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
Two key elements of metrological quality control are the initial verification of measuring instruments before being placed on the market, and their subsequent verification at periodic intervals. Sampling procedures allow for efficient inspection of random subsets of these measuring instruments.
Hypothesis-based acceptance sampling for the MID
In the EU, the initial conformity assessment of measuring instruments is regulated by the Measuring Instruments Directive (MID). In particular, the modules F and F1 allow product verification on a “statistical basis”. PTB working group 8.42, together with the Bayerisches Landesamt für Maß und Gewicht, has re-interpreted the conditions formulated in the MID for these acceptance sampling procedures and contrasted them with the interpretation advanced in WELMEC guide 8.10. [Klauenberg et al., 2021, Müller and Klauenberg, 2021]. The new interpretation has economic as well as conceptual advantages, and is less ambiguous for finite and small lot sizes. For this new, hypothesis-based interpretation of the MID conditions sampling plans were developed, see [Klauenberg et al., 2021, Müller and Klauenberg, 2021] and made freely available in an interactive 
web-application as R Shiny app.
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 Klauenberg and 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 (Klauenberg and 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 Klauenberg and 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 Klauenberg and 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
Committee work
In order to support legal metrology with respect to statistical questions, the PTB Subgroup "Statistics for the Measures and Verification Act" was established. For example, this subgroup has initiated the development of sampling procedures to implement section 35 of the new Measures and Verification Ordinance.
In addition, PTB working group 8.42 has supported the verification authorities in the AGME committee „Prüfstellen und Stichprobenverfahren“ during the implementation of the new section 35 of the Measures and Verification Ordinance.
Publications
Publication single view
Article
| Title: | A tutorial on Bayesian Normal linear regression |
|---|---|
| Author(s): | K. Klauenberg, G. Wübbeler, B. Mickan, P. Harris;C. Elster |
| Journal: | Metrologia |
| Year: | 2015 |
| Volume: | 52 |
| Issue: | 6 |
| Pages: | 878--892 |
| DOI: | 10.1088/0026-1394/52/6/878 |
| Tags: | 8.42, Regression, Unsicherheit |
| Abstract: | Regression is a common task in metrology and often applied to calibrate instruments, evaluate inter-laboratory comparisons or determine fundamental constants, for example. Yet, a regression model cannot be uniquely formulated as a measurement function, and consequently the Guide to the Expression of Uncertainty in Measurement (GUM) and its supplements are not applicable directly. Bayesian inference, however, is well suited to regression tasks, and has the advantage of accounting for additional a priori information, which typically robustifies analyses. Furthermore, it is anticipated that future revisions of the GUM shall also embrace the Bayesian view.Guidance on Bayesian inference for regression tasks is largely lacking in metrology. For linear regression models with Gaussian measurement errors this tutorial gives explicit guidance. Divided into three steps, the tutorial first illustrates how a priori knowledge, which is available from previous experiments, can be translated into prior distributions from a specific class. These prior distributions have the advantage of yielding analytical, closed form results, thus avoiding the need to apply numerical methods such as Markov Chain Monte Carlo. Secondly, formulas for the posterior results are given, explained and illustrated, and software implementations are provided. In the third step, Bayesian tools are used to assess the assumptions behind the suggested approach.These three steps (prior elicitation, posterior calculation, and robustness to prior uncertainty and model adequacy) are critical to Bayesian inference. The general guidance given here for Normal linear regression tasks is accompanied by a simple, but real-world, metrological example. The calibration of a flow device serves as a running example and illustrates the three steps. It is shown that prior knowledge from previous calibrations of the same sonic nozzle enables robust predictions even for extrapolations. |