Two well-known methods of improving the reliability of a system are (i) provision of redundant units, and (ii) repair maintenance. In a redundant system more units are made available for performing the sys- tem function when fewer are required actually. There are two major of types of redundancy - parallel and standby. In this thesis we are concerned with both these types. Some of the typical assumptions made in the analysis of redundant systems are 1. the life time and the repair time distributions are assumed to be exponential 2. the repair rate is assumed to be constant 3. the repairman is assumed to be perfect, and hence go with only one repairman 4. the repair facility can take up a failed unit for repair at any time, if no other unit is undergoing repair 5. the system under consideration is needed all the time 6. usage of only conventional methods for the analysis of the estimated reliability of systems. However, we frequently come across systems where one or more of these assumptions have to be dropped. This is the motivation for the detailed study of the models presented in this thesis. In this thesis we present several models of redundant systems relaxing one or more of these assumptions simultaneously. More specifically it is a study of stochastic models of redundant repairable systems with non-exponential life time and repair times, varying repair rate, different types of repairmen, intermittent use and the use of time series in reliability modelling. The thesis contains seven chapters. Chapter 1 is introductory in nature and contains a brief description of the mathematical techniques used in the analysis of redundant systems. In chapter 2 assumption (1) is relaxed while studying two models with the assumption of life times and repair times to follow bivariate exponential distributions. Various operating characteristics have been obtained and the confidence limits have been established analytically for the system measure, availability for both the models. Reliability analysis of a two unit standby system with varying repair rate is studied in chapter 3, by relaxing the assumption (2). In this chapter a similar study of chapter 2 is studied with assumption that the repair time distribution is generalised Erlangian. Assumption (3) is relaxed in chapter 4, and we introduced two repairman (one regular repairman and the other expert repairman) to so that the system will be more efficient. The asymptotic confidence limits are obtained for the study state availability of such a system. A three-unit system in which the ”preparation time” is introduced, and hence the assumption (4) is relaxed in this chapter 5. The difference-differential equations for the state probabilities are derived. The confidence limits for the steady state availability are obtained analytically and illustrated numerically. In chapter 6, assumption (5) is relaxed. An intermittently used k our of n:F system with a single repair facility is condered with the assumption that failures will not be detected during a no need period. Identifying regeneration points expressions are derived for the survivor function of the time to the first disappointment and the mean number of disappointments and the sys- tem recoveries in an interval. Expressions are also deduced for the stationary rate of occurrence of these events. Chapter 7 presents an unconventional but powerful method for the analysis of the estimated reliability of systems constituted of subsystems (compo- nents) operating in series and/or in parallel under varying operational and environmental conditions. In this chapter assumption (vi) is relaxed. The proposed method construes the estimated reliability data as time series which are analysed using the well-known time series techniques. / Thesis (PhD (Industrial Systems))--University of Pretoria, 2006. / Industrial and Systems Engineering / unrestricted

Complex systems offer broad, unique research challenges due to their inability to be understood through a classic reductionist perspective, as they exhibit emergent phenomena that arise through the interactions of their components. In this thesis, we briefly review some characteristics of complex systems and the interplay of mathematical and computational methods to study them. We then discuss these approaches, how they are implemented, and how they support one another in three settings. First, we present a study that connects weather data to seasonal population-abundance of mosquitoes, using a microscopic model. Secondly, we consider the collective motions that arise in ensembles of disks interacting through non-elastic collisions and investigate how such behaviors affect macroscopic transport properties. Finally, we consider a 'self-sorting' one-dimensional collection of point-particles. In all of these cases, agent-based models and simulations are used to guide analysis, and in the final example, we explain how the simulations led to new theorems. Articles and molecular dynamics computer codes are provided as appendices.

Plus de 50% de la population mondiale vit dans des zones urbaines et cette proportion devrait augmenter dans les prochaines décennies. Comprendre ce qui régit l'évolution des systèmes urbains est donc devenu d'une importance fondamentale. Ce renouveau d'intérêt combiné avec la disponibilité de données à grande échelle, permet d'entrevoir l'avènement d'une nouvelle science des villes, interdisciplinaire et basée sur les données.Des études récentes ont montré l'existence de régularités statistiques et de lois d'échelle pour plusieurs indicateurs socio-économiques, tels que la consommation d'essence, la distance moyenne parcourue quotidiennement, le cout des infrastructures, etc. Malgré plusieurs tentatives récentes, la compréhension théorique de ces résultats observés empiriquement demeure très partielle.Le but de cette thèse est d'obtenir une modélisation simplifiée, hors-équilibre de la croissance urbaine, en s'appuyant sur un petit nombre de mécanismesimportants et qui fournit des prédictions quantitatives en accord avec lesdonnées empiriques. Pour cela, nous nous inspirerons des études en géographiequantitative et en économie spatiale et nous revisiterons certains de ces anciens modèles avec une nouvelle approche intégrant les outils et concepts de la physique. / More than 50 % of the world population lives in urban areas and this proportion is expected to increase in the coming decades. Understanding what governs the evolution of urban systems has thus become of paramount importance.This renewed interest combined with the availability of large-scale data, allows a glimpse into the dawn of a new science of cities, interdisciplinary and based on data.Recent studies have shown the existence of statistical regularities and scaling laws for several socio-economic indicators such as fuel consumption, average commuting distance, cost of infrastructure, etc., and despite several recent attempts, the theoretical understanding of these results empirically observed remains very partial. The purpose of this thesis is to obtain a simplified, out of equilibrium model of urban growth, based on a small number of important mechanisms and which provides quantitative predictions in agreement with empirical data. For this, we will draw on studies in quantitative geography and spatial economy and we will revisit some of these old models with a new approach that integrates the tools and concepts of physics.

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Stigmergy refers to indirect communication that was originally found in biological systems. It is used for self-organization by ants, bees, and flocks of birds, by allowing individuals to focus on local information. Through local communication among individuals, larger patterns are formed without centralized communication. This self-organization is just one type of system studied within complex systems. Systems of ants, bees, and flocks of birds are considered complex because they exhibit emergent behavior: the outcome is more than the sum of the individual parts. Emergent behavior can be found in many other systems as well. One example is the Internet, which is a series of computers organized in a self-organized fashion. Complexity can also be defined through properties other than emergent behavior, such as existing on multiple scales. Many biological systems are multi-scale. For instance, cancer exists on many scales, including the sub-cellular and cellular levels. Many computing systems are also multi-scale, as there may be both individual and system-wide controls interacting together to determine the output. Many multi-agent systems would fall into this category, as would many large software systems. In this dissertation I examine complex systems in artificial intelligence and biology: the growth of cancer, population dynamics, emotions, multi-agent fault tolerance, and real-time strategic AI for games. My goal is twofold: a) to develop novel computational models of complex biological systems, and b) to tackle key AI research questions by proposing new algorithms and techniques that are inspired by those complex biological systems. In all of these cases I design variations on stigmergic communication to accomplish the task at hand. My contributions are a new agent-based cancer growth model, a proposed use of location communication for removing cancer, improved multi-agent fault tolerance through localized messaging, a new approach to modeling predator-prey dynamics using computational emotions, and improved strategic game AI through computational emotions.

Requirements engineering in a system-engineering project is a key factor in the success of a project. In the current state, stand-alone research has been conducted tackling this area, however, few studies addressed the requirements based on a probabilistic approach. In this thesis, a multi-scale probabilistic approach has been developed, named Bayesian Network, to evaluate the requirements engineering of a complex systems In order to pursue the aim of this paper, the FFG(X) navy ship is chosen to serve as a case study and to validate the proposed model. Results indicate the sub-requirements that highly affect the FFG capability/performance. These sub-requirements are: 1) guns, 2) ballistic missiles, 3) antisubmarine, and 4) radar.

We are recently witnessing an increase in large-scale micro/individual/- granular level behavioural data. Such data has been proven to have the capacity to aid the development of more accurate simulations that will ef- fectively predict the behaviours of complex systems. Despite this increase, the literature has failed to produce a structured modelling approach that will effectively take advantage of such granular data, in modelling com- plex systems that involve social phenomenons (i.e. social complex sys- tems). In this thesis, we intend to bridge this gap by answering the question of how novel structural frameworks, that systematically guides the use of micro-level behaviour and attribute data, directly extracted from the ba- sic entities within a social complex system can be created. These frame- works should involve the systematic processes of using such data to di- rectly model agent attributes, and to create agent behaviour rules, that will directly represent the unique micro entities from which the data was ex- tracted. The objective of the thesis is to define generic frameworks, that would create agent based micro simulations that would directly reflect the target complex system, so that alternative scenarios, that cannot be inves- tigated in the real system, and social policies that need to be investigated before being applied on the social system can be explored. In answering this question, we take advantage of the pros of other model- ing techniques such as micro simulation and agent based techniques in cre- ating models that have a micro-macro link, such that the micro behaviour that causes the macro emergence at the simulation’s global level can be easily investigated. which is a huge advantage in policy testing. We also utilized machine learning in the creation of behavioural rules.This created agent behaviours that were empirically defined. Therefore, this thesis also answers the question of how such structural framework will empirically create agent behaviour rules through machine learning algorithms. In this thesis we proposed two novel frameworks for the creation of more accurate simulations. The concepts within these frameworks were proved using case studies, in which these case studies where from different so- cial complex systems, so as to prove the generic nature of the proposed frameworks. In concluding of this thesis, it was obvious that the questions posed in the first chapter had been answered. The generic frameworks had been created, which bridged the existing gap in the creation of accurate mod- els from the presently available granular attribute and behavioral data, al- lowing the simulations created from these models accurately reflect their target social complex systems from which the data was extracted from.

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no / The research presented in this paper addresses the challenge of developing functional models for complex systems that have multiple modes of operation or use cases. An industrial case study of an electric vehicle is used to illustrate the proposed methodology, which is based on a systematic modelling of functions through nested systems using the system state flow diagram (SSFD) method. The paper discusses the use of SSFD parameter based state definition to identify physical and logical conditions for joining function models, and the use of heuristics to construct complex function models.

Complex socioenvironmental problems such as food, energy and water shortages, health impacts from environmental contamination and global climate change present significant challenges to the global community. Addressing these problems will require an interdisciplinary systems-thinking approach that coordinates problem-solving between practitioners of varied disciplines including engineers, physical scientists, economists and other social scientists. Civil and environmental engineers have distinct technical skills necessary to help address these challenges as part of coordinated multidisciplinary efforts towards the achievement of comprehensive and sustainable resolutions to these problems. Ensuring civil and environmental engineers are trained to think and work in this multidisciplinary exchange requires incorporation of systems-thinking into engineering academic curricula. Attempts have been made to incorporate these skill sets into civil and environmental engineering (CEE) coursework. These efforts, as well as evaluation of their effectiveness in training CEE students to think systemically, have lacked in coordination to integrate them as part of the overarching academic curricula. This research advances the current body of knowledge regarding incorporation of systems-thinking into CEE coursework by examining the impacts of system dynamics model based educational tools on systems-thinking learning outcomes of CEE students in a one-semester CEE elective course. The findings suggest that system dynamics modeling can be an effective tool in educating future systems thinkers in the CEE disciplines. / Doctor of Philosophy / Complex socioenvironmental problems such as food, energy and water shortages, health impacts from environmental contamination and global climate change present significant challenges to the global community. Addressing these problems will require an interdisciplinary systems-thinking approach that coordinates problem-solving between practitioners of varied disciplines including engineers, physical scientists, economists and other social scientists. Civil and environmental engineers have distinct technical skills necessary to help address these challenges as part of coordinated multidisciplinary efforts towards the achievement of comprehensive and sustainable resolutions to these problems. Ensuring civil and environmental engineers are trained to think and work in this multidisciplinary exchange requires incorporation of systems-thinking into engineering academic curricula. Attempts have been made to incorporate these skill sets into civil and environmental engineering (CEE) coursework. These efforts, as well as evaluation of their effectiveness in training CEE students to think systemically, have lacked in coordination to integrate them as part of the overarching academic curricula. This research advances the current body of knowledge regarding incorporation of systems-thinking into CEE coursework by examining the impacts of system dynamics model based educational tools on systems-thinking learning outcomes of CEE students in a one-semester CEE elective course. The findings suggest that system dynamics modeling can be an effective tool in educating future systems thinkers in the CEE disciplines.