132 Measurement Uncertainty
For Whom Intended Engineers, scientists and managers. This course will be of interest to personnel involved in SPC, Metrology, Bio-medical, Aerospace, Automobile, Electronics industries and those making and understanding experimental test measurements in a wide range of other industries.
Brief Course Description Every measurement is made for a purpose: to make a judgment about something. It can be to judge the accuracy of an instrument or data, to accept or reject a product or to determine the price charged in everyday commerce. In order to have confidence that the measurement, which is actually only the best estimate of the quantity considered, is acceptable, an estimate of the uncertainty of the measurement also needs to be undertaken.
This course is frequently presented as part of course 132/435, a "combo" course that starts with course 435, a one-day review of engineering statistics, which covers all the usual topics in reliability and statistics and explains how the theory is applied in engineering. See outline 435 for details.
Course 132 begins with an introduction to measurement uncertainty and to the terms associated with it. Then the accuracy and limitations of statistics are discussed, with examples of the various types of distributions encountered in statistical tests. A discussion of sources of errors and their classification into random and systematic follow, before presenting the details of using traditional versus expanded uncertainty equations.
Equations for calculating the propagation of errors are presented next, along with a “special case” method that avoids the use of calculus in many cases. The course covers control charts and their applicability to uncertainty before covering a step-by-step process of calculating uncertainty for a typical application.
Methods of reporting uncertainty, along with how to state or interpret statements of uncertainty, confidence intervals and confidence levels and coverage factors, are covered in some detail.
The course concludes with specific examples of applications involving various measured quantities.
Successful completion of this course will enable participants to understand, evaluate and express measurement uncertainty.
Bonus Chapters Chapters 10-1 through 10-6 are shown in the course outline below, but they are not presented in the classroom, and they are not included in the Complete Video Course. However, they are provided in the course materials for self-study by interested students, and may be included in on-site presentations at the client's request.
Diploma Programs A related course, 132/435, Measurement Uncertainty/Engineering Statistics, is required for TTi’s Metrology/Calibration Specialist (MCS) diploma program. Course 132 does not satisfy the MCS requirements but may be used as an optional course for any other TTi specialist diploma program.
Related Courses Course 132/435 includes a one-day version of TTi’s Course 435, Engineering Statistics.
Prerequisites There are no definite prerequisites for this course. However, this course is aimed toward individuals involved in a related technical field. An understanding of basic algebra will be useful.
Text Each student will receive 180 days access to the on-line electronic course workbook. Renewals and printed textbooks are available for an additional fee.
Course Hours, Certificate and CEUs Class hours/days for on-site courses can vary from 14-35 hours over 2-5 days as requested by our clients. Upon successful course completion, each participant receives a certificate of completion and one Continuing Education Unit (CEU) for every ten class hours.
OnDemand OnDemand Internet Complete Course 132 features 17 hours of video as well as more in-depth reading material. Most chapters of course 132 are also available as OnDemand Internet Short Topics. See the outline below for details.
Course Outline
Chapter 1 - Introduction to Uncertainty
- Measured Quantities
- Calculated Quantities
- Measurement Errors
- Definitions
- Absolute and Relative Error
- Uncertainty
- The Importance of Measurement Uncertainty
- Undertainty Examples
- Basic Concepts
Chapter 2 - Definitions
- Application examples of terms encountered in measurement uncertainty
Chapter 3 - Statistical concepts in measurement
- A brief history of statistics
- Accuracy and Limitations of Statistics
- Probability
- Categories of Uncertainty Components
- Error types
- Distributions and Transformation Factors
- t-test
- f-test
Chapter 4 - Elemental Errors
- Type A Random Errors
- Some examples of Random Errors
- Sources of Type B Systematic Errors
- Accuracy
- Errors caused by Standard
- Measurand Errors
- Environmental Condition Errors
- Method Errors/Operator Errors
- Other External Sources
- Gross Errors
- Error classification example
Chapter 5A - Calculating Uncertainty: The Traditional Approach
- Uncertainty: Traditional vs. Expanded Equation
- Confidence Levels
- Maximum Expected Error or Best Estimate?
- Combining Elemental Uncertainties
- Student-t
- Example
Chapter 5B - Calculating Uncertainty: Expanded Equations
- Expanded Uncertainty Equation
- Estimating Uncertainty—Principles
- Combined Uncertainty
- The Application of Resolution
- Derivation of Standard Uncertainty When Considering Full Resolution
Chapter 6 - Propagation of Errors
- General Principles
- Maximum Possible Error
- Example: modulus of cantilever
- The Sensitivities
- Uncertainty in E
- Best Estimate of Uncertainty
- Radiation Heat Transfer Example
- Rod Example
- Warehouse Example
- Class project
- Propagation of Errors—Special Case
- Perturbation
- Sensitivity from Perturbation
Chapter 7 - Control Charts
- Control Chart—Example
- Building a Control Chart
- Planning
- Collecting Data
- Monitoring the Process
- Analysis of Control Charts
- Reviewing a Control Chart
- Using a Control Chart
- Example: Mass Calibration Control Chart
Chapter 8 - Calculating Uncertainty
- Uncertainty Calculation—Expanded Formula
- Standard Uncertainty of Other Factors
- Uncertainty of the Assumed Density of Weights
- Calculating Surveillance Limits
- Uncertainty Difference ud vs. Surveillance Limits
- Combined Uncertainty
- Expanded Uncertainty
- Use of Level of Confidence
Chapter 9 - Reporting Uncertainty
Chapter 10-1 (Optional) - Examples of Estimating Uncertainty: Mass—Electronic Scale
Chapter 10-2 (optional) - Examples of Estimating Uncertainty: Indication of an External Micrometer
Chapter 10-3 (optional) - Examples of Estimating Uncertainty: Pressure
Chapter 10-4 (Optional) - Examples of Estimating Uncertainty: Chemical
Chapter 10-5 (optional) - Examples of Estimating Uncertainty: Electrical
Chapter 10-6 (optional) - Examples of Estimating Uncertainty: Temperature
Appendix A - Index of Equations
Appendix B - Metrology Reference Information
- Organizations
- Applicable Standards and Reccommended Practices
- Magazines and Software Applications
- Uncertainty Reference Sources
Summary, Final Review
Award of Certificates for Successful Completion
Click for a printable course outline (pdf).
Revised 2/19/2019
