Contents -- Foreword -- Estimation of Precision and Uncertainty of a Calibration Artefact for CMMs S. D. Antunes and M. A. F. Vicente -- 1. Introduction -- 2. Calibration Artefacts for CMMs -- 3. Modeling Artefact for Global Calibration of CMMs -- 4. Self-calibration of the Artefact -- 5. Simulating Calibration Artefact -- 6. Reference Values for CMM Calibration - Uncertainty Propagation -- 7. Conclusions -- References -- Uncertainty in Semi-Qualitative Testing W. Bremser and W. Hasselbarth -- 1. Introduction -- 2. Principle of the approach -- 3. Example: Explosion limit determination -- 4. Conclusions -- Acknowledgments -- References -- Processing the Coherent Anomalies on Digitalized Surfaces in Wavelet Domain P. Ciarlini and M. L. Lo Cascio -- 1. Introduction -- 2. The three-step method for scratch removal -- 3. Calibration of the tests for feature recognition -- 4. The metrological case-study in nanotechnology -- 5. Conclusions -- Appendix A. -- References -- Least Squares Adjustment in the Presence of Discrepant Data M. G. Cox, A. B. Forbes, J. L. Flowers and P. M. Harris -- 1. Introduction -- 2. Least squares analysis -- 2.1. Uncertainty matrix associated with the least squares estimate -- 2.2. Conformity -- 2.3. Example applications -- 3. Adjustment procedures -- 3.1. One-parameter adjustment -- 3.2. Maximum likelihood approaches to adjustment -- 3.3. Algorithms for diagonal uncertainty matrices -- 3.4. Algorithms for general uncertainty matrices -- 4. Numerical examples -- 4.1. Measurements of G -- 4.2. Simple adjustment model -- 5. Concluding remarks -- References -- Harmonization of Correlated Calibration Curves with an Application to the Analysis of Natural Gases M. G. Cox, S. Kamvissis, M. J. T. Milton and G. Vargha -- 1. Introduction -- 1.1. Measurement process -- 1.2. Experimental considerations.

2. Determination and use of the calibration curves -- 2.1. Straight-line model -- 2.2. Multiplicative model -- 2.3. Use of the calibration curves -- 3. Numerical methods -- 4. Uncertainties -- 4.1. Uncorrected measurements -- 4.2. Corrected measurements -- 4.3. Use of the calibration curves -- 5. Results -- 5.1. Five minor gas components (26 standards) -- 5.2. Seven minor gas components (26 standards) -- 6. Extensions -- 6.1. Higher-order models -- 6.2. Other uncertainty structures -- 7. Conclusions -- References -- Parametrized Approximation Estimators for Mixed Noise Distributions D. P. Jenkinson, J. C. Mason, A. Crampton, M. G. Cox, A. B. Forbes and R. Boudjemaa -- 1. Introduction -- 2. Asymptotic least squares -- 3. Algorithms for asymptotic least squares -- 3.1. Nonlinear least squares optimization -- 3.2. Iteratively weighted least squares -- 3.3. Maximum likelihood approaches -- 4. Example: polynomial approximation -- 5. Example: approximation with radial basis functions -- 6. Example: assessment of aspheric surfaces -- 7. Concluding remarks -- References -- Algorithms for the Calibration of Laser-Plane Sensors on CMMs C. Lartigue, P. Bourdet, L. Mathieu and C. Mehdi-Souzani -- 1. Introduction -- 2. Calibration process -- 2.1. Modelling of the acquisition system -- 2.2. Modelling the CCD Camera -- 2.3. Modelling in relation with the laser plane -- 2.4. Expression of the global transfer function of calibration -- 3. Identification of calibration parameters -- 4. Calibration process using a specific artefact: the facet sphere -- 5. Uncertainty linked to the calibration method -- 6. Conclusion -- References -- Some Differences between the Applied Statistical Approach for Measurement Uncertainty Theory and the Traditional Approach in Metrology and Testing C. Perruchet -- 1. The place of Statistics -- 2. Issues in Metrology.

2.1. Terminology and concepts -- 2.2. Usual assumptions and robustness -- 2.3. p values -- 2.4. Intervals -- 2.5. Use of measurement uncertainty -- 2.6. Metrology and Testing -- 3. Resources: standardization committees -- References -- Metrology Software for the Expression of Measurement Results by Direct Calculation of Probability Distributions G. B. Rossi, F. Crenna and M. Codda -- 1 Introduction -- 2 The probabilistic model -- 2.1 The probabilistic reference model -- 2.2 The mainstream-GUM model -- 2.3 A stochastic observation scheme -- 3 The Package UNCERT -- 3.1 General features of the package -- 3.2 Levels A through C -- 3.3 Level D -- 3.4 Software quality assurance -- 4 Application Examples -- 4.1 Calibration of an end-gauge -- 4.2 Repeated observations -- 4.3 Measuring device with hysteresis -- 5 Conclusions -- 6 Acknowledgments -- References -- Feasibility Study of Using Bootstrap to Compute the Uncertainty Contribution from Few Repeated Measurements B. R. L. Siebert and P. Ciarlini -- 1. Introduction -- 2. Approaches for Type A evaluations -- 2.1. The t-distribution approach -- 2.2. The Bootstrap approach -- 3. Computational tools for a systematic comparison -- 3.1. "Brute force" and total bootstrap -- 3.2. Total bootstrap and the median -- 3.3. The bootstrap approach and discretely represented distributions -- 4. Systematic comparison of t-distribution and bootstrap approach -- 5. Summary and Conclusions -- Acknowledgments -- References -- Recursive and Parallel Algorithms for Approximating Surface Data on a Family of Lines or Curves G. Allasia -- 1. Introduction -- 2. Interpolation and Near-Interpolation Operators -- 3. Basic Procedure -- 4. Special Devices -- 5. Some Tests and a Practical Application -- 6. Conclusion -- Acknowledgments -- References.

Process Measurement Impact on the Verification Uncertainty J. Bachmann, J. M. Linares, S. Aranda and J. M. Sprauel -- 1. Introduction -- 2. Experimental study -- 3. Statistical Confidence Boundary (SCB) -- 3.1. SCB definition -- 3.2. Explanation of the results using the SCB concept -- 4. Conclusion -- Acknowledgments -- References -- On the In-Use Uncertainty of an Instrument W. Bich and F. Pennecchi -- 1. Introduction -- 2. The calibration of a measuring instrument -- 3. Using the calibrated instrument -- 4. The linear case -- 5. Higher-order fits -- 6. Comments -- References -- Automatic Differentiation and Its Application in Metrology R. Boudjemaa, M. G. Cox, A. B. Forbes and P. M. Harris -- 1. Introduction -- 2. Nonlinear problems in data analysis in metrology -- 2.1. Nonlinear least squares approximation -- 2.2. Uncertainty evaluation -- 2.3. Maximum likelihood estimation and numerical optimization -- 3. Finite differences -- 3.1. Description -- 3.2. Advantages -- 3.3. Disadvantages -- 4. The complex step method -- 4.1. Description -- 4.2. Advantages -- 4.3. Disadvantages -- 5. Program differentiation techniques -- 5.1. Advantages -- 5.2. Disadvantages -- 6. Examples -- 6.1. f(x) = x-1 cos x-1 -- 6.2. Uncertainty in interferometric length measurements -- 7. Concluding remarks -- Acknowledgements -- References -- Usage of Non-Central Probability Distributions for Data Analysis in Metrology A. Chunovkina -- 1. Introduction -- 2. Example A. Testing the null hypothesis about equality of the measurand value and a specified standard value -- 2.1. Estimation of the criterion power -- 2.2. The choice of a number of the repeated observations -- 2.3. Testing the systematic differences between measurement results -- 2.4. The way of the handling systematic biases in measurement result.

2.5. Has the original values to be retained or the measurement uncertainty has to be increased in accordance with the test results? -- 3. Example B. Testing the hypothesis about the model between variables -- 4. Conclusions -- References -- Implementation of a General Least Squares Method in Mass Measurements J. Hald and L. Nielsen -- 1. Introduction -- 2. The principle of subdivision and multiplication -- 3. The real measurement model -- 4. The general least squares solution -- 5. DFM Calibration of Weights -- 6. Validation of DFM Calibration of Weights -- 7. Conclusion -- References -- The GUM Tree Design Pattern for Uncertainty Software B. D. Hall -- 1. Introduction -- 2. Calculation of value and uncertainty in modular systems -- 2.1. The measurement finction -- 2.2. Decomposing the measurement function -- 2.3. Standard uncertainty and components of uncertainty -- 2.4. Decomposition of the uncertainty components -- 3. A design pattern for uncertainty software -- 3.1. The requirements of a module interface -- 3.2. The Context -- 3.3. Applying the pattern -- 4. Discussion and Conclusions -- Acknowledgements -- References -- Statistical Hypotheses Testing for Phase Transition Identification in Cryogenic Thermometry D. Ichim, I. Peroni and F: Sparasci -- 1. Introduction -- 1.1. Assessed problem -- 2. Structural Change Model -- 2.1. Parametric hypotheses testing -- 2.2. Structural change hypotheses testing: the known change point case -- 2.3. Structural change hypotheses testing: the unknown change point case -- 3. Application to phase transition identification in cryogenic thermometry -- 3.1. On-line change detection -- 4. Conclusions -- References -- The Impact of Entropy Optimization Principles on the Probability Assignment to the Measurement Uncertainty G. Iuculano, A. Zanobini and G. Pellegrini -- 1. Introduction.

2. The Entropy Optimization Principles and the Measurement Models.