TMA 4275 LIFETIME ANALYSIS

SPRING 2009

 

Messages

05.03  Meeting times for Bo L next week: Tuesday and Wednesday from 13:00 to 14:00. (11th floor, Sentralbygg II).

05.03  The reserved time at the computer lab Vegas, Sentralbygg 2 (Central building 2) has now been extended by 1 hour and is now Mondays 14.15-17.00.

26.02  Some supplementary literature has been listed under “Course book” below.

25.02  There is a reference group meeting on Thursday 26.02. You may contact members of  the reference group before the meeting for comments about the course.

19.02  The first obligatory exercise will be posted on the exercise website on Tuesday 24 February. Deadline for submission  is March 13. There are no other exercises for the Mondays March 2 and 9. Instead these exercise hours are for guidance in the obligatory exercise.

05.02  There will be no lectures in the week before Easter, i.e. April 2 and 3.

30.01 The computer lab Vegas, Sentralbygg 2 (Central building 2) has been reserved for the course Mondays 14.15-16.00. Some of the exercise meetings will be here instead of F2. See information on exercise webpage.

30.01 There will be no lecture on Friday 6 February, due to Ph.d.-disputation. (No changes for lecture on Thursday 5 February and exercises on Monday 9 February). 

27.01 The ordinary exercises in the course are not obligatory. There are just two obligatory exercises, which will be announced separately later. These two exercises count together 20% of the final grade in the course.

21.01 Here is link to exercise website.

19.01 First exercise meeting is Tuesday 24 January:

Exercise 1 (due 26 Jan): From book: 2.1, 2.2, 2.8, 2.10.

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

19.01.09 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.)

18.12.08 First lecture is Thursday, January 15, 12:15 – 14:00 F2

 

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, or TMA4255 Experimental design 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.
Email: bo@math.ntnu.no

 

Exercise lab teacher

Research assistant Rupali Akerkar, room 1124, Sentralbygg II. Tlf. (735)92021
Office hours: To be announced.
Email:

 

Reference group

Ole Thomas Helgesen (olethoh@stud.ntnu.no)

Olakunle Olamilehin (olamileh@stud.ntnu.no)

Shahrukh Hussain (shahrukhuaar@yahoo.com)

 

Course book

The main source will be the book Rausand & Høyland: System Reliability Theory: Models, Statistical Methods, and Applications, 2nd Edition. Wiley 2004.

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

Supplementary reading (available at Tapir):

Jayant V. Deshpande & Sudha G. Purohit: Life time data: statistical models and methods, World Scientific, 2005.

For background in basic statistics: Walpole, Myers, Myers and Ye: Probability and Statistics for Engineers and Scientists, Prentice Hall.

For background in stochastic processes: Sheldon M. Ross: Introduction to probability models, Academic Press.

 

 

Curriculum

PRELIMINARY CURRICULUM can be found here.  

 

Lectures

Thursdays 12.15-14.00 in room F6.
Fridays 10.15-12.00 in room F2.
First lecture is January 15.

 

Exercises

Mondays 15.15-16.00 in room F2 or computer lab Vegas, Sentralbygg 2 (Central building 2). See exercise webpage for information on place.


First time: January 26.

Link to exercise website.

Some exercises (including the obligatory ones) require use of the statistics computer package MINITAB, see http://www.ntnu.no/adm/it/brukerstotte/programvare/minitab.

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 several computer labs.

 

Final exam:

May 18, 2009. Written. 4 hours (9:00-13:00).
Permitted aids: B - All printed and handwritten aids permitted, approved simple calculator.

 

Earlier exams

June 2008 (English), Solution (Norwegian)

May 2006 (Norwegian), Solution (English)

June 2005 (English) (Norwegian), Solution (English).

June 2004, Solution (English)

August 2003 Here is solution

May 2003 Here is solution

Mai 2002 Here is solution

May 2001 Here is solution. Solution exercise 3c.
August 2000 Here is solution
May 2000 Here is solution

Progress

12.03  Continue with Cox regression. You may download a case study in medical statistics, copied from a book by Fleming and Harrington ("Counting Processes & Survival Analysis"), and a case study in reliability engineering.

06.03  Cox regression. The partial likelihood. Simple example for hand-calculations. Real data example with comparison of two groups. Testing for significant coefficients. 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 27.02 below.

05.03  Residuals and residual plots for survival regression. Example: Alloy-data.

27.02  Finish threshold parameter models. Exact confidence interval for exponential distribution under Type II censoring. Then move to survival regression analysis using log-location-scale models. Likelihood function. Foils can be downloaded here: Slides pages 101-156. You may also download Copies on survival regression etc. from a book by Ansell and Phillips (A & P), and the MINITAB note Regression with Life Data.

26.02  Statistical inference and probability plotting in log-location-scale models (e.g. lognormal).

20.02  Finish inference in Weibull distributions. Probability plots for model checking.

19.02  Continue parametric inference. Confidence intervals and tests. Download note: The standard confidence interval for positive parameters. Start with inference in Weibull distributions (likelihood).

13.02   Parametric inference in lifetime models. Censoring: Left, interval, right. Construction of likelihood. Examples from exponential distribution. Slides pages 69-100.  Download copies from books: On likelihood construction and On parametric inference in lifetime models.

12.02  TTT-plot with and without censoring (11.3.7). Barlow-Proschan’s test for exponential distribution (11.5.1). The logrank test (not in book). Note handed out in class: The logrank test for comparison of survival functions.

06.02  No lecture

05.02  Continue with Nelson(-Aalen) plot of cumulative hazard (11.3.6). Then start to look at TTT-plot (11.3.7).

30.01  The Nelson-Aalen estimator (11.3.6, to be continued next week). The exponential distribution and the Poisson process (2.10 in the book). Note handed out in class: About the Exponential Distribution, Poisson Process, Total Time on Test and Barlow-Proschan's Test. 

29.01  The Kaplan-Meier estimator (11.3.5 in book, slides from 24.01).

24.01  Finish log-location-scale families. Start chapter 11. Censoring. Nonparametric estimation of reliability/survival function (to be continued). Slides to this and the couple of next lectures is here: Slides pages 41-68.

For a detailed definition and discussion of independent censoring you may read Chapter 1.3 in Kalbfleisch and Prentice ("The Statistical Analysis of Failure Time Data", Wiley 2002). Disregard the ‘x’ occurring there. 

22.01  Gumbel distribution. Log-location-scale families. (Download extra note here).

16.01  MTTF (2.6). Distributions (2.9-2.14): Exponential, Weibull, lognormal.

15.01  First lecture. Introduction to course. Then 2.3-2.5 in book (general concepts for lifetime distributions, failure/hazard rate). Slides to this and the couple of next lectures is here: Slides pages 1-40.

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: 2009-03-06 13:54