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Training    Measurement Uncertainty Training   Measurement Uncertainty Analysis Course Outline


Measurement Uncertainty Analysis Course Outline

This outline applies to a comprehensive 5-day measurement uncertainty analysis course presented by Integrated Sciences Group.  This course not only includes instruction in the principles of measurement uncertainty analysis, it also emphasizes the practical application of these principles through hands-on training in the use of ISG's UncertaintyAnalyzer software.  A course segment is also devoted to discussion of specific measurement uncertainty analysis problems relevant to the students' workplace. Click class schedule for our current dates.


Course Objectives


This course is intended for engineers, scientists and other technical personnel responsible for designing, testing, calibrating, installing or maintaining measurement equipment and monitoring systems. This course is also beneficial for research and development personnel and quality assurance engineers in all fields of science and technology.  Upon completion of the course, students will know how to: 


  • Define measurement processes - direct, multivariate and system

  • Evaluate equipment specifications to identify sources of measurement error

  • Select the appropriate error distributions

  • Estimate uncertainties using Type A and Type B analysis methods

  • Identify and account for statistical outliers

  • Establish error correlations

  • Determine sensitivity coefficients

  • Combine uncertainties

  • Estimate uncertainty growth

  • Refine bias uncertainty estimates using Bayesian analysis

  • Develop and report uncertainty estimates for direct and multivariate measurements

  • Develop and report uncertainty estimates for measurement systems and system modules

  • Use uncertainty estimates to establish tolerance limits, analyze risks, perform statistical tests and establish calibration intervals for equipment parameters.


Day One - Uncertainty Analysis Concepts


The first day discusses the need for uncertainty estimation, reviews guides and standards for estimating measurement uncertainty, and presents basic concepts central to measurement uncertainty analysis. Measurement errors are defined, error distributions and statistics are discussed, and the relationship between measurement error and uncertainty is clearly established.  Instruction involves class quizzes to re-enforce key concepts and methods.


Why Estimate Uncertainty?
Standards and Guidelines
Technology Management Requirements


Uncertainty Analysis Guidelines
NIST Technical Note 1297


Error and Uncertainty
Measurement Error Definition

Error Classification
Error Description
Parameter Measurement Error
Uncertainty Definition



   Error Distributions
   Key Elements
   Attribute Measurement
   Parameter Measurement
   Error Propagation
   Applicable Distributions


   Quantifying Uncertainty
Distribution Variance
   Error Variance
   Population Variance
   The Variance Addition Rule
   Combining Uncertainties


   Class Quizzes


Day Two - Estimating Uncertainty


The second day covers methods and procedures for estimating and combining measurement uncertainties. Type A and Type B methods of estimating measurement process uncertainties are discussed and a general framework for conducting uncertainty analyses is presented.  Using uncertainty estimates to make decisions, analyze risk and perform statistical tests is also discussed.  Instruction involves class quizzes and hands-on exercises using UncertaintyAnalyzer to illustrate and re-enforce key concepts and methods.


Review of Day 1


Types of Uncertainty Estimates
Type A Estimates
Type B Estimates
Type A,B Estimates


Estimating Process Uncertainties
Bias Uncertainty
Random Uncertainty
Resolution Uncertainty
Stress Response Uncertainty
Data Acquisition Uncertainty
Environmental Factors Uncertainty
Recap of Process Uncertainty Estimation


The General Uncertainty Analysis Process
Error Modeling
Develop the Error Model
Identify the Process Errors
Recap of Error Modeling

   Using Uncertainty Estimates
Developing Tolerance Limits
   Analyzing Risks in Testing and Calibration

   Selecting Measurement Methods
   Statistical Tests
   Bayesian Analysis


   Overview of Program Features
   Main Screen Functions
   Analysis Guide Screen
   Analysis Description Screen
   User Defined Screen
   System Analysis Screen
   Measurement Units and Instrument Databases


   Class Quizzes


Day Three - Estimating Uncertainty Analysis (cont.)


The third day focuses on the all important application of measurement uncertainty analysis principles and concepts. Instruction includes hands-on use of UncertaintyAnalyzer to illustrate and re-enforce key concepts, methods and procedures for analyzing and combining uncertainties for direct measurements.  An overview of uncertainty analysis for multi-parameter (multivariate) measurements is also presented.


Review of Day 2


Direct Measurement Analysis Overview
Defining the Measurement Configuration
Analyzing Measurement Process Uncertainties
Establishing Correlations
Uncertainty Combination
Uncertainty Growth


Class Quizzes

   Direct Measurement Analysis Class Examples

   Multivariate Analysis Overview
The System Equation
   Estimating Measurement  Process Uncertainties
   Establishing Correlations
   Computing Uncertainty
   Developing a Measuring System


Day Four - Estimating Uncertainty


The fourth day of instruction continues with multivariate uncertainty analysis and includes class quizzes using UncertaintyAnalyzer to illustrate and re-enforce key concepts and methods.  The fourth day also includes hands-on class examples that reinforce multivariate analysis procedures.


Multivariate Analysis Overview (cont'd)


Class Quizzes

   Multivariate Analysis Class Examples

Day Five - Applying Uncertainty Estimates


The fifth day of instruction includes an overview of measurement system analysis procedures and hands-on class examples using UncertaintyAnalyzer that illustrate and re-enforce key concepts and methods. Other analysis examples, relevant to the students' workplace, will also be discussed as time allows.   


System Analysis Overview
Defining the System
Characterizing the Modules

Evaluating Module Uncertainties  
Evaluating System Uncertainty

   System Analysis Class Examples


   Other Analysis Examples


Training Materials


Student workbook, UncertaintyAnalyzer software and user manual are provided.



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Integrated Sciences Group
14608 Casitas Canyon Road Bakersfield, CA 93306
Phone 1-661-872-1683 FAX 1-661-872-3669


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Page Updated February 06, 2018