Lecture plan and progress
R&H refers to relevant sections in Rausand & Høyland: System Reliability Theory: Models, Statistical Methods, and Applications, 2nd Edition. Wiley 2004.
| Date | R&H | Topic | Slides | Notes/Supplementary reading |
|---|---|---|---|---|
| 06.01 | 2.3-2.6, 2.9-2.14 | Introduction and motivation. General concepts for lifetime modeling. | Slides 1, Slides 2 | |
| 07.01 | 2.9-2.14 | Parametric families of lifetime distributions. | Slides 3 | Alternative formula for MTTF |
| 13.01 | 2.9-2.14, 2.17 | Extreme value distributions and the Gumbel distribution. Log-location-scale families. Censoring. | Slides 4, Slides 5 | Extreme value distributions, More on log-location-scale families |
| 14.01 | 11.1-11.3.3, 11.3.5 | Empirical survival function; Kaplan-Meier estimator. | Slides 5 | Extra on Kaplan-Meier |
| 20.01 | 11.3.6 | Kaplan-Meier estimator (cont.). Nelson-Aalen estimator. | Slides 5, Slides 6 | R-programs for KM and NA plot |
| 21.01 | 11.3.7 | Properties of the exponential distribution. Derivation of the Nelson-Aalen estimator. | Slides 6 | About the Exponential Distribution, Poisson Process, Total Time on Test and Barlow-Proschan's Test. |
| 27.01 | 11.3.7 | Derivation of the Nelson-Aalen estimator (cont.) TTT-plot. | Slides 6 | Algorithm for TTT and BP |
| 28.01 | 11.4.3, 11.4.4 | Barlow-Proschans test. The logrank test. Introduction to parametric methods. | Slides 7 (p. 1-12) | Note on the logrank test |
| 03.02 | 11.4.4 | Introduction to parametric methods (cont.) Parametric inference for the exponential model. | Slides 7 (rest), Slides 8 | The standard confidence interval for positive parameters. Some likelihood theory. R-programs for parametric estimation. |
| 04.02 | 11.4.5 | Parametric inference for the Weibull model. | Slides 9 | |
| 10.02 | Inference in log-location-scale models. Threshold models (3-parameter Weibull). | Slides 10 | ||
| 11.02 | Parametric survival regression. | Slides 11 | Book chapter on survival regression, | |
| 17.02 | Parametric survival regression (cont.). | Slides 11 | Modelling of covariates and factors | |
| 18.02 | Proportional hazards and Cox-regression. | Slides 12 | R-codes for Cox-regression and parametric regression with survreg. | |
| 24.02 | Cox regression (cont.) Model checking in Cox-regression. Case study of Cox-regression. | Slides 12 | Case study in Cox regression | |
| 25.02 | 12, 7.3.1, 7.4.1, 7.4.2, 7.4.3 | Accelerated life testing. Recurrent events and repairable systems. The nonhomogeneous Poisson process (NHPP). | Slides 13, Slides 14 | Download INSULATE.mwx |
| 02.03 | 7.3.1, 7.4.1, 7.4.2, 7.4.3 | Recurrent events and repairable systems. The nonhomogeneous Poisson process (NHPP). Nonparametric estimation of cumulative ROCOF. | Slides 14, p. 1-27 | |
| 03.03 | 7.3.1, 7.4.1, 7.4.2, 7.4.3, 7.4.4 | Nonparametric estimation of cumulative ROCOF (cont.). Parametric estimation in NHPPs. | Slides 14, p. 28-41, Slides 15 | |
| 09.03 | 7.4.5 | Parametric estimation in NHPPs (cont.), Trend testing in NHPPs. | Slides 15, Slides 16 | |
| 10.03 | 7.4.5 | Trend testing in NHPPs (cont.). TTT-plots for repairable systems. | Slides 16. | |
| 16.03 | NO LECTURE (Obligatory 2) | |||
| 17.03 | NO LECTURE (Obligatory 2) | |||
| 23.03 | 7.3.1, 7.3.2, 7.3.3 | NO LECTURE (Obligatory 2) Self-study: Renewal processes. | Slides 16, | |
| 24.03 | NO LECTURE (Obligatory 2) Self-study: Unobserved heterogeneity in NHPPs | Slides 17, | Article on unobserved heterogeneity, Exercise on heterogeneity in HPP. | |
| 30.03, 31.03 | Go through and discuss topics from exam exercises: 2019, 2: Accelerated testing 2016, 3: log-logistic distribution 2009, 2: Nelson-Aalen for repairable system 2009, 3: Parametric estimation in NHPP 2010, 2: A new cdf F(t) 2012, 1: Parametric estimation with censored data 2012, 2: Kaplan-Meier, logrank, Cox | |||
| 06.04 | Easter break | |||
| 07.04 | Easter break | |||
| 13.04 | Easter break | |||
| 14.04 | Easter break | |||
| 20.04, 21.04 | 2014, 1: Weibull regression 2008, 2: Hazard rate, renewal process, NHPP 2015, 1: Nelson-Aalen, Total Time on Test 2005, 1: Cox-regression 2019, 3: NHPP, software reliability 2013, 1: Weibull-regression |