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A collection of formulas is updated after each lectureduring the semester. This collection may be brought to the exam.
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| Week | Date
| Subject | Lectured topics | Motivation | Lecturer | Tutorials | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 34 | 19 & 20.8 | All | 1st hour:
2nd-3rd hours
| Inform the students about the course objectives, intended learning outcomes, and practicalities.
| Mary Ann and Jørn | Introduction to|||||
| 35 | 26.-27.8 | 1 | Safety-critical systems: | IEC 61508 is a key standard on design of safety-critical systems, when the technology used include electrical, | Mary Ann | |||||
| 36 | 2.-3.9 | 1 | Safety-critical systems: (chapter 2, plus supplemented material: | The mentioned IEC standard(s) require a structured process for defining SIL requirements. Methods like layers of protection analysis (LOPA) and risk graph are often used for this purpose. Risk graph is used with many applications, such as for machinery and process industry, whereas LOPA is mainly used in the process industry. In the oil and gas industry, for example, it is common to have LOPA-sessions/workshops in an early planning of new systems. A special case of defining SIL requirements is the minimum SIL, advocated in a Norwegian guideline for offshore oil and gas facility, Norsk Olje og Gass guideline 070. This approach builds on principles called GALE or GAMAB. | Mary Ann | Problems chapter 2: 21, 22, NEW (on|||||
| 37 | 9.-10.9 | 1 | Safety-critical systems: Quantification of reliability for systems operating on demand - Extending the simplified formulas (Textbook chapter 8) | Students that take this course are familiar with simplified formulas for calculating the average probability of failure on demand (PFD).
| Mary Ann |
| ||||
| 38 | 16.-17.9 | 1 | Safety-critical systems: (Textbook chapter 5 and 8) | PetriNets is an alternative approach for calculating the the the average probability of failure on demand (PFD). | Yiliu (Mary Ann | |||||
| problems39 | 23.-24.9 | 1 | Safety-critical systems: Modeling Quantification of CCFs and determining of the value of the beta factor.reliability for systems operating in the high demand mode (Textbook chapter 109) | Common cause failures (CCFs) are often the main contributor to the probability of failure for redundant systems. The students
| Mary Ann | Not all safety-critical systems operate on demand. For example, many machinery safety functions are always or so often demanded that the PFD is no longer a useful reliability measure. Another example is railway signaling systems controlling the setting of light signals and position of rails switches. In this case, another reliability measure is suggested in standards like IEC 61508, called failure frequency (PFH). This lecture explains how the PFH is calculated for typical system architectures. (Guest lecture was added here) | Mary AnnProblems chapter 10: 3 (excluding c)), NEW PROBLEM: Application of the Humphrey's method for determining beta. | |||
| 40 | 30.9-1.10 | 1 | Safety-critical systems | Continue high-demand systems Choice of reliability data | Mary Ann | |||||
| 41 | 7.-8.10 | 1 | Safety-critical systems: Quantification of reliability for systems operating on demand with focus on partial and imperfect testing (Textbook chapter 11) | It is not always realistic that the proof tests and the associated repair actions are "perfect", meaning that the system is restored to an as good as new state after each test. One reason may be that it is not safe to simulate a real "demand" (would you test fire detectors by putting fire to a room?). The simulated test (pressing a test-button) may not be so extensive, and some failures may be left undiscovered also after the test. Another reason may be that it is not desired to carry out a perfect test. Testing of valves, for example, require that the valve is operated from opened to closed position (or visa versa), but this may require a full stop of the plant. Instead, it may be suggested to replace some perfect tests with partial tests, so that the valve is just operated some %, and then returned to its initial position. This lecture focus on how to account for such factors in the quantification of PFD. | Mary Ann |
| 41 | 7.-8.10 | 1 | Safety-critical systems: Quantification of reliability for systems operating in the high demand mode (Textbook chapter 9) |
| Not all safety-critical systems operate on demand. For example, many machinery safety functions are always or so often demanded that the PFD is no longer a useful reliability measure. Another example is railway signaling systems controlling the setting of light signals and position of rails switches. In this case, another reliability measure is suggested in standards like IEC 61508, called failure frequency (PFH). This lecture explains how the PFH is calculated for typical system architectures. | Mary Ann |
| 42 | 14.-15.10 | 1 | Safety-critical systems: Quantification of spurious trips (Textbook chapter 10) | A fail-safe design of a safety-critical system favors a transition to the safe state, which in most | Mary Ann |
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| 43 | 21-22.10 | 2 | Spare-part optimization | Spare parts may be costly to have on the stock, but at the same time it is costly not to have a spare part available when it is needed. This topic concern how to calculate the probability of running out of spares, using simple formulas and Markov analyses. The use of PetriNets for this purpose is also shown. This topic may not be some relevant for very specialized systems, where it is not possible to acquire a spare within short time. For a manufacturer that develops products, such as sensors, in a large scale to e.g. the oil and gas industry, it may be relevant to find the optimal number of spare parts for warranty and repair services. | Yiliu | |||||
| 44 | 27&28.10 | 2 | Maintenance interval optimization and related issues | The main objective of the lectures on maintenance interval optimization is to understand a set of classical mathematical models for maintenance interval optimization. In the introduction course in maintenance four failure models were introduced, (i) gradual failure progression, (ii) fast failure progression, (iii) non-observable failure progression and (iv) shock type failures. For all four situations the standard cost function to minimize will be developed. Essential in the modelling is the understanding of the effective failure rate¸ and how to calculate it given reliability parameters like MTTF, aging parameter, PF-interval and so on. In this lecture the classical age, block, and minimal repair policies are introduced as a motivation for the modelling. Next we discuss how these models align to the general modelling framework, and the concept of effective failure rate. Special emphasise will be paid on the calculation of the effective failure rate in various situations. This involves use of renewal theory, use of the law of total probability, and Markov methods. | JørnSelected problems from http://frigg.ivt.ntnu.no/ross/elearning/maintop/exercises/ | |||||
| 45 | 4&5.11 | 2 | Maintenance interval optimization and related issues (continued) | The second lecture on interval optimization completes the presentation of the four failure models introduced. In the standard cost functions the cost of preventive maintenance is fixed, and not influenced by other tasks. In reality preventive maintenance cost could be reduced by coordination of various maintenance tasks. Models for maintenance grouping are introduced to formulate the optimization problem in such situations. A distinction is made between static and dynamic grouping. The optimization problem now deals both with forming the groups, and determining when to execute each group of activity. Some heuristics are introduced for selected situations. | JørnSelected problems from http://frigg.ivt.ntnu.no/ross/elearning/maintop/exercises/ | |||||
| 46 | 11&12.11 | 2 | Degradation modeling and condition based maintenance | This lecture is an introduction to condition based maintenance, that is to say maintenance which is based on a degradation indicator of the system. It mainly concerns preventive maintenance actions which are triggered before failure, in order to avoid failure costs. This kind of maintenance actions are relevant when the failure cost is high compared with the maintenance costs and when at least one degradation indicator is available for the system. This lecture aims at i) giving an overview of useful tools to model degradation (especially continuous state space degradation, e.g. crack propagation), ii) showing how such models can be used for failures prognosis and condition based maintenance optimization.
| Anne | |||||
| 47 | 18.&19.11 | N/A | Student presentations (also using tutorial hours) | Summary lecture | Students get the possibility to reflect on the lectured topics and in particular to see how these are related to their specialization project, and how they may be applicable for their master project. | Mary Ann | ||||
| 48 | 26.11 | Summary (in tutorial hours, due to IPK traveling on 24-25.11) | Mary Ann | |||||||