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Tableau d'honneur de la Faculté des études supérieures et postdoctorales, 2023 / Afin d'augmenter la fiabilité d'un système, la méthode de conception la plus populaire consiste à augmenter le nombre de composantes redondantes. En général, quatre stratégies de redondance ont été développées dans la littérature, à savoir les stratégies active, passive, mixte et K-mixte. Les stratégies de redondance peuvent être utilisées pour des systèmes binaires et pour des systèmes multi-états. La complexité de l'évaluation de la fiabilité dépend de la configuration du système et de ses propriétés. Dans la littérature actuelle, il existe certaines limitations importantes relatives aux stratégies de redondance qui n'ont pas été suffisamment étudiées, aussi bien pour les systèmes binaires que pour les systèmes multi-états. Cette thèse identifie et aborde quelques questions importantes et difficiles à travers les contributions suivantes. Premièrement, pour les systèmes binaires, les stratégies de redondance présentent un degré élevé de complexité de calcul dans les modèles de fiabilité qui fournissent dans certains cas des limites inférieures de la fiabilité du système. Afin de réduire cette complexité, nous proposons un modèle basé sur des chaines de Markov à temps continu pour le calcul de la fiabilité exacte de systèmes *k* parmi *n* assujettis à des redondances active, passive, mixte et K-mixte. De plus, un modèle de simulation séquentiel de Monte Carlo est développé et une analyse de fiabilité est menée pour valider le modèle proposé. Un algorithme génétique est finalement développé pour résoudre un problème d'optimisation résultant de l'application des stratégies existantes aux systèmes parallèles-séries dans le contexte du modèle proposé. La seconde contribution de cette thèse concerne les systèmes multi-états dont les composantes peuvent fonctionner avec des niveaux de performances différents. Une analyse de fiabilité est conduite pour un système multi-état qui se détériore avec l'âge et qui est régi par une stratégie de redondance passive basée sur la demande. La fiabilité est évaluée pour différentes gammes de fréquences d'inspection et de maintenance. Nous examinons également un cas industriel de génération de l'énergie électrique pour lequel des opérations de maintenance et de réhabilitation sont implémentées. Un algorithme génétique est développé pour déterminer la fréquence optimale d'inspection, de maintenance et de réhabilitation tout en considérant la fiabilité du système. C'est la première fois que ce type d'analyse et d'optimisation de la fiabilité est considéré dans la littérature. Les résultats numériques illustrent l'efficacité de l'approche proposée. La dernière contribution de la thèse consiste à proposer un nouveau concept appelé Stratégie de Redondance Universelle (SRU) pour les systèmes binaires et multi-états. La SRU inclut toutes les stratégies précédentes tout en offrant la possibilité d'explorer une variété d'autres options jamais explorées dans la littérature. Dans toutes les stratégies existantes, l'insertion de composantes redondantes est déclenchée par des défaillances spécifiques des composantes fonctionnelles, mais la stratégie nouvellement développée permet le changement des composantes redondantes en tout temps par des insertions ou des retraits séparés ou simultanés. Comme la SRU permet l'activation de n'importe quel nombre de composantes redondantes en tout temps, la redondance du système peut être configurée de façon optimale en changeant la configuration au temps optimal. Le concept de la SRU est illustré dans un contexte de maximisation de la fiabilité d'un système parallèle-série avec des composantes binaires. / Increasing the number of redundant components in a system is the most popular design method to increase reliability. In general, four strategies have been proposed in the literature: active, standby, mixed, and K-mixed. Redundancy strategies can be used in both binary and multi-state systems. The complexity of reliability calculation depends on the system configuration and properties. In the existing literature, there are some important limitations to redundancy strategies that have not been fully addressed in both binary and multi-state systems. The present thesis identifies and addresses some important and challenging issues through the following contributions. First, for binary systems, redundancy strategies present a high degree of computational complexity in reliability models, which in some cases provide lower bounds of the system reliability. To reduce this complexity, we propose a model based on Continuous Time Markov Chains (CTMC) for calculating the exact reliability of *k*-out-of-*n* systems under active, standby, mixed, and K-mixed redundancy strategies. Furthermore, a sequential Monte Carlo simulation model is developed, and a reliability analysis is conducted to validate the proposed model. A genetic algorithm is finally developed to solve an optimization problem resulting from the application of the existing strategies to series-parallel systems in the context of the proposed model. The second contribution of this thesis is related to multi-state systems, where components can have different performance levels. A reliability analysis is conducted for an aging multi-state system under a demand-based cold-standby redundancy strategy. Reliability is evaluated for different frequency ranges of inspection and maintenance. We also examine an aging power plant designed under a standby strategy, in which maintenance and rehabilitation operations are implemented. In order to determine the optimal frequency of inspection, maintenance and rehabilitation, while considering system reliability, a genetic algorithm is developed. This is the first time that this kind of reliability analysis and optimization is considered in the literature. The numerical results illustrate the effectiveness of the proposed approach. The last contribution of the thesis consists of proposing a new concept called Universal Redundancy Strategy (URS) for binary and multi-state systems. The URS includes all of the previous strategies while providing a variety of other options never explored in the literature. In all existing strategies, the insertion of redundant components has been triggered by specific failures of operating components, but the newly developed strategy allows for the change of redundant components at any time, by inserting or removing these components separately or simultaneously. As the URS allows any number of redundant components to be activated at any time, system redundancy can be configured optimally by changing the configuration at the optimal time. The URS concept is illustrated in the context of reliability maximization of a series-parallel system with binary components.

Yes / This paper investigates time-varying characteristics of illiquidity and the pricing of its risk using a liquidity-adjusted capital asset pricing model (L-CAPM). Collecting data from a pool of Eurozone countries between 1990 and 2018, we employ Markov switching models to assess the degree of persistence of illiquidity shocks. Contrary to prior research, which largely makes use of autoregressive (AR) processes, we provide strong evidence that illiquidity is time-varying and the persistence of shocks determines two distinct regimes characterised by high and low illiquidity. We assess pricing of illiquidity risk by developing and empirically testing a conditional L-CAPM model, where different regimes constitute priced risk factors for the cross-section of stock returns. We extend previous unconditional versions of L-CAPM models and we show that the various channels through which illiquidity affects asset returns and price of risks are time-varying. We find strong support for our conditional L-CAPM and our results are robust to alternative specifications and estimation techniques. These findings have important implications for portfolio management practices and are relevant to portfolio and risk managers and regulatory institutions.

The main focus of this thesis is Markovian decision processes with an emphasis on incorporating time-dependence into the system dynamics. When considering such decision processes, we provide value equations that apply to a large range of classes of Markovian decision processes, including Markov decision processes (MDPs) and semi-Markov decision processes (SMDPs), time-homogeneous or otherwise. We then formulate a simple decision process with exponential state transitions and solve this decision process using two separate techniques. The first technique solves the value equations directly, and the second utilizes an existing continuous-time MDP solution technique. To incorporate time-dependence into the transition dynamics of the process, we examine a particular decision process with state transitions determined by the Erlang distribution. Although this process is originally classed as a generalized semi-Markov decision process, we re-define it as a time-inhomogeneous SMDP. We show that even for a simply stated process with desirable state-space properties, the complexity of the value equations becomes so substantial that useful analytic expressions for the optimal solutions for all states of the process are unattainable. We develop a new technique, utilizing phase-type (PH) distributions, in an effort to address these complexity issues. By using PH representations, we construct a new state-space for the process, referred to as the phase-space, incorporating the phases of the state transition probability distributions. In performing this step, we effectively model the original process as a continuous-time MDP. The information available in this system is, however, richer than that of the original system. In the interest of maintaining the physical characteristics of the original system, we define a new valuation technique for the phase-space that shields some of this information from the decision maker. Using the process of phase-space construction and our valuation technique, we define an original system of value equations for this phasespace that are equivalent to those for the general Markovian decision processes mentioned earlier. An example of our own phase-space technique is given for the aforementioned Erlang decision process and we identify certain characteristics of the optimal solution such that, when applicable, the implementation of our phase-space technique is greatly simplified. These newly defined value equations for the phase-space are potentially as complex to solve as those defined for the original model. Restricting our focus to systems with acyclic state-spaces though, we describe a top-down approach to solution of the phase-space value equations for more general processes than those considered thus far. Again, we identify characteristics of the optimal solution to look for when implementing this technique and provide simplifications of the value equations where these characteristics are present. We note, however, that it is almost impossible to determine a priori the class of processes for which the simplifications outlined in our phase-space technique will be applicable. Nevertheless, we do no worse in terms of complexity by utilizing our phase-space technique, and leave open the opportunity to simplify the solution process if an appropriate situation arises. The phase-space technique can handle time-dependence in the state transition probabilities, but is insufficient for any process with time-dependent reward structures or discounting. To address such decision processes, we define an approximation technique for the solution of the class of infinite horizon decision processes whose state transitions and reward structures are described with reference to a single global clock. This technique discretizes time into exponentially distributed length intervals and incorporates this absolute time information into the state-space. For processes where the state-transitions are not exponentially distributed, we use the hazard rates of the transition probability distributions evaluated at the discrete time points to model the transition dynamics of the system. We provide a suitable reward structure approximation using our discrete time points and guidelines for sensible truncation, using an MDP approximation to the tail behaviour of the original infinite horizon process. The result is a finite-state time-homogeneous MDP approximation to the original process and this MDP may be solved using standard existing solution techniques. The approximate solution to the original process can then be inferred from the solution to our MDP approximation. / Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2008

Freiburg i. Br., Univ., Diss., 2005.