Single-Course English 2.5 ECTS

Measurement uncertainty estimation using statistical methods

Overall Course Objectives

Statement of uncertainty is mandatory by current quality standards, starting from ISO
9001 and, more specifically, ISO 17025, that governs management of testing and
measurement laboratories. A fundamental reference text on this topic has been published
by ISO: “Guide to the expression of Uncertainty in Measurement”, currently referred to as
“The GUM” and embodied into the ENV 13005 European standard. Statistical procedures
dictated by GUM cover a broad range of applications. Besides definition of such a delicate
undertaking as evaluation of measurement uncertainty with a clear set of rules accepted
worldwide, they cater for planning measurement and testing work aimed at specific levels
of uncertainty, in order to avoid failure to reach required accuracy, and costly overdesign.
These methods – covering both specific metrological work, such as e.g. calibration of
sensors and instrument systems, and generic testing work –also deal with applications in
the activities of design and planning of production processes. The objectives of this course
are to describe the main methods to be adopted and to present some applications in the
field of measurement, design and production engineering.

Learning Objectives

  • Describe the relevance of uncertainty in measurement
  • Recognise the main factors affecting the uncertainty of a measurement
  • Describe the international approach to expressing the uncertainty of measurement
  • Apply the uncertainty evaluation technique proposed by GUM
  • Analyse the uncertainty budget connected with a measurement procedure
  • Produce an uncertainty budget for a given engineering application
  • Manage the problems connected with mechanical design in statistical way
  • Manage the problems connected with production engineering in statistical way

Course Content

1 Basic concepts
Introduction. Why it is necessary to evaluate uncertainty: requirements of Quality
Standards and transfer of measurement information
1.1 Measurement uncertainty
Typical contributes to measurement uncertainty: random and systematic effects and
measurement accidents (outliers)
1.2 Metrological characteristics
Relationship between uncertainty contributes and instrument characteristics (bias,
repeatability, resolution) and measurement complex (reproducibility, considering
instrument, operator, ambient conditions and measurand).
2 Stages of uncertainty evaluation
Theoretical basis: theorem of the central limit
2.1 Modelling the process
Use of theoretical or empirical models to identify the measurement procedure: correlation
uncertainty (ISO GPS Standards)
2.2 Evaluation of uncertainty
Type A and Type B uncertainty contributes (ISO GUM)
2.3 Determining expanded uncertainty
Uncertainty propagation and relevant degrees of freedom
2.4 Critical points
Independent variables correlation, non linearity, asymmetry of probability distributions
3 Uncertainty table
Practical method for evaluating uncertainty
4 Typical examples
Applications to case studies on measurement, mechanical design and production process

Recommended prerequisites

Basic knowledge about statistics

Teaching Method

Lectures by visiting lecturers and personal study case



The PhD course is based on very short presentations by the teacher and ample discussions
with students that beforehand have read relevant papers. The course couples lectures and
activities on measurement uncertainty evaluation with practical cases. Students are
invited to present simple case studies involving their activity with measurement,
mechanical design and production engineering for a discussion and further analysis using
the methods described in the course.

Limited number of seats

Minimum: 8, Maximum: 24.

Please be aware that this course has a minimum requirement for the number of participants needed, in order for it to be held. If these requirements are not met, then the course will not be held. Furthermore, there is a limited number of seats available. If there are too many applicants, a pool will be created for the remainder of the qualified applicants, and they will be selected at random. You will be informed 8 days before the start of the course, whether you have been allocated a spot.

See course in the course database.





3 weeks


DTU Lyngby Campus

Course code 41792
Course type PhD
Semester start Week 32
Semester end Week 34
Days Mon-fri 8:00-17:00

10.600,00 DKK

Please note that this course has participants limitation. Read more