On the reliability of multistate systems with imprecise probabilities

Розглядається обчислення надійності в складних системах за наявності випадкового набору оцінок працездатності елементів. Виявлено, що підхід Демпстер-Шефера є відповідним математичним інструментом, який відповідає поставленим задачам. Для випадку, коли взаємозалежності елементів невідомі, наведено також оцінки ефективності системи переконань і правдоподібність функції.Рассматривается вычисления надежности в сложных системах при наличии случайного набора оце- нок работоспособности элементов. Выявлено, что подход Демпстер-Шефера является соответствующим математическим инструментом, который соответствует поставленным задачам. Для случая, когда взаимозависимости элементов неизвестны, приведены также оценки эффективности системы убеждений и правдоподобность функции.We consider the computation of multistate systems reliabilities in the presence of random set estimations for the elements' working abilities. It turns out that the Dempster-Shafer approach is a suitable mathematical tool. For the case that the interdependence of the elements is unknown, bounds for the system's performance belief and plausibility functions are given as well

Fuzzy Reliability Assessment of Systems with Multiple Dependent Competing Degradation Processes

International audienceComponents are often subject to multiple competing degradation processes. For multi-component systems, the degradation dependency within one component or/and among components need to be considered. Physics-based models (PBMs) and multi-state models (MSMs) are often used for component degradation processes, particularly when statistical data are limited. In this paper, we treat dependencies between degradation processes within a piecewise-deterministic Markov process (PDMP) modeling framework. Epistemic (subjective) uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters: to take into account this, we describe the parameters of the PDMP model as fuzzy numbers. Then, we extend the finite-volume (FV) method to quantify the (fuzzy) reliability of the system. The proposed method is tested on one subsystem of the residual heat removal system (RHRS) of a nuclear power plant, and a comparison is offered with a Monte Carlo (MC) simulation solution: the results show that our method can be most efficient

Population Models: Flexibility, Advances, and Applications to Wildlife Conservation. The Bonelli’s Eagle as a Study Case

[eng] In this thesis, we took advantage of recent advances in the degree of sophistication and flexibility of population models to study the population dynamics and conservation of long-lived species. As main objective, we aimed at understanding the effects of permanent emigration in the estimation of survival from mark-recapture analyses and its multiple implications for the interpretation of population dynamics and the reliability of population viability projections. In second term, we aimed at generating evidence-based knowledge based on quantitative population analysis to guide the management of long-lived raptors. To address these issues, we used two populations of the long-lived Bonelli’s eagle as study cases (Catalonia and Mallorca, western Mediterranean), for which extensive demographic and ecological data were available. The thesis was divided into the four following chapters. In Chapter 1, we implemented individual-based population viability analyses (PVA) to evaluate the effectiveness of different release strategies used in the reintroduction of the Bonelli’s eagle in Mallorca. Our results suggested that relocating wild-reared nonjuvenile raptors from natural populations to reintroduction areas may better favour reintroduction success in comparison to more expensive, widely implemented alternatives based on captive breeding. The better performance of relocations was related to their capacity to promote early reproduction in the reintroduction area, which may enhance population growth. In Chapter 2, we developed a spatially-explicit capture-mark-recapture model adapted to the multistate formulation to separate true survival and permanent emigration in longlived species. In addition, we compared the obtained stage-structured true survival estimates to apparent survival estimates. Our results showed that the magnitude of the differences between true and apparent survival may vary across population stages in longlived species (i.e., age, sex, breeding status) because of intrapopulation variation in the effect of permanent emigration. In addition, our findings suggested that the use of heavytailed distributions to model natal dispersal may provide more effective separations of true survival and permanent emigration in cases of mark-recapture data limited to restricted study areas. In Chapter 3, we integrated the model developed in chapter 2 into a spatially-explicit Integrated Population Model (SEIPM) aimed at insightfully describing the long-term dynamics of the Bonelli’s eagle population in Catalonia (1986-2020) and extracting relevant knowledge for long-lived species demography. The use of SEIPMs enabled an explicit estimation of emigration, immigration, and sink-source status along time, together with key demographic parameters and the dynamics of relevant population stages. Our results allowed a deep understanding of the retrospective dynamics of the study population and revealed new insights about the long-term variations of sink-source status and floater populations in long-lived species. In Chapter 4, we used the estimates of apparent and true survival from chapter 2 to compare the outcomes of PVAs using both types of estimates and their respective fits to census data. In addition, we explicitly modelled emigration and immigration to evaluate how these processes may improve or decrease the fits of PVAs based on each type of survival estimate. Our results suggested that each of both survival types may only provide accurate PVA projections in specific population scenarios where emigration and immigration match the particularities of each type of estimate. Thus, we emphasized the importance of either modelling migration processes or using calibration to real data for accurate PVA outcomes. In conclusion, this thesis provided useful extensions of demographic models for the estimation of true survival and the fine-scale study of population dynamics in long-lived species. In addition, important insights were revealed about the reliability of PVA outcomes relative to the characteristics of survival estimates. Finally, the thesis emphasized the relevance of generating evidence-based knowledge from the analysis of quantitative data for conservation decision-making.[cat] Aquesta tesi utilitza els avenços recents en el grau de sofisticació i la flexibilitat dels models poblacions per a generar coneixement rellevant per a l’estudi de la dinàmica de poblacions i la conservació d’espècies de vida llarga. Com a objectiu principal, la tesi se centra en entendre els efectes de la migració permanent en l’estimació de supervivència en anàlisis de captura-recaptura, així com els efectes que això pot tenir per a la interpretació de la demografia, les estimes de viabilitat, l’estat de conservació i la gestió de les poblacions de vida llarga. En segon pla, la tesi se centra en generar coneixement basat en evidències quantitatives per guiar la gestió d’aus rapinyaires de vida llarga. Per afrontar aquests objectius, hem utilitzat com a casos d’estudi dues poblacions de l’àliga perdiguera (Catalunya i l’illa de Mallorca), de les quals es disposa d’una extensa quantitat de dades de seguiment demogràfic i ecològic. La tesi s’ha dividit en els següents capítols: Al Capítol 1, es van desenvolupar anàlisis de viabilitat poblacional basades en individus (PVA) per avaluar l’efectivitat de les diferents estratègies d’alliberament emprades en la reintroducció de l’àliga perdiguera a Mallorca. Els resultats suggerien que la translocació d’individus no-polls salvatges d’altres poblacions cap a l’àrea de reintroducció afavoria l’èxit de la reintroducció en comparació amb altres metodologies més cares basades en la cria en captivitat. Aquesta major efectivitat estava lligada a la capacitat de les translocacions de no-polls d’accelerar una ràpida reproducció a l’àrea d’estudi, fet que promovia un ràpid creixement poblacional. Al Capítol 2, vam desenvolupar models de captura-recaptura espacialment explícits adaptats a la formulació multi-estat per estimar separadament supervivència real i migració permanent en espècies de vida llarga. Les estimes de supervivència real obtingudes, estructurades per fracció poblacional, van ser comparades amb estimes de supervivència aparent. Les comparacions mostraven que aquestes diferències variaven en intensitat al llarg de les diferents fraccions (edat, sexe, estat reproductor) degut a variacions intrapoblacionals en l’efecte de la migració permanent. Per altra banda, els nostres resultats suggereixen que l’ús de distribucions estadístiques de cua ampla per modelar dispersió natal poden ajudar a separar supervivència real i migració permanent de manera més efectiva quan les dades disponibles sobre captura-recaptura estan restringides a l’àrea d’estudi. Al Capítol 3, vam incorporar el model desenvolupat al capítol 2 dins un model integrat poblacional espacialment explícit (SEIPM) amb l’objectiu de descriure detalladament la dinàmica de la població d’àliga perdiguera a Catalunya durant les darreres quatre dècades (1986-2020), i extreure coneixement general rellevant sobre la demografia de les espècies de vida llarga. L’ús de SEIPMs va permetre una estimació explícita dels processos d’immigració i emigració, així com de l’estat font-embornal de la població al llarg del temps, juntament amb paràmetres demogràfics clau i la dinàmica d’importants fraccions poblacionals. Els resultats van permetre entendre detalladament la dinàmica retrospectiva de la població, i van revelar nous aspectes sobre la demografia de les poblacions flotants i les dinàmiques font embornal a llarg termini. Al Capítol 4, vam emprar les estimes de supervivència aparent i real del capítol 2 per comparar els resultats de PVAs basats en ambdós tipus d’estimes i el respectiu ajust de cada model a dades reals de cens. A més, vam modelar de manera explícita emigració i immigració per avaluar com aquests dos processos poden millorar o empobrir l’ajust dels models basats en els dos tipus d’estima de supervivència. Els resultats mostraven que ambdues supervivències només tenien capacitat de generar estimes precises de viabilitat en escenaris poblacionals específics on els processos d’emigració i immigració tinguessin unes magnituds molt concretes. En conseqüència, vam subratllar la importància de modelitzar processos migratoris dins els PVAs - o bé de calibrar els resultats amb dades reals - per millorar la fiabilitat d’aquests models. En resum, en aquesta tesi s’han desenvolupat extensions de models poblacionals per a l’estimació de supervivència real i l’estudi detallat de les dinàmiques poblacionals en espècies de vida llarga. A més, la tesi ha aportat troballes importants sobre la fiabilitat i la precisió dels PVAs segons les particularitats de les estimes de supervivència emprades. Finalment, s’hi ha destacat la importància de generar coneixement basat en l’evidència científica per a la gestió de poblacions salvatges a través de models poblacionals

Uncertainty in Engineering

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners

Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective

Armitage Lecture 2011: The Design and Analysis of Life History Studies

This is the peer reviewed version of the following article: Lawless, J.F. (2013). Armitage Lecture 2011: the design and analysis of life history studies. Statistics in Medicine, 32 (13), 2155--2172, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/sim.5754/full. DOI: 10.1002/sim.5754 This article may be used for non-commercial purposes in accordance with http://olabout.wiley.com/WileyCDA/Section/id-828039.html Wiley Terms and Conditions for Self-ArchivingLife history studies collect information on events and other outcomes during people’s lifetimes. For example, these may be related to childhood development, education, fertility, health, or employment. Such longitudinal studies have constraints on the selection of study members, the duration and frequency of follow-up, and the accuracy and completeness of information obtained. These constraints, along with factors associated with the definition and measurement of certain outcomes, affect our ability to understand, model, and analyze life history processes. My objective here is to discuss and illustrate some issues associated with the design and analysis of life history studies.Natural Sciences and Engineering Research Council of Canada || JFL RGPIN 859

Uncertainty in Engineering

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners

Un cadre holistique de la modélisation de la dégradation pour l’analyse de fiabilité et optimisation de la maintenance de systèmes de sécurité nucléaires

Components of nuclear safety systems are in general highly reliable, which leads to a difficulty in modeling their degradation and failure behaviors due to the limited amount of data available. Besides, the complexity of such modeling task is increased by the fact that these systems are often subject to multiple competing degradation processes and that these can be dependent under certain circumstances, and influenced by a number of external factors (e.g. temperature, stress, mechanical shocks, etc.). In this complicated problem setting, this PhD work aims to develop a holistic framework of models and computational methods for the reliability-based analysis and maintenance optimization of nuclear safety systems taking into account the available knowledge on the systems, degradation and failure behaviors, their dependencies, the external influencing factors and the associated uncertainties.The original scientific contributions of the work are: (1) For single components, we integrate random shocks into multi-state physics models for component reliability analysis, considering general dependencies between the degradation and two types of random shocks. (2) For multi-component systems (with a limited number of components):(a) a piecewise-deterministic Markov process modeling framework is developed to treat degradation dependency in a system whose degradation processes are modeled by physics-based models and multi-state models; (b) epistemic uncertainty due to incomplete or imprecise knowledge is considered and a finite-volume scheme is extended to assess the (fuzzy) system reliability; (c) the mean absolute deviation importance measures are extended for components with multiple dependent competing degradation processes and subject to maintenance; (d) the optimal maintenance policy considering epistemic uncertainty and degradation dependency is derived by combining finite-volume scheme, differential evolution and non-dominated sorting differential evolution; (e) the modeling framework of (a) is extended by including the impacts of random shocks on the dependent degradation processes.(3) For multi-component systems (with a large number of components), a reliability assessment method is proposed considering degradation dependency, by combining binary decision diagrams and Monte Carlo simulation to reduce computational costs.Composants de systèmes de sûreté nucléaire sont en général très fiable, ce qui conduit à une difficulté de modéliser leurs comportements de dégradation et d'échec en raison de la quantité limitée de données disponibles. Par ailleurs, la complexité de cette tâche de modélisation est augmentée par le fait que ces systèmes sont souvent l'objet de multiples processus concurrents de dégradation et que ceux-ci peut être dépendants dans certaines circonstances, et influencé par un certain nombre de facteurs externes (par exemple la température, le stress, les chocs mécaniques, etc.).Dans ce cadre de problème compliqué, ce travail de thèse vise à développer un cadre holistique de modèles et de méthodes de calcul pour l'analyse basée sur la fiabilité et la maintenance d'optimisation des systèmes de sûreté nucléaire en tenant compte des connaissances disponibles sur les systèmes, les comportements de dégradation et de défaillance, de leurs dépendances, les facteurs influençant externes et les incertitudes associées.Les contributions scientifiques originales dans la thèse sont:(1) Pour les composants simples, nous intégrons des chocs aléatoires dans les modèles de physique multi-états pour l'analyse de la fiabilité des composants qui envisagent dépendances générales entre la dégradation et de deux types de chocs aléatoires.(2) Pour les systèmes multi-composants (avec un nombre limité de composants):(a) un cadre de modélisation de processus de Markov déterministes par morceaux est développé pour traiter la dépendance de dégradation dans un système dont les processus de dégradation sont modélisées par des modèles basés sur la physique et des modèles multi-états; (b) l'incertitude épistémique à cause de la connaissance incomplète ou imprécise est considéré et une méthode volumes finis est prolongée pour évaluer la fiabilité (floue) du système; (c) les mesures d'importance de l'écart moyen absolu sont étendues pour les composants avec multiples processus concurrents dépendants de dégradation et soumis à l'entretien; (d) la politique optimale de maintenance compte tenu de l'incertitude épistémique et la dépendance de dégradation est dérivé en combinant schéma volumes finis, évolution différentielle et non-dominée de tri évolution différentielle; (e) le cadre de la modélisation de (a) est étendu en incluant les impacts des chocs aléatoires sur les processus dépendants de dégradation.(3) Pour les systèmes multi-composants (avec un grand nombre de composants), une méthode d'évaluation de la fiabilité est proposé considérant la dépendance dégradation en combinant des diagrammes de décision binaires et simulation de Monte Carlo pour réduire le coût de calcul

The Pseudo-Pascal Triangle of Maximum Deng Entropy

PPascal triangle (known as Yang Hui Triangle in Chinese) is an important model in mathematics while the entropy has been heavily studied in physics or as uncertainty measure in information science. How to construct the the connection between Pascal triangle and uncertainty measure is an interesting topic. One of the most used entropy, Tasllis entropy, has been modelled with Pascal triangle. But the relationship of the other entropy functions with Pascal triangle is still an open issue. Dempster-Shafer evidence theory takes the advantage to deal with uncertainty than probability theory since the probability distribution is generalized as basic probability assignment, which is more efficient to model and handle uncertain information. Given a basic probability assignment, its corresponding uncertainty measure can be determined by Deng entropy, which is the generalization of Shannon entropy. In this paper, a Pseudo-Pascal triangle based the maximum Deng entropy is constructed. Similar to the Pascal triangle modelling of Tasllis entropy, this work provides the a possible way of Deng entropy in physics and information theory

Efficient resilience analysis and decision-making for complex engineering systems

Modern societies around the world are increasingly dependent on the smooth functionality of progressively more complex systems, such as infrastructure systems, digital systems like the internet, and sophisticated machinery. They form the cornerstones of our technologically advanced world and their efficiency is directly related to our well-being and the progress of society. However, these important systems are constantly exposed to a wide range of threats of natural, technological, and anthropogenic origin. The emergence of global crises such as the COVID-19 pandemic and the ongoing threat of climate change have starkly illustrated the vulnerability of these widely ramified and interdependent systems, as well as the impossibility of predicting threats entirely. The pandemic, with its widespread and unexpected impacts, demonstrated how an external shock can bring even the most advanced systems to a standstill, while the ongoing climate change continues to produce unprecedented risks to system stability and performance. These global crises underscore the need for systems that can not only withstand disruptions, but also, recover from them efficiently and rapidly. The concept of resilience and related developments encompass these requirements: analyzing, balancing, and optimizing the reliability, robustness, redundancy, adaptability, and recoverability of systems -- from both technical and economic perspectives. This cumulative dissertation, therefore, focuses on developing comprehensive and efficient tools for resilience-based analysis and decision-making of complex engineering systems. The newly developed resilience decision-making procedure is at the core of these developments. It is based on an adapted systemic risk measure, a time-dependent probabilistic resilience metric, as well as a grid search algorithm, and represents a significant innovation as it enables decision-makers to identify an optimal balance between different types of resilience-enhancing measures, taking into account monetary aspects. Increasingly, system components have significant inherent complexity, requiring them to be modeled as systems themselves. Thus, this leads to systems-of-systems with a high degree of complexity. To address this challenge, a novel methodology is derived by extending the previously introduced resilience framework to multidimensional use cases and synergistically merging it with an established concept from reliability theory, the survival signature. The new approach combines the advantages of both original components: a direct comparison of different resilience-enhancing measures from a multidimensional search space leading to an optimal trade-off in terms of system resilience, and a significant reduction in computational effort due to the separation property of the survival signature. It enables that once a subsystem structure has been computed -- a typically computational expensive process -- any characterization of the probabilistic failure behavior of components can be validated without having to recompute the structure. In reality, measurements, expert knowledge, and other sources of information are loaded with multiple uncertainties. For this purpose, an efficient method based on the combination of survival signature, fuzzy probability theory, and non-intrusive stochastic simulation (NISS) is proposed. This results in an efficient approach to quantify the reliability of complex systems, taking into account the entire uncertainty spectrum. The new approach, which synergizes the advantageous properties of its original components, achieves a significant decrease in computational effort due to the separation property of the survival signature. In addition, it attains a dramatic reduction in sample size due to the adapted NISS method: only a single stochastic simulation is required to account for uncertainties. The novel methodology not only represents an innovation in the field of reliability analysis, but can also be integrated into the resilience framework. For a resilience analysis of existing systems, the consideration of continuous component functionality is essential. This is addressed in a further novel development. By introducing the continuous survival function and the concept of the Diagonal Approximated Signature as a corresponding surrogate model, the existing resilience framework can be usefully extended without compromising its fundamental advantages. In the context of the regeneration of complex capital goods, a comprehensive analytical framework is presented to demonstrate the transferability and applicability of all developed methods to complex systems of any type. The framework integrates the previously developed resilience, reliability, and uncertainty analysis methods. It provides decision-makers with the basis for identifying resilient regeneration paths in two ways: first, in terms of regeneration paths with inherent resilience, and second, regeneration paths that lead to maximum system resilience, taking into account technical and monetary factors affecting the complex capital good under analysis. In summary, this dissertation offers innovative contributions to efficient resilience analysis and decision-making for complex engineering systems. It presents universally applicable methods and frameworks that are flexible enough to consider system types and performance measures of any kind. This is demonstrated in numerous case studies ranging from arbitrary flow networks, functional models of axial compressors to substructured infrastructure systems with several thousand individual components.Moderne Gesellschaften sind weltweit zunehmend von der reibungslosen Funktionalität immer komplexer werdender Systeme, wie beispielsweise Infrastruktursysteme, digitale Systeme wie das Internet oder hochentwickelten Maschinen, abhängig. Sie bilden die Eckpfeiler unserer technologisch fortgeschrittenen Welt, und ihre Effizienz steht in direktem Zusammenhang mit unserem Wohlbefinden sowie dem Fortschritt der Gesellschaft. Diese wichtigen Systeme sind jedoch einer ständigen und breiten Palette von Bedrohungen natürlichen, technischen und anthropogenen Ursprungs ausgesetzt. Das Auftreten globaler Krisen wie die COVID-19-Pandemie und die anhaltende Bedrohung durch den Klimawandel haben die Anfälligkeit der weit verzweigten und voneinander abhängigen Systeme sowie die Unmöglichkeit einer Gefahrenvorhersage in voller Gänze eindrücklich verdeutlicht. Die Pandemie mit ihren weitreichenden und unerwarteten Auswirkungen hat gezeigt, wie ein externer Schock selbst die fortschrittlichsten Systeme zum Stillstand bringen kann, während der anhaltende Klimawandel immer wieder beispiellose Risiken für die Systemstabilität und -leistung hervorbringt. Diese globalen Krisen unterstreichen den Bedarf an Systemen, die nicht nur Störungen standhalten, sondern sich auch schnell und effizient von ihnen erholen können. Das Konzept der Resilienz und die damit verbundenen Entwicklungen umfassen diese Anforderungen: Analyse, Abwägung und Optimierung der Zuverlässigkeit, Robustheit, Redundanz, Anpassungsfähigkeit und Wiederherstellbarkeit von Systemen -- sowohl aus technischer als auch aus wirtschaftlicher Sicht. In dieser kumulativen Dissertation steht daher die Entwicklung umfassender und effizienter Instrumente für die Resilienz-basierte Analyse und Entscheidungsfindung von komplexen Systemen im Mittelpunkt. Das neu entwickelte Resilienz-Entscheidungsfindungsverfahren steht im Kern dieser Entwicklungen. Es basiert auf einem adaptierten systemischen Risikomaß, einer zeitabhängigen, probabilistischen Resilienzmetrik sowie einem Gittersuchalgorithmus und stellt eine bedeutende Innovation dar, da es Entscheidungsträgern ermöglicht, ein optimales Gleichgewicht zwischen verschiedenen Arten von Resilienz-steigernden Maßnahmen unter Berücksichtigung monetärer Aspekte zu identifizieren. Zunehmend weisen Systemkomponenten eine erhebliche Eigenkomplexität auf, was dazu führt, dass sie selbst als Systeme modelliert werden müssen. Hieraus ergeben sich Systeme aus Systemen mit hoher Komplexität. Um diese Herausforderung zu adressieren, wird eine neue Methodik abgeleitet, indem das zuvor eingeführte Resilienzrahmenwerk auf multidimensionale Anwendungsfälle erweitert und synergetisch mit einem etablierten Konzept aus der Zuverlässigkeitstheorie, der Überlebenssignatur, zusammengeführt wird. Der neue Ansatz kombiniert die Vorteile beider ursprünglichen Komponenten: Einerseits ermöglicht er einen direkten Vergleich verschiedener Resilienz-steigernder Maßnahmen aus einem mehrdimensionalen Suchraum, der zu einem optimalen Kompromiss in Bezug auf die Systemresilienz führt. Andererseits ermöglicht er durch die Separationseigenschaft der Überlebenssignatur eine signifikante Reduktion des Rechenaufwands. Sobald eine Subsystemstruktur berechnet wurde -- ein typischerweise rechenintensiver Prozess -- kann jede Charakterisierung des probabilistischen Ausfallverhaltens von Komponenten validiert werden, ohne dass die Struktur erneut berechnet werden muss. In der Realität sind Messungen, Expertenwissen sowie weitere Informationsquellen mit vielfältigen Unsicherheiten belastet. Hierfür wird eine effiziente Methode vorgeschlagen, die auf der Kombination von Überlebenssignatur, unscharfer Wahrscheinlichkeitstheorie und nicht-intrusiver stochastischer Simulation (NISS) basiert. Dadurch entsteht ein effizienter Ansatz zur Quantifizierung der Zuverlässigkeit komplexer Systeme unter Berücksichtigung des gesamten Unsicherheitsspektrums. Der neue Ansatz, der die vorteilhaften Eigenschaften seiner ursprünglichen Komponenten synergetisch zusammenführt, erreicht eine bedeutende Verringerung des Rechenaufwands aufgrund der Separationseigenschaft der Überlebenssignatur. Er erzielt zudem eine drastische Reduzierung der Stichprobengröße aufgrund der adaptierten NISS-Methode: Es wird nur eine einzige stochastische Simulation benötigt, um Unsicherheiten zu berücksichtigen. Die neue Methodik stellt nicht nur eine Neuerung auf dem Gebiet der Zuverlässigkeitsanalyse dar, sondern kann auch in das Resilienzrahmenwerk integriert werden. Für eine Resilienzanalyse von real existierenden Systemen ist die Berücksichtigung kontinuierlicher Komponentenfunktionalität unerlässlich. Diese wird in einer weiteren Neuentwicklung adressiert. Durch die Einführung der kontinuierlichen Überlebensfunktion und dem Konzept der Diagonal Approximated Signature als entsprechendes Ersatzmodell kann das bestehende Resilienzrahmenwerk sinnvoll erweitert werden, ohne seine grundlegenden Vorteile zu beeinträchtigen. Im Kontext der Regeneration komplexer Investitionsgüter wird ein umfassendes Analyserahmenwerk vorgestellt, um die Übertragbarkeit und Anwendbarkeit aller entwickelten Methoden auf komplexe Systeme jeglicher Art zu demonstrieren. Das Rahmenwerk integriert die zuvor entwickelten Methoden der Resilienz-, Zuverlässigkeits- und Unsicherheitsanalyse. Es bietet Entscheidungsträgern die Basis für die Identifikation resilienter Regenerationspfade in zweierlei Hinsicht: Zum einen im Sinne von Regenerationspfaden mit inhärenter Resilienz und zum anderen Regenerationspfade, die zu einer maximalen Systemresilienz unter Berücksichtigung technischer und monetärer Einflussgrößen des zu analysierenden komplexen Investitionsgutes führen. Zusammenfassend bietet diese Dissertation innovative Beiträge zur effizienten Resilienzanalyse und Entscheidungsfindung für komplexe Ingenieursysteme. Sie präsentiert universell anwendbare Methoden und Rahmenwerke, die flexibel genug sind, um beliebige Systemtypen und Leistungsmaße zu berücksichtigen. Dies wird in zahlreichen Fallstudien von willkürlichen Flussnetzwerken, funktionalen Modellen von Axialkompressoren bis hin zu substrukturierten Infrastruktursystemen mit mehreren tausend Einzelkomponenten demonstriert