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Reliability evaluation by analytic modelling constitute an important issue of designing a reliable multiprocessor system. In this thesis, a model for reliability and fault tolerance analysis of the interconnection network is presented, based on graph theory. Reliability and fault tolerance are considered as deterministic and probabilistic measures of connectivity. Exact techniques for reliability evaluation fail for large multiprocessor systems because of the enormous computational resources required. Therefore, approximation techniques have to be used. Three approaches are proposed, the first by simplifying the symbolic expression of reliability; the other two by applying a hierarchical decomposition to the system. All these methods give results close to those obtained by exact techniques.

In 1996, a concept was proposed by the UK Ministry of Defence with the intention of making the field of reliability more useful to the end user, particularly within the field of military aerospace. This idea was the Maintenance Free Operating Period (MFOP), a duration of time in which the overall system can complete all of its required missions without the need to undergo emergency repairs or maintenance, with a defined probability of success. The system can encounter component or subsystem failures, but these must be carried with no effect to the overall mission, until such time as repair takes place. It is thought that advanced technologies such as redundant systems, prognostics and diagnostics will play a major role in the successful use of MFOP in practical applications. Many types of system operate missions that are made up of several sequential phases. For a mission to be successful, the system must satisfactorily complete each of the objectives in each of the phases. If the system fails or cannot complete its goals in any one phase, the mission has failed. Each phase will require the system to use different items, and so the failure logic changes from phase to phase. Mission unreliability is defined as the probability that the system fails to function successfully during at least one phase of the mission. An important problem is the efficient calculation of the value of mission unreliability. This thesis investigates the creation of a modelling method to consider as many features of systems undergoing both MFOPs and phased missions as possible. This uses Petri nets, a type of digraph allowing storage and transit of tokens which represent system states. A simple model is presented, following which, a more complex model is developed and explained, encompassing those ideas which are believed to be important in delivering a long MFOP with a high degree of confidence. A demonstration of the process by which the modelling method could be used to improve the reliability performance of a large system is then shown. The complex model is employed in the form of a Monte-Carlo simulation program, which is applied to a life-size system such as may be encountered in the real world. Improvements are suggested and results from their implementation analysed.

Linear assets are among the largest and most important engineered systems; their reliability is of the utmost importance. This thesis presents an overview of the reliability estimation methods used for the various types of linear assets, both observation- and statistically-based. While observation-based reliability monitoring and estimation methods are necessarily particular to a certain type of asset, statistically-based methods developed for one type can potentially inform those used for another. Therefore, this thesis looks to point out commonalities in the methods for the statistical evaluation of the reliability of various types of linear assets, develop and extend reliability models and methods with this knowledge, and suggest how maintenance strategies may be improved. To help illustrate and test the models described in this paper a case study was conducted with a utility operator; this thesis shows the modelling results from the study, and demonstrates the model’s use in a maintenance decision model.

Linear assets are among the largest and most important engineered systems; their reliability is of the utmost importance. This thesis presents an overview of the reliability estimation methods used for the various types of linear assets, both observation- and statistically-based. While observation-based reliability monitoring and estimation methods are necessarily particular to a certain type of asset, statistically-based methods developed for one type can potentially inform those used for another. Therefore, this thesis looks to point out commonalities in the methods for the statistical evaluation of the reliability of various types of linear assets, develop and extend reliability models and methods with this knowledge, and suggest how maintenance strategies may be improved. To help illustrate and test the models described in this paper a case study was conducted with a utility operator; this thesis shows the modelling results from the study, and demonstrates the model’s use in a maintenance decision model.

<p>Power system maintenance optimisation involves obtaining the minimum total costs, including preventive and corrective maintenance costs and the cost of failures for both supplier and customer. To calculate the cost of failure, information is needed about the equipment reliability characteristics. It is also necessary to know how maintenance affects component reliability. The aim of the work leading up to this thesis has been to develop reliability models that include the effect of maintenance.</p><p>Three case studies have been carried out for different types of power system components using three distinct methods. In the first study the reliability of the first generation XLPE cables was modelled with respect to failures caused by water treeing using load-strength modelling. The model was based on assumptions of the ageing process and the distribution system characteristics. This study showed that it is possible to and overvoltage and insulation characteristics that can be fitted to agree with failure statistics for water tree ageing in XLPE cables. The second case study included a study of all circuit breaker failures in the Swedish transmission grid during the period from 1 January 1999 to 30 June 2003. In a subsequent investigation a method to combine information from the design process with maintenance records and failure statistics was employed using Bayesian methods. The resulting reliability model is continuously updated as more failure and maintenance data</p><p>becomes available. This case study showed that it is possible to develop reliability models for components that have not yet failed by utilising information from the design process and right-censored observations from inspections. Finally, in the third case study a quantitative method for establishing the condition of disconnector contacts by the use of thermography was developed. Two sets of measurements on disconnector contacts in the Swedish transmission</p><p>grid were carried out to establish the accuracy of the method. By utilising the results from the measurements estimates of the statistical distributions of the error sources were produced.</p><p>The results from the case studies show that the lack of detailed, high-quality data remains a critical problem when modelling reliability of power system equipment, even when using methods that require a minimum of data.</p>

Power system maintenance optimisation involves obtaining the minimum total costs, including preventive and corrective maintenance costs and the cost of failures for both supplier and customer. To calculate the cost of failure, information is needed about the equipment reliability characteristics. It is also necessary to know how maintenance affects component reliability. The aim of the work leading up to this thesis has been to develop reliability models that include the effect of maintenance. Three case studies have been carried out for different types of power system components using three distinct methods. In the first study the reliability of the first generation XLPE cables was modelled with respect to failures caused by water treeing using load-strength modelling. The model was based on assumptions of the ageing process and the distribution system characteristics. This study showed that it is possible to and overvoltage and insulation characteristics that can be fitted to agree with failure statistics for water tree ageing in XLPE cables. The second case study included a study of all circuit breaker failures in the Swedish transmission grid during the period from 1 January 1999 to 30 June 2003. In a subsequent investigation a method to combine information from the design process with maintenance records and failure statistics was employed using Bayesian methods. The resulting reliability model is continuously updated as more failure and maintenance data becomes available. This case study showed that it is possible to develop reliability models for components that have not yet failed by utilising information from the design process and right-censored observations from inspections. Finally, in the third case study a quantitative method for establishing the condition of disconnector contacts by the use of thermography was developed. Two sets of measurements on disconnector contacts in the Swedish transmission grid were carried out to establish the accuracy of the method. By utilising the results from the measurements estimates of the statistical distributions of the error sources were produced. The results from the case studies show that the lack of detailed, high-quality data remains a critical problem when modelling reliability of power system equipment, even when using methods that require a minimum of data. / QC 20101209

Reliability modelling of RAID storage systems with its various components such as RAID controllers, enclosures, expanders, interconnects and disks is important from a storage system designer's point of view. A model that can express all the failure characteristics of the whole RAID storage system can be used to evaluate design choices, perform cost reliability trade-offs and conduct sensitivity analyses. We present a reliability model for RAID storage systems where we try to model all the components as accurately as possible. We use several state-space reduction techniques, such as aggregating all in-series components and hierarchical decomposition, to reduce the size of our model. To automate computation of reliability, we use the PRISM model checker as a CTMC solver where appropriate. Initially, we assume a simple 3-state disk reliability model with independent disk failures. Later, we assume a Weibull model for the disks; we also consider a correlated disk failure model to check correspondence with the field data available. For all other components in the system, we assume exponential failure distribution. To use the CTMC solver, we approximate the Weibull distribution for a disk using sum of exponentials and we first confirm that this model gives results that are in reasonably good agreement with those from the sequential Monte Carlo simulation methods for RAID disk subsystems. Next, our model for whole RAID storage systems (that includes, for example, disks, expanders, enclosures) uses Weibull distributions and, where appropriate, correlated failure modes for disks, and exponential distributions with independent failure modes for all other components. Since the CTMC solver cannot handle the size of the resulting models, we solve such models using hierarchical decomposition technique. We are able to model fairly large configurations with upto 600 disks using this model. We can use such reasonably complete models to conduct several "what-if" analyses for many RAID storage systems of interest. Our results show that, depending on the configuration, spanning a RAID group across enclosures may increase or decrease reliability. Another key finding from our model results is that redundancy mechanisms such as multipathing is beneficial only if a single failure of some other component does not cause data inaccessibility of a whole RAID group.