| Date | Teacher | Place | Topic | Lecture notes / comments |
| 19.01.2011 | Bent Natvig? | B81 N.H. Abels hus? | Multistate reliability theory? | From Natvig (2011) the following was covered: chapter 1 Introduction, except 1.3 Basic definitions from binary theory, and chapter 2 Basics, 2.1 Multistate monotone and coherent systems to the end of Definition 2.4. From pages 11 and 12 only Definition 2.1 was covered.? |
| 26.01.2011 | Bent Natvig? | B81 N.H. Abels hus? | Multistate reliability theory? | From Natvig (2011) the following was covered: the rest of 2.1, 2.2 Binary type multistate systems, without the proofs of Theorems 2.9 and 2.11, and 2.3 Multistate minimal path and cut vectors, to the end of Definition 2.13. The following exercises from Natvig (2011) 1.1-1.6 ought to be done. ? |
| 02.02.2011 | Bent Natvig? | B81 N.H. Abels hus? | Multistate reliability theory? | From Natvig (2011) the following was covered: the rest of 2.3 except for Theorems 2.14 and 2.17, and 2.4 Stochastic performance of multistate monotone and coherent systems except for Theorem 2.23 until Theorem 2.24. The following exercises from Natvig (2011) 2.1-2.5 ought to be done.? |
| 09.02.2011 | Bent Natvig? | B81 N.H. Abels hus? | Multistate reliability theory? | From Natvig (2011) the following was covered: the rest of 2.4 except for the proofs of Theorem 2.24 and Theorem 2.29, Theorem 2.34 and Corollary 2.35, and 2.5 Stochastic performance of binary type multistate strongly coherent systems except Theorem 2.38. The following exercises from Natvig (2011) 2.6-2.10 ought to be done.? |
| 16.02.2011 | Bent Natvig? | B81 N.H. Abels hus? | Multistate reliability theory? | Chapter 6 in Natvig (2011), Measures of importance of system components, without proofs of theorems and technical details, was covered. The following exercises from Natvig (2011) 2.11, 2.12, 2.17 and 2.18 ought to be done.? |
| 23.02.2011 | Arne Bang Huseby? | B81 N.H. Abels hus? | Simulation methods for repairable systems? | Discrete event simulation of pure jump processes, some basic results, application to repairable binary and multi-state systems.? |
| 02.03.2011 | Arne Bang Huseby? | B81 N.H. Abels hus? | Load sharing in binary systems? | We consider a system consisting of n components that is exposed to the load of supplying a certain amount of utility, e.g., electrical power. The load on the system is distributed among the components. When functioning each component is capable of handling a certain amount of load. The load capacity of a component is assumed to be constant throughout its lifetime. The main objective of the present paper is developing methods for optimal load sharing among the components subject to the constraints imposed by the load capacities and demand on the system. In the paper we show how to solve the problem in several special cases, and outline a greedy algorithm for handling the general case.? |
| 09.03.2011 | Arne Bang Huseby? | B81 N.H. Abels hus? | Multi-reservoir production optimization? | When a large oil or gas field is produced, several reservoirs often share the same processing facility. This facility is typically capable of processing only a limited amount of commodities per unit of time. In order to satisfy these processing limitations, the production needs to be choked, i.e., scaled down by a suitable choke factor. A production strategy is defined as a vector valued function defined for all points of time rep- resenting the choke factors applied to reservoirs at any given time. In the present paper we consider the problem of optimizing such production strategies with respect to various types of objective functions. A general framework for handling this problem is developed.? |
| 16.03.2011 | Arne Bang Huseby? | B81 N.H. Abels hus? | Multi-reservoir production optimization (cont.)? | The solution to the optimization problem depends on certain key properties, e.g., convexity or concavity, of the objective function and of the potential production rate functions. Using these properties several important special cases can be solved. An admissible production strategy is a strategy where the total processing capacity is fully utilized throughout a plateau phase. This phase lasts until the total potential production rate falls below the processing capacity, and after this all the reservoirs are pro- duced without any choking. Under mild restrictions on the objective function the performance of an admissible strategy is uniquely characterized by the state of the reservoirs at the end of the plateau phase. Thus, finding an optimal admissible production strategy, is essentially equivalent to finding the optimal state at the end of the plateau phase. Given the optimal state a backtracking algorithm can then used to derive an optimal production strategy.? |
| 23.03.2011 | Arne Bang Huseby? | B81 N.H. Abels hus? | Sequential optimization of oil production under uncertainty? | We study how to optimize oil production with respect to revenue in a situation where the production rate is uncertain. The oil production in a given period is described in terms of a difference equa- tion, where this equation contains several uncertain parameters. The uncertainty about these parameteres are expressed in terms of a suitable prior distribution. As the production develops, more information about the production parameters is gained. Hence, the uncertainty distributions need to be updated. However, the infor- mation comes in the form of inequalities and equalities which makes it very difficult to obtain exact analytical expressions for the posteriors. Still it is possible to estimate the distributions using a combination of rejection sampling and the well-known Metropolis-Hastings algorithm.? |
| 30.03.2011 | Bo Lindqvist? | B81 N.H. Abels hus? | Introduction to repairable systems? | Repairable systems; Repair strategies: Perfect and minimal repair; Renewal processes, nonhomogeneous Poisson processes; Nonparametric inference in repair processes.Here are slides? |
| 06.04.2011 | Bo Lindqvist? | B81 N.H. Abels hus? | Minimal and imperfect repair models? | Parametric inference in nonhomogeneous Poisson processes; Trend testing for repairable systems data. (Same set of slides as for 30 March).? |
| 13.04.2011 | Bo Lindqvist? | B81 N.H. Abels hus? | Maintenance models? | Imperfect repair: Brown-Proschan model; Virtual age models; Trend-renewal process. Slides on imperfect repair are found here?? |
| 27.04.2011 | Bo Lindqvist? | B81 N.H. Abels hus? | Inference in trend-renewal processes. Heterogeneity ("frailty") in repairable systems? | More on the trend-renewal process. Heterogeneity (frailty) for Poisson processes and generalization to trend-renewal processes. Examples. Slides are found here? |
Teaching plan
Published Nov. 25, 2010 11:03 AM
- Last modified Apr. 26, 2011 6:22 PM