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Lecture
  • Slides 
  •  Subject area: Reliability assessment of safety-critical systems                                                                       critical systems       

     Lecture material:

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    • Slides

    Lectured topic

    Motivation

    Development of reliability requirements

     

    "Safety integrity level (SIL) is a key reliability performance measure used for safety-critical systems. Reliability requirements are therefore often given as SIL requirements are identified in an extension of the risk analysis, using methods often refered to as SIL allocation, SIL targeting and SIL classification. Key methods like Layers of protection analysis (LOPA), risk graph, and minimum SIL are presented and discussed."

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     New reliability assessment methods 
    In TPK 4120, some analytical formulas were introduced to calculate the average probability of failure on demand (PFD). It was also shown how the average PFD may be calculated using Markov methods and fault tree analysis. This reliability measure is of high importance in relation to SIL, as a relationship is established between a SIL requirement and the maximum PFD tolerated for a safety function. In this course, we go a step further and introduce the foundations for analytical formulas presented in IEC 61508 (a key standard for reliability of safety-critical systems), the PDS method (a method along with a set of analytical formulas widely adapted in the Norwegian oil and gas industry, but which has a wider application area), and dynamic modeling, using Petri Nets."

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     Special analysis challenges (possible candidates for under this heading):
    • Partial and imperfect testing
    • Follow-up of SIL requirements in the operational phase
    • Hardware fault tolerance - Hardware design constraints of safety-critical functions
     

     Subject area: Maintenance optimization                                                                                                        

    Lecture material:

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     Lectured topics within this area are:
    • Age, block and minimal repair strategies.

    The intervals of maintenance for safety-critical systems are normally determined from the reliability analyses. For other systems, we may use decide upon intervals of testing using different maintenance strategies. These models include parameters like costs, failure rates, and aging. The models come of with the answer to the following two questions: When should we do maintenance and what tasks and equipment should be included. The application of these methods are many. Two examples are maintenance planning of railway tracks and another is planning of intervention (for maintenance purposes) of subsea equipment.
    Sub-topics also covered under the same "umbrella" are:

      • Modeling of effective failure rate:

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      • Maintenance interval and and intervention level (extensiveness of maintenance) is obviously influencing the failure rate of the components. This topic concerns the modeling of the relationship between these two parameters and what we can refer to as the effective (or resulting) failure rate.
      • Weibull renewal:

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      • **Say something here** 
      • PF models and state based models:

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      • **Say something here** 
    •  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 Monte-carlo simulations for this purpose is also shown. This topic may not be some relevant for very specialized systems, where it is not possible to aquire 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. 

     

    •  Prognostics and remaining useful life:

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    • **Say something here**
    • Bayesian methods
    • Counting processes

      

     

    Tutorials & Project

    There will be mandatory problems/tasks to solve as part of the course.

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