| Messages | Here is the solution of the exam
TMA4275 of June 04, 2008 28.04 The results of the second obligatory exercise can be found in the exercise web page. 13.04 Tomorrow we will go through some more exercises. Tomorrow will also be the last lecture. 17.04 The final curriculm is available here. Note that there will be no more exercises after the second obligatory one. 16.04 In the lecture of tomorrow i will go through the following exercises taken from previous exams: May 2002 - ex1 May 2002-ex2 May 2004 -ex 2 04.04 The second obligatory exercise is now available in the exercise web page. The deadline for delivering is Monday 21th April. Please note that you may work in pairs but everyone must submit an individual report, i.e. two sudent cannot deliver two copies of the same report. 12.03 The results of the first obligatory exercise can be found in the exercise web page. 03.03 There will be no more lectures before easter. 14.02 The first obligatory exercise will be posted tomorrow in the exercise web page. The deadline for delivering the exercise is Monday 3th March. 31.01 A preliminary curriculum and lecture plan is provided here. 31.01 The 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 5). 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). 14.01 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.) |
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| 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.
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| Lecturer | Sara Martino, room
1122, Sentralbygg II. Tlf. (735) 50221 Office hours: To be announced. Email: martino@math.ntnu.no |
| Exercise lab teacher | Research assistant Clara-Cecilie Gunter,
room 1126, Sentralbygg II. Tlf. (735)93591 Office hours: To be announced. Email: claracec@math.ntnu.no |
| 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 | A
preliminary curriculum can be found here
later a final curriculm will be
provided. A final curriculum is now also available here |
| Lectures | Mondays
12.15-14.00 in room F3 (Weeks 2-11 and 14-19) Wednesday 10.15-12.00 in room B22 (Week 19). Thursdays 10.15-12.00 in room R4 (Weeks 2-11 and 13-18). |
| Exercises | Tuesdays
17.15-18.00 in room F2. First time: January 22. Some exercises (including the
obligatory ones) require use of the statistics computer package
MINITAB, see
http://www.ntnu.no/itea.info/programvare/minitab.html |
| Final exam: | 04/06/2008 h 9.00
Written. 4 hours. Permitted aids: B - All printed and hadwritten aids permitted, approved simple calculator. |
| Earlier exams | 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). 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 16:(14/04)
Finished Bayesian analysis. Week 15:(7/04) Main results for renewal processes (Ch 7.3). INtroduction to Bayesian analysis (Ch 13) Week 14: (3/04) Parametric estimation in NHPP, model check, trend testing in single and multiple processes. (31/03) Parametric estimation in NHPP, likelihood derivation. Observed information in power law NHPP and confidence intervals. Week 13: (27/03) Repairable systems and counting processes. Non homogeneous Poisson processes. Non parametric estimation (Nelson Aalen estimator). Week 10-12: No Lectures Week 9: (28/02) Repairable systems and counting processe. Main definition (Ch 7.1.1-7.1.4). Homogeneous Poisson processe (main features in Ch 7.2). (25/2) Finished cox regression and ALT models, some examples and exercises Week 8: (21/02) Accelerated life test (ALT) (Ch 12 of the book, only until pag. 532) (19/02) Cox regression, estimation of the baseline hazard function, model diagnostic. You might also download a case study on Cox regression, copied from a book by Flaming and Harrington ("Counting processes and Survival analysis") Week 7:(14/02) Cox regression, definition of partial likelihood. Simple example and real data example. Tests for regression coefficients. (11/02) Weibull regression, woked out example with dataset which can be downloaded here. Week 6: (07/02) Survival regression for log-location scale models (Weibull and LogNormal), Chapter 3 in a book form Ansell and Phillips . Definition of different residuals. Accelerated life test (Ch 12) . You may also download the MINITAB note on survival regression. (04/02) Parametric inference for log-location scale models (you con dowload here some notes.) Confidence intervals under type II censuring. Threshold parameter models. Week 5: (31.01) MLE estimation for one parameters family: estimation, confidente intervals tests. Examples from the exponential distribution. (Ch 3 in On parametric inference in lifetime models.) MLE for Weibull model. Probability plots for Weibull distribution (11.3.4). (28.01) TTT plot for censured data (the definition given in the lecture is different from the one in the book) Barlow-Prochan's test for exponentiality (complete and censured data) (11.5) Logrank test for camparison of survival curves in several groups. Parametric inference. Censoring (right, left, interval). Construction of the likelihood (On likelihood construction). Week 4 (21-24/01): Types of censuring (11.2 ) Empirical distribution function (11.3.1-11.3.3) The Kaplan-Mayer estimator for complete and censured data (11.3.5) Nelson plot of cumulative hazard rate for complere and censured data (11.3.6) TTT plot for complete data (11.3.7 only main concepts) . Some additiona notes to be downloaded About the exponential distribution, Poisson process, TTT and Barlow-Prochan-s test. Week 3 (14-17/01): Basic concepts and distributions (Chapter 2: 2.1-2.9, 2.11-2.14, 2.17, 2.20) |
| 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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