During the past decade, piezo-resistive cantilever type silicon microprobes for high-speed roughness measurements inside high-aspect-ratio microstructures, like injection nozzles or critical gas nozzles have been developed. This article summarizes their metrological properties for fast roughness and shape measurements including noise, damping, tip form, tip wear, and probing forces and presents the first results on the measurement of mechanical surface parameters. Due to the small mass of the cantilever microprobes, roughness measurements at very high traverse speeds up to 15 mm/s are possible. At these high scanning speeds, considerable wear of the integrated silicon tips was observed in the past. In this paper, a new tip-testing artefact with rectangular grooves of different width was used to measure this wear and to measure the tip shape, which is needed for morphological filtering of the measured profiles and, thus, for accurate form measurements. To reduce tip wear, the integrated silicon tips were replaced by low-wear spherical diamond tips of a 2 µm radius. Currently, a compact microprobe device with an integrated feed-unit is being developed for high-speed roughness measurements on manufacturing machines. First measurements on sinusoidal artefacts were carried out successfully. Moreover, the first measurements of the elastic modulus of a polymer surface applying the contact resonance measurement principle are presented, which indicates the high potential of these microprobes for simultaneous high-speed roughness and mechanical parameter measurements.

No 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.

The degrees of equivalence are the main outcome in the analysis of key comparison data, and they are used for the approval of the calibration and measurement capabilities of the participating laboratories. Typically, the calibration and measurement capability of a participating laboratory is seen as being approved when the corresponding unilateral degree of equivalence does not differ significantly from zero.The relevance of degrees of equivalence may deteriorate in the presence of an instability of the common measurand. In order to quantitatively assess this deterioration we propose to consider the loss of power of a hypothesis test that can be associated with checking whether a degree of equivalence differs significantly from zero. Based on the resulting loss of power, one can decide whether the size of the instability of the common measurand may be tolerated. We illustrate the concept in terms of results obtained for the recent key comparison CCM. FF-K6.2011.

The comparison CCM.FF-K6.2011 was organized for the purpose of determination of the degree of equivalence of the national standards for low-pressure gas flow measurement over the range (2 to 100) m3/h. A rotary gas meter was used as a transfer standard. The measurements were provided at prescribed reference conditions. Eleven laboratories from four RMOs participated in this key comparison—EURAMET: PTB, Germany; SMU, Slovakia; LNE-LADG, France; SIM: NIST, USA; CENAM, Mexico; APMP: NMIJ AIST Japan; KRISS, Korea; NMI, Australia; NIM, China; CMS, Chinese Taipei; COOMET: GP GP Ivano-Frankivs'kstandart-metrologia, Ukraine and all participants reported independent traceability chains to the SI. All results were used in the determination of the key comparison reference value (KCRV) and the uncertainty of the KCRV. The reference value was determined at each flow separately following procedure A presented by M G Cox. The degree of equivalence with the KCRV was also calculated for each flow and laboratory. All reported results were consistent with the KCRV. This KCRV can now be used in the further regional comparisons.Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).