included for

completeness.

The standard ISO 21749 covers experimental situations where the components of uncertainty can be

estimated from statistical analysis of repeated measurements, instruments, test items or check

standards. It provides methods for obtaining uncertainties from single-, two- and three-level nested

designs only. More complicated experimental situations where, for example, there is interaction

between operator effects and instrument effects or a cross effect, are not covered.

When results from interlaboratory studies can be used, techniques are presented in the companion

standard ISO/TS 21748. The main difference between standards ISO/TS 21748 and ISO 21749 is that

the standard ISO/TS 21748 is concerned with reproducibility data (with the inevitable repeatability

effects), whereas standard ISO 21749 concentrates on repeatability data and the use of the analysis of

variance for its treatment.

Main approaches for uncertainty assessment in environmental and metrological guides are considered

in [15–17]. The use of GUM in development of new and reconsideration of old international

environmental guides is recommended.

IMEKO IOP Publishing

Journal of Physics: Conference Series 588 (2015) 012017 doi:10.1088/1742-6596/588/1/012017



Summary

Plenty of international standards and guides regulate various statistical methods that apply for the

analysis of technical measurements. Practically all these standards are developed by the specialized

technical committee of ISO concerning application of statistical methods.

Having regard to plenty of standards that regulate application of statistical methods expedient and

necessary development of the special recommendations concerning their application in laboratories.

For realization of analysis of these standards the useful to use of cause and effect Ishikawa diagram.

References

[1] Roedler G. J., Martin L., Jones C. 2005. Technical Measurement. A Collaborative Project of

PSM, INCOSE, and Industry. Technical Report . INCOSE-TP-2003-020-01.

[2] ISO/TR 18532:2009. Guidance on the application of statistical methods to quality and to

industrial standardization

[3] ISO 13528:2005. Statistical methods for use in proficiency testing by interlaboratory compari-

sons.

[4] Velychko O., Gordiyenko T. 2010. The implementation of general guides and standards on

regional level in the field of metrology. J of Physics: Conf. Series . 238 . Numb. 1. 012044. 6 p.

[5] ISO 5725-1:1994. Accuracy (trueness and precision) of measurement methods and results. –

Part 1: General principles and definitions.

[6] ISO 5725-2:1994. Accuracy (trueness and precision) of measurement methods and results. –

Part 2: Basic methods for the of repeatability and reproducibility of a standard measurement

method.

[7] ISO 5725-3:1994. Accuracy (trueness and precision) of measurement methods and results. –

Part 3: Intermediate measures of the precision of a standard measurement method.

[8] ISO 5725-4:1994. Accuracy (trueness and precision) of measurement methods and results. –

Part 4: Basic methods for the determination of the trueness of a standard measurement method.

[9] ISO 5725-5:1994. Accuracy (trueness and precision) of measurement methods and results. –

Part 5: Alternative methods for the determination of the precision of a standard measurement

method.

[10] ISO 5725-6:1994. Accuracy (trueness and precision) of measurement methods and results. –

Part 6: Use in practice of accuracy values.

[11] ISO/TR 22971:2005. Accuracy (trueness and precision) of measurement methods and results --

Practical guidance for the use of ISO 5725-2:1994 in designing, implementing and statistically

analysing interlaboratory repeatability and reproducibility results.

[12] ISO/ІЕС 17043:2010. Conformity assessment. – General requirements for proficiency testing.

[13] ISO/TS 21748:2004. Guidance for the use of repeatability, reproducibility and trueness

estimates in measurement uncertainty estimation.

[14] ISO/TS 21749:2005. Measurement uncertainty for metrological applications. – Repeated

measurements and nested experiments.

[15] Velychko O., Gordiyenko T. 2012. The Uncertainty Estimation and Use of Measurement Units

in National Inventories of Anthropogenic Emission of Greenhouse Gas. Greenhouse Gases –

Emission, Measurement and Management. InTech : Croatia. 187–213.

[16] Velychko O., Gordiyenko T. 2009. The Use of Guide to the Expression of Uncertainty in

Measurement for Uncertainty Management in National Greenhouse Gas Inventories.

International J of Greenhouse Gas Control. 3 . Issue 4. 514 –517.

[17] Velychko O., Gordiyenko T. 2007. The use of metrological terms and SI units in environmental

guides and international standards. Measurement . 40 . Issue 2. 202–212.

IMEKO IOP Publishing

Journal of Physics: Conference Series 588 (2015) 012017 doi:10.1088/1742-6596/588/1/012017

... The use of appropriate methods for processing results is important for obtaining reliable data about IC of accredited laboratories. These methods are based on various data processing algorithms in accordance with the requirements of international and regional guidelines and standards [8,9]. However, in addition to the data processing method, other factors that may influence IC should be taken into account. ...

... A thorough analysis of normative documents concerning the processing of data obtained in IC, based on statistical methods, is made in [6][7][8][9]. In particular, a procedure for linking the results of IC of national standards and IC at the national level, using the example of AC/DC voltage standards was proposed in [6]. ...

... [8] analyzed the internatio nal and regional guidelines and standards on which the me thods for processing of IC results are based. In [9], the application of a data processing method that has a minimal number of restrictions and allows for reliable results was justified. It should be noted that the available scientific publications on the topic of the study cover the peculiarities of conducting IC for analytical (physical and chemical) test laboratories or the issues of the specificity of IC for CL for specific types of measurements [6,7]. ...

The data of interlaboratory comparisons of calibration results of signal generators at three calibration points are presented. The choice of methodology for processing the results of interlaboratory comparisons is made taking into account the long-term drift of the comparison sample. The modernization and research of the comparison sample for interlaboratory comparisons of calibration results of signal generators are carried out. The assigned values for the three calibration points and their extended uncertainties are determined. Expressions are obtained for the approximation of the long-term drift of the comparison sample and uncertainty budgets for all assigned values of the comparison sample at the frequencies of 130 MHz, 168 MHz and 223 MHz are compiled. The interlaboratory deviations of the results obtained by laboratories are determined and the consistency of the data obtained using the En and z indicators is estimated. This characterizes the reliability and accuracy of laboratory measurement results, and is also important for confirming technical competence. The presented results of interlaboratory comparisons of the signal generator calibration results show that all participating laboratories meet the requirements by the En indicator. At the same time, two out of ten laboratories require certain substantial corrective measures, as they do not meet the requirements by the z indicator. It is established that the En indicator is not always self-sufficient. It largely characterizes only the reliability of laboratory measurement results. For this purpose, the z indicator is more informative, which provides more information on the accuracy of laboratory measurement, that is, the proximity of measurement results to the true value.

... The CIPM MRA describes in general how the data of KC should be evaluated but it does not provide enough specifics to define an unambiguous analysis. Consequently, many different ways of evaluating KC data have been suggested over the years [3][4][5]. The degree of equivalence (DoE) of a laboratory is obtained as the deviation of its measurement result from the KC reference value (RV), together with the uncertainty associated with this deviation according to the CIPM MRA [6]. ...

... The RV x ref calculated as the mean of participant results with GULFМЕТ.EM-S4 data are given by [3][4][5] x The UMTS as pilot laboratory has provided the traceability to the SI of the national measurement standards. All of the participating NMIs made measurements at the same measurement points for 10 and 100 mH at 1 kHz. ...

Main results participating laboratories which are measuring the same inductance travelling standard for 10 mH and 100 mH at 1 kHz in a framework of GULFMET.EM-S4 Supplementary Comparison of Inductance are presented. The paper describes the evaluation of travelling standard drift effect and Reference Value of a Supplement Comparison. Degrees of Equivalence and Expanded Uncertainties of NMI participants are set. number was calculated for each participating NMI GULFMET.EM-S4 comparison with the aim of determining data consistency. Linked results of COOMET.EM-S14 and GULFMET.EM-S4 supplementary comparisons for inductance were presented.

... For their implementation, various calibration objects are used. To evaluate the ILC data, various methods of their data processing are used [25][26][27][28][29][30], and to estimate the measurement uncertainty, the regional guidance EA-04/02 М [31] is additionally used, in addition to the ILAC documents [8,13]. However, in addition to the method of data evaluation, it is necessary to take into account other influencing factors on the CL result of ILC. ...

National accreditation agencies in different countries have set quite strict requirements for accreditation of testing and calibration laboratories. Interlaboratory comparisons (ILCs) are a form of experimental verification of laboratory activities to determine technical competence in a particular activity. Successful results of conducting ILCs for the laboratory are a confirmation of competence in carrying out certain types of measurements by a specific specialist on specific equipment. To obtain reliable results of ILC accredited laboratories, it is necessary to improve the methods of processing these results. These methods are based on various data processing algorithms. Therefore, it is necessary to choose the most optimal method of processing the obtained data, which would allow to obtain reliable results. In addition, it is necessary to take into account the peculiarities of the calibration laboratories (CLs) when evaluating the results of ILС. Such features are related to the need to provide calibration of measuring instruments for testing laboratories. The evaluation results for ILCs for CLs are presented. The results for all participants of ILCs were evaluated using the E n and z indexes. The obtained results showed that for the such ILCs it is also necessary to evaluate the data using the z index also.

... For KCs degree of equivalence (DoE) of national standard of NMI and its expanded uncertainty are established [7], [8]. DoE and its expanded uncertainty for NMI-participants of KCs are presented both in tabular form and in graphic form in KCDB BIPM [4]. ...

The practical application of traditional evaluation of the results of key comparisons of measurement standards may be difficult for accredited laboratories that wish to use National Metrology Institutes calibration service. Traditional using only the degree of equivalence of a National Metrology Institute standard with corresponding expanded uncertainty without any other characteristics for evaluating of calibration or measurement capabilities. The paper presents a proposed alternative evaluation of the results of key comparisons, which simplifies the analysis of National Metrology Institute calibration services. It envisages the use as a criterion of consistency of the obtained results of key comparisons of the En index to analyze of the degree of equivalence of National Metrology Institute standard and its expanded uncertainty. The practical application of the alternative evaluation for key comparison results for electrical capacitance standards is considered. This contributes to a more streamlined calibration of working standards of accredited laboratories for specific purposes.

... For the processing of KCs data, both special RMO recommendation and scientific work [11], [12], [13], [14] are used to calculate degree of equivalence (DoE) of national standard of NMI and its expanded uncertainty. [15], [16]. ...

... This KC was carried out between 13 NMIs/DIs which are the member of 5 RMOs: COOMET, EURAMET, APMP, GULFMET and AFRIMET. Low-frequency travelling standard (TS) of 50/60 Hz power was KC RVs x ref for COOMET.EM-K5 KC were calculated of traditional method (TM) [12][13][14] as the mean of NMI/DI results and were given by [11]. Linked results of EURAMET.EM-K5.1 and COOMET.EM-K5 KCs were presented [15]. ...

Particular interest is the question of the development and practical application of alternative methods for processing data of international comparisons. The paper is considered the alternative method for processing of international comparison results, which based on preference aggregation method. Processing of COOMET.EM-K5 key comparison data for power by the preferences aggregation method is presented. The results are compared with the traditional approach and the considered alternative method.

... DoE derived from an RMO KC has the same status as that derived from a CC KC. The CIPM MRA describes in general how the data of KC will be evaluated, but many different ways of evaluating KC data have been suggested [4][5][6]. ...

... The analysis applied the Shewhart chart, which is a control chart to determine the characterization of measurement data. This data characterization was based on ISO 8258, where at least ten data readings were required for each measurement [29]. ...

This paper describes the work on the development of disposable micro sample cell for optical spectroscopy. The disposable flow cell is an attractive approach to ensure cleanliness of the sample container and to avoid contamination between samples and residual detergents. The main objective of this work is to develop a disposable flow cell made of Poly-(methyl methacrylate) (PMMA) with polymer optical fiber (POF) connections that is easy to install and has a performance measurement that meets ISO standards. The research involved three stages namely fiber optic preparation, design of the flow cell and analysis of the flow cell design. Chemometrics methods, internal quality control standards, calibration and performance characterization instruments are used for the analysis. The POF fiber performance is described by a linear calibration graph. The Shewhart chart for uncertainty analysis shows no data out of the chart, with mean value meeting the ISO 8258 standard. Comparisons of the calibration to other disposable sample cells show better results in linearity. Chemometrics analysis specified the reading data to be within the warning line in accordance with ISO 8258. Validation of the mathematical model is acceptable as none exceed 95% for the F-test. Average precision and sensitivity are 0.9 and 0.3, respectively. Limit of detection and limit of quantification are 0.07 and 0.25, respectively. Based on the results, the design of a disposable flow cell with POF fiber meets the standards of analysis for sample containers used in a spectrometer.

... As was calculated, the drifts effect was linear and small for all measurement points, so it can be neglected. [21,22]: ...

... For CC KC and RMO KC, the reference value (RV) of KC and degree of equivalence (DoE) of national standards with corresponding uncertainty are established [4,5]. DoE derived from an RMO KC has the same status as that derived from a CC KC. ...

The international agreements are the basis for establishing the global metrological traceability at different measurement levels. The concepts and concept relations around metrological traceability are presented. An important element of providing the metrological traceability is the evaluation of measurement uncertainty. The procedure of linking of key and supplementary comparison results is described. Linking of key and supplementary comparison results of the Regional Metrology Organization for some quantities according to the described procedure was presented. Results for all participants of presented key and supplementary comparisons are satisfactory for chi-square test and E n number. The procedure of linking of key or supplementary comparison and national inter-laboratory comparison results is described. This procedure can be used for practical evaluation of specific inter-laboratory comparison results on a national level in different countries by means of laboratory results of the National Metrology Institute and Designated Institute. This procedure can contribute the mutual recognition of measurement and testing results by different countries. Linking of key comparison and inter-laboratory comparison results for some quantities according to the described procedure was presented. Results for all participants of presented key comparison and inter-laboratory comparison are satisfactory for chi-square test, E n number, z scores and ζ scores.

This paper describes the basis for development of regional documents in field of metrology and state of harmonization of those general international guides and standards on regional levels as for example in European region.

This paper describes the basis for development of regional documents in the field of metrology and a state of harmonization of those general international guides and standards on regional levels as for example in European region.

Understanding greenhouse gas sources, emissions, measurements, and management is essential for capture, utilization, reduction, and storage of greenhouse gas, which plays a crucial role in issues such as global warming and climate change. Taking advantage of the authors' experience in greenhouse gases, this book discusses an overview of recently developed techniques, methods, and strategies: - A comprehensive source investigation of greenhouse gases that are emitted from hydrocarbon reservoirs, vehicle transportation, agricultural landscapes, farms, non-cattle confined buildings, and so on. - Recently developed detection and measurement techniques and methods such as photoacoustic spectroscopy, landfill-based carbon dioxide and methane measurement, and miniaturized mass spectrometer.

Research basis for annual greenhouse gases (GHG) emissions assessment is national and branch statistics data. Quality and confidence of greenhouse gases inventory through assessment methodologies, preparation procedures and processing of data is confirm. Request at National Greenhouse Gases Inventory which contain assessment and analyses uncertainty elements on Intergovernmental Panel on Climate Change-GPG 2000 and IPCC 2006 are determine. Main approaches for uncertainty assessment in environmental and metrological guides are considered. The algorithm of expressing uncertainty and scheme for estimating uncertainty according to GPG 2000 and IPCC 2006 are proposed. The use approaches GUM 1993 for uncertainty assessment for greenhouse gases inventory are proposed.

Peculiarities of the metrological impact on the solution of global environmental problems, in particular, the use of the elements of global metrology system for the decision of the affairs of environmental monitoring objects, the receiving of credible information about the condition of environment are shown in the paper. The use of metrological terms in environmental guides are considered and differences in definitions of the same names of metrological terms, which are applied in international environmental guides and international standards, are shown.Significant attention is paid to common questions relative to the methods of the expression of the uncertainty of measurements and the estimates of the results of the definition of the environmental characteristics of global objects. The bases analysis of uncertainty and its main sources are considered. Peculiarities of the expression of uncertainty and the variants of its estimation in international metrological and environmental guides are shown. Basic positions concerning the uncertainty estimates obtained results, shown in well-known international guides of inventory of greenhouse gases, are considered. The use of international metrological guidance of expression of measurement uncertainty in the development of new and reconsideration of old international environmental guides is recommended.Environmental international guides and international standards used units of measurements, which are not used in the system of SI units, are considered. The maximally possible use of the SI units in international environmental guides is recommended.

Guidance for the use of repeatability, reproducibility and trueness estimates in measurement uncertainty estimation

Iso Ts

Accuracy (trueness and precision) of measurement methods and results-Practical guidance for the use of ISO 5725-2:1994 in designing, implementing and statistically analysing interlaboratory repeatability and reproducibility results