Reliability Theory, 7.5 Credits

Contents

In the course the theory of Markov processes, and reliability theory, are treated, Life length distributions and estimation methods for them, based on both complete and censored data are included. Methods for deciding lifelengths for systems of independent components are studied, both for repairable and non-repairable systems. For non-repairable systems, methods for computing reliability for whole systems and different measures of the importance of the individual components, are introduced. For repairable systems, the theory of Markov processes is used, to compute various life length- and reliability measures.

Element 1 (6 ECTS): Theory and application
Element 2: (1.5 ECTS): Lab assignments using statistical software

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• thoroughly account for industrial applications of different methods in reliability theory

Skills

• analyze non-repairable systems of independent components, with and without redundance
• estimate life length distributions, using complete or censored data
• apply the theory of Markov processes to compute the properties of repairable systems
• decide the asymptotic properties of birth-and-death-processes

Judgement and approach

• evaluate the results of a reliability analysis and present them in written form in a scientific way

Required Knowledge

The course requires 90 ECTS including courses in Mathematical Statistics, minimum 12 ECTS, or courses in Statistics, minimum 75 ECTS and in both cases a course in Basic Calculus, 7,5 ECTC. Proficiency in English equivalent to Swedish upper secondary course English A/5. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.

Form of instruction

Teaching is mainly in the form of lectures and lessons.

Examination modes

Element 1 is assessed by written examination. Element 2 is assessed by written lab reports. On Element 1, one of the following judgements is assigned: Fail (U), Pass (3), Pass with merit (4) or Pass with distinction (5). On Element 2, one of the following judgements is assigned: Fail (U) or Pass (G). For the whole course, one of the following grades is assigned: Fail (U), Pass (3), Pass with merit (4) or Pass with distinction (5). In order to receive a passing grade on the course, all parts must be completed with a passing grade. The course grade is decided by the grade on Element 1, and is assigned only when all mandatory examination has been completed.

A student who has received a passing grade on a test is not allowed to retake the test in order to receive a higher grade. A student who has not received a passing grade after participating in two tests has the right to be assigned another examiner, unless there are certain circumstances prohibiting this (see the Higher Education Ordinance, chapter 6, 22§). A request to be assigned another examiner should be addressed to the head of department for the department of mathematics and mathematical statistics. The possibility of being examined based on the current version of the syllabus is guaranteed for at least two years following the student's first participation in the course.

Credit transfer
All students have the right to have their previous education or equivalent, and  their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications.
 

Other regulations

This course can not be included in a degree together with another course with similar contents. When in doubt, the student should consult the director of study at the department of mathematics and mathematical statistics. The course can also be included in the subject area of computational science and engineering.