MEK2200 Statistics and Risk Management Course description

The course includes training in statistical methods used for the processing of measurement data, handling sources of error, calculating probability and estimating measurement uncertainty. Furthermore, an introduction will be provided into regression analysis and methods for calibration and quantification, hypothesis testing and variance analysis. Emphasis will be placed on showing the application of statistical theory through examples and statistical problems. The course also includes definitions and discussions of basic concepts in risk management. The course gives the students basic knowledge and an understanding of quality control and quality assurance through, amongst other things, the application of knowledge acquired in statistics and risk management.

Admission requirements.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student is capable of explaining:

• probability, probability calculation and probability distribution
• basic statistical processing of measurement data
• confidence and significance, confidence intervals and hypothesis testing, variance analysis
• errors and uncertainty, error accumulation and uncertainty estimates
• calibration and calibration curves
• what a risk assessment is, how a risk assessment is conducted, common methods used and how risk assessment is used in risk management
• quality control and quality assessment principles

Skills

The student is capable of:

• assessing uncertainty and sources of error in measurement results
• using statistical methods to interpret and quality check measurement results
• performing risk assessments of various problems and interpreting and presenting the results of the analysis as a contribution to decisions concerning risk and quality

General competence

The student:

• has basic insight into quality assessments and requirements
• has knowledge of how accuracy and precision in measurement results are affected by sources of error and uncertainty in instrumentation, procedures and work techniques
• has insight into statistical methods for the processing and interpretation of measurement data
• has a basic understanding of ethical issues relating to risk assessment, the use of risk acceptance criteria and how risk assessments can be used and abused

The teaching will mainly consist of lectures and exercises.

The following coursework is compulsory and must be approved before the student can take the exam:

• Two individual written assignments (1-10 pages each), which correspond to a total of approximately 15 hours of work.
• One project assignment in groups, 1-5 students per group, which corresponds to approximately 10 hours of work per student.

Individual written exam under supervision, 3 hours

The exam result can be appealed.

In the event of a resit or rescheduled exam, oral examination may be used instead of written. If oral exams are used for resit and rescheduled exams, the exam result cannot be appealed.

Knowledge of linear dynamic systems is important in many applications, including electronics, signal processing, communications, biomedical engineering, robotics and control systems. The course deals with analysis of linear dynamic systems in the time domain and the frequency domain. The course also is an introduction to modeling of systems as differential equations and solving them by application of the Laplace transform. The systems are analyzed by their transfer function and frequency response. The frequency response also reveals the filter characteristics of the system and how it affects the frequency content of a signal.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student has knowledge of:

• modelling first and second order physical systems (e.g., mechanical, electrical, thermal, and fluid systems) as ordinary differential equations
• unilateral Laplace transformation and its main properties (including calculations of Laplace transformation of functions such as impulse, step, ramp, exponential, sinusoidal)

• inverse Laplace transform using partial fraction expansion to find the systems time response
• stability analysis of transfer functions
• frequency response analysis of stable systems
• the Fourier transform and its main properties
• concepts of basic filter design (such as low-pass, band-pass, and high-pass) and how a signals changes after filtering (both time domain and frequency domain aspects)

• properties of first order and second order systems (such as time constant, rise-time, overshoot, settling time)

Skills

The student is capable of:

• setting up mathematical models of simple physical systems

• solving ordinary differential equations with the use of the unilateral Laplace transform
• finding the time response of linear time invariant systems (such as impulse response and step response)
• finding the frequency content of a signal by using the Fourier transform
• designing filters and finding their frequency response
• identifying first-order and second-order systems based on their response in time and frequency domain

• using MatLab to solve relevant problems

General competence

The student is capable of:

• setting up a mathematical model of a physical system in form of differential equations and solving them by application of the Laplace transform
• analyze linear systems both in the frequency and time domain

• design filters to limit the frequency content of a signal

The teaching consists of lectures combined with exercises, laboratory work and a small project.

Individual written exam, under supervison 3 hours

The exam result can be appealed.

In the event of a resit or rescheduled exam, an oral examination may be used instead. In case an oral exam is used, the examination result cannot be appealed.