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TMA 4275 LIFETIME ANALYSIS SPRING 2009 |
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04.06 The grades
for the course are found here. 18.05 Here are exercises and solution to today’s exam! 14.05 I think
one of you might have forgotten the course book in my office. You may get it
back tomorrow (Friday). 13.05 Office
hours for Bo L. before the exam: Thursday May 14, Friday May 15 – both
days from 13:30 to 15:30. 13.05 Results
from the second obligatory exercise are now posted on the exercise website,
together with a solution. 12.05 ABOUT THE EXAM: The main language of the exam is English, but all
students will get the Norwegian translation appended to the exam (in bokmål).
A translation in nynorsk will be available if someone asks for it (send an
email to bo@math.ntnu.no no later than
Thursday May 14 at 15:00 to ask for
it). You may use either English or Norwegian in your solution. 06.05 We are missing the Obligatory2 reports
from the students with numbers: 684033, 692621, 669256, 676421, 665901. Please
contact us immediately. 05.05 Siste forelesning er onsdag 06.05 kl
10.15-12 i F2. (Dette er til erstatning for forelesningen som skulle vært 1.
mai). 30.04 The final
curriculum can now be found here.
Basically, the curriculum is defined to be all that is covered in lectures
and exercises. Please notify the lecturer if you have comments or questions
to the curriculum. 21.04
Some clarifications
regarding a couple of sub-problems of the obligatory exercise are now posted
on the exercise website. 17.04
In the lecture time
10.15-12 Friday April 24, Rupali will be in the computer lab Vegas to guide
in second obligatory exercise. 17.04 There is NO LECTURE on Friday April 24. This gives you extra time to
work on the obligatory exercise! For help you may contact Rupali by email
with your question or to make an appointment. 03.04
The second obligatory
exercise has been posted on the exercise website. It is ordinarily due April
30, but you may have your deadline extended to May 5 if you notify Rupali by
email before April 30. 27.03 The second obligatory exercise
will be posted on the website on April 3, and should be submitted May 5. 26.03 Teacher’s lecture notes for 26-27 March can be downloaded here. 26.03 See “Progess” below for tentative program for the next
weeks. 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 |
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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.
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Professor Bo Lindqvist, room 1129, Sentralbygg
II. Tlf. (735)93532 |
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Research assistant Rupali Akerkar,
room 1124, Sentralbygg II. Tlf. (735)92021 |
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Reference group |
Ole Thomas Helgesen (olethoh@stud.ntnu.no) Olakunle Olamilehin (olamileh@stud.ntnu.no) Shahrukh Hussain (shahrukhuaar@yahoo.com) |
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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. |
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FINAL CURRICULUM can be found here. LECTURE PLAN can be found here.
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Thursdays 12.15-14.00 in room F6. |
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Mondays 15.15-16.00 in room F2 or computer lab
Vegas, Sentralbygg 2 (Central building 2). See exercise webpage for
information on place.
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. |
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May 18, 2009. Written. 4 hours (9:00-13:00). The main language of the exam is English, but all
students will get the Norwegian translation appended to the exam (in bokmål).
A translation in nynorsk will be available if someone asks for it (send an
email to bo@math.ntnu.no no later than Thursday May 14 at 15:00
to ask for it). You may use either English or Norwegian in your solution. |
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Earlier exams |
June 2008 (English), Solution (Norwegian) May
2006 (Norwegian), Solution
(English) June 2005 (English) (Norwegian), Solution (English). August 2003 Here
is solution May 2001
Here is solution. Solution exercise 3c. |
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06.05 Went through exam June
2008. Final meeting! 01.05 30.04 Tests for trend in
repairable systems when there are several systems. Some theory for renewal
processes. 24.04 No lecture (guidance in
obligatory exercise in Vegas computer lab). 23.04 Tests for trend in
repairable systems. The 17.04 Finished exam June 2005.. 16.04 Went through exam June 2005, problem 1 and
problem 2a. 03.04 No lecture 02.04 No lecture 27.03 More on parametric estimation in NHPP models. Detailed analysis
of power law NHPP. 26.03 Finish Nonparametric
estimation in repairable systems (Nelson-Aalen estimator). Parametric
estimation in NHPP models: The likelihood function. 20.03 Recurrent events and
repairable systems: Nonparametric estimation. 19.03 Case study in Cox
regression, reliability testing (see
12.03 for downloads). Recurrent events and repairable systems. Nonhomogeneous
Poisson processes (NHPP). 13.03 Accelerated life testing.
12.03 Continue with Cox
regression. Model checking: Cox-Snell residuals, Schoenfeld residuals,
“log minus log” plot. You may download extra slides on the simple
Cox-example, 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(- 30.01 The Nelson- 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. |
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Downloads |
Data files |
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Miscellanea |
Link to course in reliability at |
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Last updated: 2009-04-06 13:49