Introduction to Uncertainty Budgets

1 J&G technology 1. J&G technology Gary C. Meyer, ASQ CCT/CQE. J&G technology 2. Uncertainty Reporting Requirements What is an Uncertainty budget ? Steps for Creating an Uncertainty budget Review of Distributions Understanding the Numbers Examples of Uncertainty Budgets Measurement Uncertainty Software During the presentation some questions will popup on your screen. See how many you can get correct. The correct answer will be revealed in ten seconds. J&G technology 3. J&G technology 4. Section Provides NIST. Guidelines Regarding GUM. State the U (Expanded Uncertainty ). and K (coverage factor). OR uc (Combined Uncertainty ).

2 Give detailed description of how each component of standard Uncertainty was evaluated . J&G technology 5. Description of how K was chosen when K not equal to 2 (Footnotes). State the Confidence factor ( 95%). Identify the type of evaluation as Type A (Statistical Evaluation) or Type B (Non-Statistical Evaluation). J&G technology 6. J&G technology 7. Header Individual Uncertainties: Type A & B. Grahics Section (optional). Summary Block Footnotes J&G technology 8. Header Information J&G technology 9. Individual Uncertainties J&G technology 10. Graphic Section (Optional). J&G technology 11. Summary Section J&G technology 12.

3 Footnotes Provide detailed notes on each individual Uncertainty item entered into the budget . Notes are useful when 1. Revising Budgets at a later date 2. Presenting your Budgets to auditors 3. Documenting the method used for each item 4. Analyzing possible reductions in Uncertainty Add additional page(s) to the budget Describe why you chose to leave out certain items of budget ( an insignificant value). J&G technology 13. A. Type A. B. Type B. C. Combined Uncertainty J&G technology 14. J&G technology 15. Identify possible sources of Uncertainty (Research and brainstorming). Determine the assignable variation of each Assign a distribution type to each item Determine if there is an correlation between items and assign sensitivity coefficients List the divisors for each distribution Calculate the combined Uncertainty , uc.

4 Assign a k factor and calculate expanded Uncertainty , U = k x uc J&G technology 16. Identifying Sources Identifying Sources is the most difficult part of creating an Uncertainty budget . Common sources for many measurements 1. Effects of Temperature 2. Resolution of the Measurement 3. Calibration Standard Uncertainty 4. Repeatability or Reproducibility Information can come from lab tests, calibration certificates, instrument specifications, R&R studies, knowledge about the process, SPC charts, inter- laboratory-comparisons, historical data, etc. J&G technology 17. Assigning Distributions Assign a normal distribution to items with a specified k factor and given CF.

5 If the sample of readings is <30, assign the t . distribution Assign a rectangular distributions to items where only the two end points are known ( Specifications). Assign triangular or U-shaped if your knowledge of the system supports these types J&G technology 18. A. Normal B. Rectangular C. Triangular D. U Shaped J&G technology 19. Correlation One column of the Uncertainty budget is labeled ci . This creates a multiplier called sensitivity. If one line item does not effect any other line item, there is no correlation. The multiplier is 1 . Correlation can be determined by plotting scatter charts of the two variables.

6 This is covered in our two day Basic SPC seminar. J&G technology 20. DIVISORS. Normal 1. Expanded Normal 2. J&G technology 21. A. Greater than 95%. B. Less than 95%. C. Exactly 95%. D. 97%. J&G technology 22. DIVISORS. Rectangular a/ 3. -a 0 +a Triangular a/ 6. -a 0 +a U Shaped a/ 2. a J&G technology 23. A. Square root of 3. B. Square root of 6. C. Square root of 2. D. 2. J&G technology 24. J&G technology 25. Accelerometer Calibration for Vibration Measurement J&G technology 26. Each Frequency Range has a unique budget . Footnotes contain a complete description of the test method showing equipment setup. J&G technology 27.

7 Example one line calculation: ( ) x 1 = J&G technology 28. RSS (root-sum-squares) Calculates Type A Uncertainty . Type A uc = + + + = J&G technology 29. RSS (root-sum-squares) Calculates Type B Uncertainty . Type B uc = + = J&G technology 30. Combining Type A and Type B Evaluations uc = + U = k x uc = = 2 x = J&G technology 31. A. Add the individual uncertainties B. Add the individual variances C. Find RSS value of the individual uncertainties D. Multiply the standard combined Uncertainty by the k factor J&G technology 32. J&G technology 33. Uncertainty Calculator Version is a free measurement Uncertainty calculator contributed by Chris Grachanen of HP/Compaq.

8 (Freeware). Integrated Services Group Uncertainty Sidekick (Free Download). Quametec Uncertainty Toolbox ($695 USD). Integrated Services Group Uncertainty Analyzer ($995 USD). GUM Workbench ($1200-$1500 USD). J&G technology 34. J&G technology 35. J&G technology 36. Uncertainty Calculator Version is a free measurement Uncertainty calculator contributed by Chris Grachanen of HP/Compaq. The program (runs on windows operating systems ) can be downloaded at several internet sites. One download site is located at: J&G technology 37. J&G technology 38. Enter Type A or B. Enters Data to Type A. or B Lines Below Data Entry Line J&G technology 39.

9 Type A Entries Type B Entries J&G technology 40. Calculated Summary Type A & B. Combined uc Expanded Uncertainty U . J&G technology 41. Final report can be generated using: Word Excel Write Setup paths to the programs in the software Export data from to chosen application J&G technology 42. Resistance 10K. PARAMETER Resistance NOMINAL or RANGE 10K. PRIMARY EQUIPMENT Long Scale Voltmeter PERSONNEL Joe Metrologist DATE 3/23/1999. ANCILLARY EQUIPMENT. Constant Current Source Oil Bath TYPE A DESCRIPTION UNCERT UNITS COR SENS DIST DEG DIV STD UNCERT. V: Repeatability N/A 1 Norm 4 1 TYPE B DESCRIPTION UNCERT UNITS COR SENS DIST DEG DIV STD UNCERT.

10 Rs: Cal of Std Resistor N/A 1 2u >100 2 Rd: Uncorrect Drift N/A 1 Rec >100 Rt: Effect Oil Bath Temp. N/A 1 Rec >100 Vs: Voltmeter Across Rs N/A 1 Rec >100 Vx: Voltmeter Across Rx N/A 1 Rec >100 RESULTS. TYPE A UNCERT TYPE A STD UNCERT TYPE A VARIANCE TYPE B UNCERT TYPE B STD UNCERT TYPE B VARIANCE COMBINED UNCERT COMBINED STD UNCERT COMBINED VARIANCE EFFECTIVE DEGREES OF FREEDOM >100. COVERAGE FACTOR (k) 2. EXPANDED Uncertainty J&G technology 43. Example: A high-resolution voltmeter is used to measure the voltage developed across a Std resistor and an unknown resistor of the same nominal value as the Std, when the series connected resistors are fed from a constant current source.