2. Measurement Process Characterization

2. Measurement Process Characterization - Detailed Table of Contents

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.]
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.]
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.]
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.]
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.]
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.]
References [2.7.]