Norges teknisk-naturvitenskapelige universitet Fakultet for informasjonsteknologi, matematikk og elektroteknikk Institutt for matematiske fag


About the course The course gives an introduction to stochastic modelling and statistical methods for use in lifetime data analysis, with particular view to applications in reliability analysis and medicine.

The lectures are based on knowledge from TMA4240/TMA4245 Statistics or equivalent. It will be an advantage to have taken one of the courses TPK4120 Industrial safety and reliability, TMA4260 Industrial statistics, and TMA4255 Design of experiments and applied statistical methods.

Contents: Basic concepts in lifetime modelling. Censored observations. Nonparametric estimation and graphical plotting for lifetime data (Kaplan-Meier, Nelson-plot). Estimation and testing in parametric lifetime distributions. Analysis of lifetimes with covariates. (Cox-regression, accelerated lifetime testing). Modelling and analysis of recurrent events. Nonhomogeneous Poisson-processes. Nelson-Aalen estimators. Bayesian lifetime analysis.

  • Weekly hours: Spring: 4F+1Ø+7S = 7,5 SP
  • Course type: Lectures and exercises with the use of a computer (MINITAB). Lectures may be given in English. Portfolio assessment is the basis for the grade awarded in the course. This portfolio comprises a written final examination 80% and selected parts of the exercises 20%. The results for the constituent parts are to be given in %-points, while the grade for the whole portfolio (course grade) is given by the letter grading system. Retake of examination may be given as an oral examination.
Lecturer Professor Bo Lindqvist, room 1129, Sentralbygg II. Tlf. (735)93532
Office hours: To be announced.
Exercise lab teacher Research assistant Inge Christoffer Olsen, room 1126, Sentralbygg II. Tlf. (735)91671
Office hours: To be announced.
Course book The main source will be the book Rausand & Høyland: System Reliability Theory: Models, Statistical Methods, and Applications, 2nd Edition. Wiley 2004.

Alternatively you may use the 1st edition: Høyland & Rausand: System Reliability Theory: Models and Statistical Methods, Wiley 1994.

Notes/copies about certain topics will be handed out. Foils from the lectures can be downloaded as pdf-files from this website.

Curriculum THE FINAL CURRICULUM can be found here.  
Lectures Tuesdays 10.15-12.00 in room 546, Sentralbygg II.
Fridays 12.15-14.00 in room 546, Sentralbygg II.
First ordinary lecture is January 18.
Exercises Tuesdays 12.15-14.00. Room will be announced. First time January 25.

Some exercises (including the obligatory ones) require use of the statistics computer package MINITAB, see
Note that NTNU has an unlimited site licence for Windows and Macintosh for installation of MINITAB on NTNUs area and on private machines of students and staff. MINITAB is also available on computer labs Gombe (Realfagbygget R90, 24 machines) and Chobe (Realfagbygget R91, 12 machines).

Final exam: June 4, 2005. Written. 4 hours.
Permitted aids: A. All printed or handwritten aids permitted. All calculators permitted.

The examination and a solution can be downloaded here:
Eksamen TMA4275 4. juni 2005 (norsk),
Exam TMA4275 June 4, 2005 (English).
Solution, TMA4275 June 4, 2005 (English).
Earlier exams Mai 2000 Her er løsningsforslag
August 2000 Her er løsningsforslag
Mai 2001 Her er løsningsforslag. Løsning oppgave 3c.
Mai 2002 (pdf) Mai 2002 (ps) Her er løsningsforslag
Mai 2003 (pdf) Mai 2003 (ps) Her er løsningsforslag
August 2003 (pdf) August 2003 (ps) Her er løsningsforslag
June 2004 (pdf) Here is solution (in English)
Noen eksamensoppgaver m/løsning 1991-95
Diverse oppgaver m/løsning
Progress Lecture week 13 (06.05 and 10.05): Will go through earlier exams, with the aim of repeting important topics of the course. The exercises will be (in this order:)
- Mai 2002: 2
- Mai 2003: 2
- Mai 2002: 1
- Mai 2001: 2
- Mai 1987: 2 (In the beginning of the file "Diverse oppgaver m/løsning")
- Mai 2002: 3
- August 2003: 4

Lecture week 12 (26.04): Observed information in power law NHPP. Confidence intervals. Trend testing. (29.04): Trend testing with several processes. Bayesian analysis of lifetime data (start). (03.05): Completion of Bayesian analysis theory. Foils can be downloaded here: Lecture week 12. Lecture week 12, supplement.

Lecture week 11 (19.04): Recurrent events and repairable systems: Nonparametric estimation. (22.04): Parametric estimation in NHPP. Foils can be downloaded here: Lecture week 11. Lecture week 11, supplement.

Lecture week 10 (12.04): Accelerated life testing. (15.04): Recurrent events. Repairable systems. Foils can be downloaded here: Lecture week 10. Lecture week 10, supplement.

Lecture week 9 (01.04): Cox regression. The partial likelihood and simple example. (05.04): Cox-example with comaprison of two groups. Testing. Estimation of reliability function via estimation of baseline functions. (08.04): Example from a medical study on primnary biliary cirrhosis (PBC). Copy from book is distributed (or can be downloaded here). Foils from the lectures can be downloaded here: Lecture week 9.

Lecture week 8 (15.03): Survival regression using log-location-scale models. In particular lognormal and Weibull distributions. Foils can be downloaded here: Lecture week 8. Copies on survival regression etc. can be downloaded here. (18.03) Continue survival regression. Residuals and residual plots.

Lecture week 7. (25.2): Continue threshold parameter models. Left and right truncation. Exam June 2004, Exercise 3. Additional foils can be downloaded here: Lecture week 7, supplement.
Lecture week 7 (22.02): Obligatory Exercise 1 can now be downloaded above.
Parametric inference in log-location-scale families. Exact confidence interval for exponential distribution and Type II censoring. Threshold parameter models. Foils can be downloaded here: Lecture week 7.

Lecture week 6 (15.02): Parametric inference in two-parameter models, with emphasis on Weibull distribution. Probability plotting. Foils can be downloaded here: Lecture week 6. (18.02): Parametric inference in lognormal distributon. Additional foils can be downloaded here: Lecture week 6, supplement.

Lecture week 5 (08.02): Parametric inference in lifetime models. Censoring: Left, interval, right. Construction of likelihood. Examples from exponential distribution. Foils can be downloaded here: Lecture week 5. Download copies from books: On likelihood construction, On parametric inference in lifetime models. (11.02): Derivation of confidence intervals for one-parameter models, with emphasis on exponential distribution. Additional foils can be downloaded here: Lecture week 5, supplement.

Lecture week 4 (01.02): The TTT-plot and Barlow-Proschan's test for exponentiality. Foils can be downloaded here: Lecture week 4. (04.02): TTT and Barlow-Proshcan for censored data. Logrank test for comaparison of survival functions in several groups. Additional foils can be downloaded here: Lecture week 4, supplement.

Lecture week 3 (25.01): Types of censoring. The Kaplan-Meier estimator. (28.01): Nelson-plot of cumulative hazard. TTT-plot. Note to be downloaded: About the Exponential Distribution, Poisson Process, Total Time on Test and Barlow-Proschan's Test. Foils can be downloaded here: Lecture week 3.

Lecture week 2 (18.01): Basic concepts and distributions (chapter 2). (21.01): Weibull, lognormal, Gumbel distributions. Log-location-scale families. (Download note here). Foils can be downloaded here: Lecture week 2.

Introductory meeting (10.01): Introduction to course, some topics from 2.1-2.5 in course book. Foils can be downloaded here: Introduction.

Downloads Data files
MINITAB 14 macros
Miscellanea Link to course in reliability at Iowa State University.
Link to course in lifetime analysis at University of Tennessee.
Link to Electronic Textbook StatSoft. This is a web-based text in statistics. Note the chapter on "Survival Analysis" which contains much relevant information for the course.
Link til NIST/SEMATECH e-Handbook of Statistical Methods. Chapter 8 (see left menu) on RELIABILITY contains some relevant topics.

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Last updated:
2005-06-15 11:02