
Topics
Overview
Sampling procedures are used in industry, medicine and for election forecasts, among others. In legal metrology sampling plans are applied to verify the quantity of product in prepackages (see OIML R 87), for conformity assessment when placing utility meters on the market (see
EU-Directive 2014/32/EC and
OIML G 20) and subsequent verification of meters at predefined periodic intervals.
Research
Sampling procedures for surveilling measuring instruments
Regular inspections are a key element of metrological quality control. One aim is, that 95 % of the utility meters fulfil conformance standards at all times. To guarantee this with high confidence and without inspecting every meter, PTB working group 8.42 develops procedures for regular sampling inspections.
- PTB working group 8.42 has developed a new statistical method, which combines standard sampling plans with a reliability function. (See figure and
K. Klauenberg and C. Elster 2017)
- In addition to developing this simple and generally applicable method, the mathematical assumptions for more efficient sampling plans were researched and published (
Klauenberg et.al. 2018).
- The complementary methods 1) and 2) can be combined. One option offers high efficiency via small sample sizes and requires evidence that additional quality criteria are fulfilled. The alternative offers high flexibility via few assumptions. Both methods are readily realized by look-up tables (
K. Klauenberg and C. Elster 2018).

The aim of ongoing research is to develop new statistical approaches for a more efficient, more flexible and at the same time reliable surveillance of the quality of utility meters. Specifically, the benefit of additional information (so-called prior knowledge) shall be investigated when repeating reliability inspections and when implementing these in shorter time intervals. The methods of Bayesian experimental and adaptive design which are developed and investigated, shall identify new possibilities for repeated statistical quality control and at the same time provide the basis to suggest alternative sampling procedures, among others for section 35 of the Measures and Verification Ordinance.
Statistical verifications for a qualification procedure
The sampling procedures developed above offer the possibility to apply efficient sampling plans, if the population fulfils additional requirements (see also procedure 2 in K. Klauenberg and C. Elster 2018). To statistically verify these requirements within a so-called qualification procedure, PTB working group 8.42 has selected and adapted statistical hypothesis tests to detect violations of the Normal distribution and of a limiting small failure rate. In addition, we recommended sample sizes for these tests. An introduction to Normality testing was prepared, which exemplifies this application (
see also K. Klauenberg and C. Elster 2019).
Application
Statistical procedure enables enforcement of a change in the Measures and Verification Ordinance
Subsequent verification of utility meters is legally regulated in section 35 of the Measures and Verification Ordinance in Germany. To enforce the respective new regulation, the verification authorities have published the new administrative regulation “GM-VA SPV”. This regulation is based on the developed statistical procedures described above and on consultations carried out by PTB.
Starting 2019, a new procedure has entered into force which – by means of regular sampling inspections – will guarantee with high confidence that 95 % of the in-service measuring instruments fulfil the legal requirements at any time. Inspections carried out before then did not allow any statements about the quality of utility meters between such assessments. The new statistical procedure thus offers better consumer protection for water, electricity, gas and heat meters.
Statistical verifications enable utility meters to qualify for efficient sampling procedures
To apply efficient sampling plans according to section 35 of the German Measures and Verification Ordinance (see also section 4.3 in the administrative regulation Verfahrensanweisung für Stichprobenverfahren zur Verlängerung der Eichfrist), the associations for electricity-, gas-, water-, and heat meter industry have formulated a qualification procedure (see
qualification procedure). This procedure is based on the statistical verifications developed at PTB, as well as on consultations carried out by PTB for the expert team „Qualifikationsverfahren zur Stichprobenprüfung“ of the Forum Netztechnik/Netzbetrieb (FNN) in the Verband der Elektrotechnik Elektronik Informationstechnik e.V. (VDE). To support the implementation of the qualification procedure, PTB working group 8.42 has also developed a specific Excel application, which realizes multiple tests to detect violations of the Normal distribution (see Software).
Software
Shapiro-Wilk test for Normality
To support the statistical verification of the Normal distribution, PTB working group 8.42 has developed an Excel application, which implements the Shapiro-Wilk test for multiple samples. This application was designed specifically for the qualification procedure in legal metrology and includes the so-called Bonferroni correction.
In programming languages, often the Shapiro-Wilk test has been implemented already. For example the R-command is shapiro.test().
Committee work
PTB working group 8.42 supports the verification authorities in implementing the new section 35 of the Measures and Verification Ordinance.
Subgroup "Statistics for the Measures and Verification Act"
In order to support legal metrology in statistical questions, the PTB Subgroup "Statistics for the Measures and Verification Act" was established. As a first task, the subgroup has initiated the development of sampling plans for utility meters in order to implement section 35 of the new Measures and Verification Ordinance. Representatives of verification authorities, testing laboratories, conformity assessment bodies, utility companies and associations of the utilities gas, water, heat and electricity met with PTB experts to deliberate on new sampling plans which comply with the increased requirements of section 35, to discuss these sampling plans and to make them public.
Publications
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K. Klauenberg;C. Elster
tm - Technisches Messen,(online),
2019.
[DOI: 10.1515/teme-2019-0148]
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K. Klauenberg;C. Elster
OIML Bulletin, LIX(3),
10--16,
2018.
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K. Klauenberg, R. Kramer, C. Kroner, J. Rose;C. Elster
Quality and Reliability Engineering International,
2018.
[DOI: 10.1002/qre.2256]
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K. Klauenberg;C. Elster
Metrologia, 54(1),
59--68,
2017.
[DOI: 10.1088/1681-7575/54/1/59]
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