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



26.05 Here is SOLUTION (in English) and the Exam TMA4275 May 26, 2006 (in Norwegian).

10.05 The grading of Obligatory Exercise 2 is now found on the exercise website.

08.05 We managed to complete the first exam exercise only on May 5. Thus on May 9 we start on the exercise May 2003, 2.

28.04 There is no lecture on Thursday May 4. Instead there will be a lecture on Tuesday May 9 from 15.15-17.00 in room R56. The program for the lectures on Friday May 5 and Tuesday May 9 are found under "Progress" on this website.

26.04 This week is the last week with new topics teached. The announced treatment of Bayesian analysis of reliability data will not be included in this year's curriculum. Here is final curriculum .

04.04 The second obligatory exercise has been put on the exercise homepage today, with deadline for submission on Friday April 28.

24.03Those of you that will not be present at lectures and exercises in the next weeks can download preliminary notes, foils and exercises on the web page The contents are foils from last year (F...pdf), teacher's notes, and a preliminary list of remaining exercises (all taken from earlier exams). (

17.03The second obligatory exercise will be put on the exercise homepage on Tuesday April 4, with deadline for submission on Friday April 28. (Note that Easter vacation is within this period).

08.03The definition of left censoring in the beginning of Chapter 11.2 in the book is not according to the usual definition of the term, and not according to the lectures and a previously disitributed note (see Week 6). Also, the explanation of independent censoring given in Chapter 11.2 seems to be incorrect, although it is very vaguely formulated. For more detailed definitions and discussions of these matters you may read Chapter 1.3 in Kalbfleisch and Prentice ("The Statistical Analysis of Failure Time Data", Wiley 2002). Note that the formulation there includes a covariate 'x' which you can disregard when defining independent censoring for the case of ordinary lifetime data. The 'x' should be there, however, when we start looking at lifetime regression next week.

03.03 Note that there will be guidance of the obligatory exercise on the Fridays March 3 and 10 from 12.15 - 14.00 in Kjel 3 (lecture hours). In addition, there will be guidance in the exercise hour on Tuesday March 7. At these times you may ask questions or discuss your results with one of the teachers.

22.02 The first Obligatory Exercise is on the exercise web page now. You may submit your paper at lectures, classroom exercises, in the mailbox of Anastasia Ushakova at the department office in 7th floor SBII, or electronically to Please put your student number (and not your name) on your paper. Your solution has to be delivered not later than March 14.

15.02 NOTE: Lectures on February 16 and 17 are CANCELLED.

The students are instead encouraged to self study. Relevant exercises are EXERCISE 5 (see exercise website).
You may also have a look at the following exam exercises (see below to find their text):
May 2003, Ex 1
August 2003, Ex 3
June 2004, Ex 3a, 3c

13.02 Two relevant chapters of Minitab User's Guide (written for version 13, but also usable for version 14) can be downloaded here (or under "Downloads" below):
MINITAB Distribution Analysis ,
MINITAB Regression with Life Data .

09.02 Anastasia has reserved a computer lab for the exercises when needed: Datasal Vegas (Gløshaugen, Sentralbygg 2, Nordre lavblokk, 212). The exercise meeting on Tuesday 14.02 (and perhaps 21.02) will be in Datasal Vegas.

23.01The exercise website is found here.

20.01 First exercise meeting is Tuesday 24 January:

Exercise 1 (due 24 Jan): From book: 2.1, 2.2, 2.8, 2.10.

Exercise 2 (due 31 Jan): From book: 2.29, 2.31, 2.34, 2.36, 2.37.

20.01 Under "Progress" on this web-page you will find a short description of the topics for each week. In addition you will there find links to files that can be downloaded (foils, notes etc.)

12.01 This is to confirm that time for lectures on Fridays are changed to 12.15 - 14.00, and time for exercises is changed to Tuesdays 15.15 - 16.00. Complete schedule:

Thursdays 14.15 - 16.00 room F6. First time: January 19
Fridays 12.15 - 14.00 room KJL3

Tuesdays 15.15 - 16.00 room R56. First time: January 24.

10.01 Foils for the Introductory meeting can be downloaded here .

10.01 Introductory meeting will be Wednesday January 11, 13.15-14.00 in room 734, Sentralbygg II. The final time schedule for lectures and exercises will be decided then, but unless there are large problems with the already given schedule, it will be as already announced here :
Lectures: Thursdays 14.15 - 16.00 in F6, Fridays 14.15 - 16.00 in F4. Start: January 19.
Exercises: Mondays 15.15 - 16.00 in F3. Start: January 23.

04.01 Introduksjonsmøte blir holdt ONSDAG 11. JANUAR KL. 13.15 - 14.00 I ROM 734 SENTRALBYGG II.
I tillegg til at det gis en orientering om faget vil tidspunkter for undervisning bli bestemt i dette moetet.
Dersom du skal ta faget, men ikke kan komme paa moetet, send en epost til faglaerer (se epostadresse nedenfor). Du kan her eventuelt angi tidspunkter da det ikke vil passe med forelesning og oveing.

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 Anastasia Ushakova, 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 FINAL CURRICULUM can be found here.  
Lectures Thursdays 14.15-16.00 in room F6.
Fridays 12.15-14.00 in room KJL3.
First ordinary lecture is January 19.
Exercises Tuesdays 15.15-16.00 in room R56.
First time: January 24.

Link to exercise website.

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: May 26, 2006. Written. 4 hours.
Permitted aids: A. All printed or handwritten aids permitted. All calculators permitted.

The examination from June 2005 and a solution can be downloaded here:
Exam TMA4275 4 June 2005 (Norwegian),
Exam TMA4275 June 4, 2005 (English).
Solution, TMA4275 June 4, 2005 (English).

Earlier exams May 2000 Here is solution
August 2000 Here is solution
May 2001 Here is solution. Solution exercise 3c.
Mai 2002 Here is solution
May 2003 Here is solution
August 2003 Here is solution
June 2004 Here is solution (in English)
Some exam exercises w/solution 1991-95
Some exercises w/solution
Progress Week 18 (04-05.05 plus 09.05): No lecture on Thursday May 4. On Friday May 5 and Tuesday May 9 (15.15-17 in room R56) I will go through earlier exams, with the aim of repeting important topics of the course. The exercises will be (in this order, as far as we get:)
- Mai 2003: 1
- Mai 2003: 2
- June 2005: 1
- June 2005: 2
- June 2004: 3
- Mai 2001: 2
- Mai 2002: 2.
These exercises can be downloaded here. If you want the complete exams, these can be downloaded under "Earlier exams" above.

Week 17 (27-28.04): Trend testing with single and multiple processes. TTT-plot for recurrent events data. Foils can be downloaded here: Lectures week 17.

Week 16 (20-21.04): Parametric estimation in NHPP. Observed information in power law NHPP. Confidence intervals. Model checking. Foils can be downloaded here: Lectures week 16.

Week 14 (06-07.04): Recurrent events and repairable systems: Nonparametric estimation. Foils can be downloaded here: Lectures week 14.

Week 13 (30-31.03): Finished Cox-regression: Estimation of reliability function via estimation of baseline functions. Model checking in Cox-regression. Accelerated life testing. Foils can be downloaded here: Lectures week 13.

Week 12 (23-24.03): Cox regression. The partial likelihood. Simple example for hand-calculations. Real data example with comparison of two groups. Testing for significant coefficients. Foils from the lectures can be downloaded here: Lectures week 12.
You may also download a case study, copied from a book by Fleming and Harrington ("Counting Processes & Survival Analysis").
Note that the copies from Ansell & Phillips (A & P) that are referred to in the foils, is the "Copies on survival regression etc." that is downloadable from Week 11 below.

Week 11 (16-17.03): Survival regression using log-location-scale models. In particular lognormal and Weibull distributions. Residuals and residual plots. Foils can be downloaded here: Lectures week 11. You may also download Copies on survival regression etc. from a book by Ansell and Phillips, and the MINITAB note Regression with Life Data.

Week 9-10: Midterm weeks. No lectures.

Week 8 (22-23.02): Parametric inference in two-parameter models: Weibull model, log-location-scale models (e.g. lognormal). Probability plotting. Exact confidence interval for exponential distribution under Type II censoring. Threshold parameter models. Foils can be downloaded here: Lectures week 7-8.

Week 7 (16-17.02): Lectures cancelled.

Week 6 (09.02): Parametric inference in lifetime models. Censoring: Left, interval, right. Construction of likelihood. Examples from exponential distribution. Foils can be downloaded here: Lectures week 6.
Download copies from books: On likelihood construction and On parametric inference in lifetime models.
(10.02): Derivation of confidence intervals for one-parameter models, with emphasis on exponential distribution.

Week 5 (02.02): The TTT-plot and Barlow-Proschan's test for exponentiality. Foils can be downloaded here: Lectures week 5. (03.02): TTT and Barlow-Proshcan for censored data. Logrank test for comparison of survival functions in several groups.

Week 4 (26.01): Types of censoring. The Kaplan-Meier estimator. (27.01): Nelson-plot of cumulative hazard. Note to be downloaded: About the Exponential Distribution, Poisson Process, Total Time on Test and Barlow-Proschan's Test. Foils can be downloaded here: Lectures week 4.

Week 3 (19.01): Basic concepts and distributions (chapter 2). (20.01): Weibull, lognormal, Gumbel distributions. Log-location-scale families. (Download note here). Foils can be downloaded here: Lectures week 3.

Week 2. Introductory meeting (11.01): Times for lecture and exercises were discussed. See messages.
A brief introduction to the course was given. Foils can be downloaded here: Introduction.

Downloads Data files
MINITAB 14 macros
MINITAB Distribution Analysis ,
MINITAB Regression with Life Data .
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:
2006-05-26 13:00