A multi-center study has been set up to accurately characterize the optical properties of diffusive liquid phantoms based on Intralipid and India ink at near-infrared (NIR) wavelengths. Nine research laboratories from six countries adopting different measurement techniques, instrumental set-ups, and data analysis methods determined at their best the optical properties and relative uncertainties of diffusive dilutions prepared with common samples of the two compounds. By exploiting a suitable statistical model, comprehensive reference values at three NIR wavelengths for the intrinsic absorption coefficient of India ink and the intrinsic reduced scattering coefficient of Intralipid-20% were determined with an uncertainty of about 2% or better, depending on the wavelength considered, and 1%, respectively. Even if in this study we focused on particular batches of India ink and Intralipid, the reference values determined here represent a solid and useful starting point for preparing diffusive liquid phantoms with accurately defined optical properties. Furthermore, due to the ready availability, low cost, long-term stability and batch-to-batch reproducibility of these compounds, they provide a unique fundamental tool for the calibration and performance assessment of diffuse optical spectroscopy instrumentation intended to be used in laboratory or clinical environment. Finally, the collaborative work presented here demonstrates that the accuracy level attained in this work for optical properties of diffusive phantoms is reliable.
Ensuring measurement trueness, compliance with regulations and conformity with standards are key tasks in metrology which are often considered at the time of an inspection. Current practice does not always verify quality after or between inspections, calibrations, laboratory comparisons, conformity assessments, etc. Statistical models describing behavior over time may ensure reliability, i.e. they may give the probability of functioning, compliance or survival until some future point in time.It may not always be possible or economic to inspect a whole population of measuring devices or other units. Selecting a subset of the population according to statistical sampling plans and inspecting only these, allows conclusions about the quality of the whole population with a certain confidence.Combining these issues of sampling and aging, raises questions such as: How many devices need to be inspected, and at least how many of them must conform, so that one can be sure, that more than p 100 % of the population will comply until the next inspection? This research is to raise awareness and offer a simple answer to such time-and sample-based quality statements in metrology and beyond.Reliability demonstration methods, such as the prevailing Weibull binomial model, quantify the confidence in future reliability on the basis of a sample. We adapt the binomial model to be applicable to sampling without replacement and simplify the Weibull model so that sampling plans may be determined on the basis of existing ISO standards. Provided the model is suitable, no additional information and no software are needed; and yet, the consumer is protected against future failure.We establish new sampling plans for utility meter surveillance, which are required by a recent modification of German law. These sampling plans are given in similar tables to the previous ones, which demonstrates their suitability for everyday use.
When the Guide to the Expression of Uncertainty in Measurement (GUM) and methods from its supplements are not applicable, the Bayesian approach may be a valid and welcome alternative. Evaluating the posterior distribution, estimates or uncertainties involved in Bayesian inferences often requires numerical methods to avoid high-dimensional integrations. Markov chain Monte Carlo (MCMC) sampling is such a method-powerful, flexible and widely applied. Here, a concise introduction is given, illustrated by a simple, typical example from metrology.The Metropolis-Hastings algorithm is the most basic and yet flexible MCMC method. Its underlying concepts are explained and the algorithm is given step by step. The few lines of software code required for its implementation invite interested readers to get started. Diagnostics to evaluate the performance and common algorithmic choices are illustrated to calibrate the Metropolis-Hastings algorithm for efficiency. Routine application of MCMC algorithms may be hindered currently by the difficulty to assess the convergence of MCMC output and thus to assure the validity of results. An example points to the importance of convergence and initiates discussion about advantages as well as areas of research. Available software tools are mentioned throughout.
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.
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