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2.   Measurement Process Characterization - Detailed Table of Contents



  1. Characterization  [2.1.]
    1. What are the issues for characterization?  [2.1.1.]
      1. Purpose  [2.1.1.1.]
      2. Reference base  [2.1.1.2.]
      3. Bias and Accuracy  [2.1.1.3.]
      4. Variability  [2.1.1.4.]
    2. What is a check standard?  [2.1.2.]
      1. Assumptions  [2.1.2.1.]
      2. Data collection  [2.1.2.2.]
      3. Analysis  [2.1.2.3.]

  2. Statistical control of a measurement process  [2.2.]
    1. What are the issues in controlling the measurement process?  [2.2.1.]
    2. How are bias and variability controlled?  [2.2.2.]
      1. Shewhart control chart  [2.2.2.1.]
        1. EWMA control chart  [2.2.2.1.1.]
      2. Data collection  [2.2.2.2.]
      3. Monitoring bias and long-term variability  [2.2.2.3.]
      4. Remedial actions  [2.2.2.4.]
    3. How is short-term variability controlled?  [2.2.3.]
      1. Control chart for standard deviations  [2.2.3.1.]
      2. Data collection  [2.2.3.2.]
      3. Monitoring short-term precision  [2.2.3.3.]
      4. Remedial actions  [2.2.3.4.]

  3. Calibration  [2.3.]
    1. Issues in calibration  [2.3.1.]
      1. Reference base  [2.3.1.1.]
      2. Reference standards  [2.3.1.2.]
    2. What is artifact (single-point) calibration?  [2.3.2.]
    3. What are calibration designs?  [2.3.3.]
      1. Elimination of special types of bias  [2.3.3.1.]
        1. Left-right (constant instrument) bias  [2.3.3.1.1.]
        2. Bias caused by instrument drift  [2.3.3.1.2.]
      2. Solutions to calibration designs  [2.3.3.2.]
        1. General matrix solutions to calibration designs  [2.3.3.2.1.]
      3. Uncertainties of calibrated values  [2.3.3.3.]
        1. Type A evaluations for calibration designs  [2.3.3.3.1.]
        2. Repeatability and level-2 standard deviations  [2.3.3.3.2.]
        3. Combination of repeatability and level-2 standard deviations  [2.3.3.3.3.]
        4. Calculation of standard deviations for 1,1,1,1 design  [2.3.3.3.4.]
        5. Type B uncertainty  [2.3.3.3.5.]
        6. Expanded uncertainties  [2.3.3.3.6.]
    4. Catalog of calibration designs  [2.3.4.]
      1. Mass weights  [2.3.4.1.]
        1. Design for 1,1,1  [2.3.4.1.1.]
        2. Design for 1,1,1,1  [2.3.4.1.2.]
        3. Design for 1,1,1,1,1  [2.3.4.1.3.]
        4. Design for 1,1,1,1,1,1  [2.3.4.1.4.]
        5. Design for 2,1,1,1  [2.3.4.1.5.]
        6. Design for 2,2,1,1,1  [2.3.4.1.6.]
        7. Design for 2,2,2,1,1  [2.3.4.1.7.]
        8. Design for 5,2,2,1,1,1  [2.3.4.1.8.]
        9. Design for 5,2,2,1,1,1,1  [2.3.4.1.9.]
        10. Design for 5,3,2,1,1,1  [2.3.4.1.10.]
        11. Design for 5,3,2,1,1,1,1  [2.3.4.1.11.]
        12. Design for 5,3,2,2,1,1,1  [2.3.4.1.12.]
        13. Design for 5,4,4,3,2,2,1,1  [2.3.4.1.13.]
        14. Design for 5,5,2,2,1,1,1,1  [2.3.4.1.14.]
        15. Design for 5,5,3,2,1,1,1  [2.3.4.1.15.]
        16. Design for 1,1,1,1,1,1,1,1 weights  [2.3.4.1.16.]
        17. Design for 3,2,1,1,1 weights  [2.3.4.1.17.]
        18. Design for 10 and 20 pound weights  [2.3.4.1.18.]
      2. Drift-elimination designs for gage blocks  [2.3.4.2.]
        1. Doiron 3-6 Design  [2.3.4.2.1.]
        2. Doiron 3-9 Design  [2.3.4.2.2.]
        3. Doiron 4-8 Design  [2.3.4.2.3.]
        4. Doiron 4-12 Design  [2.3.4.2.4.]
        5. Doiron 5-10 Design  [2.3.4.2.5.]
        6. Doiron 6-12 Design  [2.3.4.2.6.]
        7. Doiron 7-14 Design  [2.3.4.2.7.]
        8. Doiron 8-16 Design  [2.3.4.2.8.]
        9. Doiron 9-18 Design  [2.3.4.2.9.]
        10. Doiron 10-20 Design  [2.3.4.2.10.]
        11. Doiron 11-22 Design  [2.3.4.2.11.]
      3. Designs for electrical quantities  [2.3.4.3.]
        1. Left-right balanced design for 3 standard cells  [2.3.4.3.1.]
        2. Left-right balanced design for 4 standard cells  [2.3.4.3.2.]
        3. Left-right balanced design for 5 standard cells  [2.3.4.3.3.]
        4. Left-right balanced design for 6 standard cells  [2.3.4.3.4.]
        5. Left-right balanced design for 4 references and 4 test items  [2.3.4.3.5.]
        6. Design for 8 references and 8 test items  [2.3.4.3.6.]
        7. Design for 4 reference zeners and 2 test zeners  [2.3.4.3.7.]
        8. Design for 4 reference zeners and 3 test zeners  [2.3.4.3.8.]
        9. Design for 3 references and 1 test resistor  [2.3.4.3.9.]
        10. Design for 4 references and 1 test resistor  [2.3.4.3.10.]
      4. Roundness measurements  [2.3.4.4.]
        1. Single trace roundness design  [2.3.4.4.1.]
        2. Multiple trace roundness designs  [2.3.4.4.2.]
      5. Designs for angle blocks  [2.3.4.5.]
        1. Design for 4 angle blocks  [2.3.4.5.1.]
        2. Design for 5 angle blocks  [2.3.4.5.2.]
        3. Design for 6 angle blocks  [2.3.4.5.3.]
      6. Thermometers in a bath  [2.3.4.6.]
      7. Humidity standards  [2.3.4.7.]
        1. Drift-elimination design for 2 reference weights and 3 cylinders  [2.3.4.7.1.]
    5. Control of artifact calibration  [2.3.5.]
      1. Control of precision  [2.3.5.1.]
        1. Example of control chart for precision  [2.3.5.1.1.]
      2. Control of bias and long-term variability  [2.3.5.2.]
        1. Example of Shewhart control chart for mass calibrations  [2.3.5.2.1.]
        2. Example of EWMA control chart for mass calibrations  [2.3.5.2.2.]
    6. Instrument calibration over a regime  [2.3.6.]
      1. Models for instrument calibration  [2.3.6.1.]
      2. Data collection  [2.3.6.2.]
      3. Assumptions for instrument calibration  [2.3.6.3.]
      4. What can go wrong with the calibration procedure  [2.3.6.4.]
        1. Example of day-to-day changes in calibration  [2.3.6.4.1.]
      5. Data analysis and model validation  [2.3.6.5.]
        1. Data on load cell #32066  [2.3.6.5.1.]
      6. Calibration of future measurements  [2.3.6.6.]
      7. Uncertainties of calibrated values  [2.3.6.7.]
        1. Uncertainty for quadratic calibration using propagation of error  [2.3.6.7.1.]
        2. Uncertainty for linear calibration using check standards  [2.3.6.7.2.]
        3. Comparison of check standard analysis and propagation of error  [2.3.6.7.3.]
    7. Instrument control for linear calibration  [2.3.7.]
      1. Control chart for a linear calibration line  [2.3.7.1.]

  4. Gauge R & R studies  [2.4.]
    1. What are the important issues?  [2.4.1.]
    2. Design considerations  [2.4.2.]
    3. Data collection for time-related sources of variability  [2.4.3.]
      1. Simple design  [2.4.3.1.]
      2. 2-level nested design  [2.4.3.2.]
      3. 3-level nested design  [2.4.3.3.]
    4. Analysis of variability  [2.4.4.]
      1. Analysis of repeatability  [2.4.4.1.]
      2. Analysis of reproducibility  [2.4.4.2.]
      3. Analysis of stability  [2.4.4.3.]
        1. Example of calculations  [2.4.4.4.4.]
    5. Analysis of bias  [2.4.5.]
      1. Resolution  [2.4.5.1.]
      2. Linearity of the gauge  [2.4.5.2.]
      3. Drift  [2.4.5.3.]
      4. Differences among gauges  [2.4.5.4.]
      5. Geometry/configuration differences  [2.4.5.5.]
      6. Remedial actions and strategies  [2.4.5.6.]
    6. Quantifying uncertainties from a gauge study  [2.4.6.]

  5. Uncertainty analysis  [2.5.]
    1. Issues  [2.5.1.]
    2. Approach  [2.5.2.]
      1. Steps  [2.5.2.1.]
    3. Type A evaluations  [2.5.3.]
      1. Type A evaluations of random components  [2.5.3.1.]
        1. Type A evaluations of time-dependent effects  [2.5.3.1.1.]
        2. Measurement configuration within the laboratory  [2.5.3.1.2.]
      2. Material inhomogeneity  [2.5.3.2.]
        1. Data collection and analysis  [2.5.3.2.1.]
      3. Type A evaluations of bias  [2.5.3.3.]
        1. Inconsistent bias  [2.5.3.3.1.]
        2. Consistent bias  [2.5.3.3.2.]
        3. Bias with sparse data  [2.5.3.3.3.]
    4. Type B evaluations  [2.5.4.]
      1. Standard deviations from assumed distributions  [2.5.4.1.]
    5. Propagation of error considerations  [2.5.5.]
      1. Formulas for functions of one variable  [2.5.5.1.]
      2. Formulas for functions of two variables  [2.5.5.2.]
      3. Propagation of error for many variables  [2.5.5.3.]
    6. Uncertainty budgets and sensitivity coefficients  [2.5.6.]
      1. Sensitivity coefficients for measurements on the test item  [2.5.6.1.]
      2. Sensitivity coefficients for measurements on a check standard  [2.5.6.2.]
      3. Sensitivity coefficients for measurements from a 2-level design  [2.5.6.3.]
      4. Sensitivity coefficients for measurements from a 3-level design  [2.5.6.4.]
      5. Example of uncertainty budget  [2.5.6.5.]
    7. Standard and expanded uncertainties  [2.5.7.]
      1. Degrees of freedom  [2.5.7.1.]
    8. Treatment of uncorrected bias  [2.5.8.]
      1. Computation of revised uncertainty  [2.5.8.1.]

  6. Case studies  [2.6.]
    1. Gauge study of resistivity probes  [2.6.1.]
      1. Background and data  [2.6.1.1.]
        1. Database of resistivity measurements  [2.6.1.1.1.]
      2. Analysis and interpretation  [2.6.1.2.]
      3. Repeatability standard deviations  [2.6.1.3.]
      4. Effects of days and long-term stability  [2.6.1.4.]
      5. Differences among 5 probes  [2.6.1.5.]
      6. Run gauge study example using Dataplot™  [2.6.1.6.]
      7. Dataplot™ macros  [2.6.1.7.]
    2. Check standard for resistivity measurements  [2.6.2.]
      1. Background and data  [2.6.2.1.]
        1. Database for resistivity check standard  [2.6.2.1.1.]
      2. Analysis and interpretation  [2.6.2.2.]
        1. Repeatability and level-2 standard deviations  [2.6.2.2.1.]
      3. Control chart for probe precision  [2.6.2.3.]
      4. Control chart for bias and long-term variability  [2.6.2.4.]
      5. Run check standard example yourself  [2.6.2.5.]
      6. Dataplot™ macros  [2.6.2.6.]
    3. Evaluation of type A uncertainty  [2.6.3.]
      1. Background and data  [2.6.3.1.]
        1. Database of resistivity measurements  [2.6.3.1.1.]
        2. Measurements on wiring configurations  [2.6.3.1.2.]
      2. Analysis and interpretation  [2.6.3.2.]
        1. Difference between 2 wiring configurations  [2.6.3.2.1.]
      3. Run the type A uncertainty analysis using Dataplot™  [2.6.3.3.]
      4. Dataplot™ macros  [2.6.3.4.]
    4. Evaluation of type B uncertainty and propagation of error  [2.6.4.]

  7. References  [2.7.]
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