Dependability Modelling Under Uncertainty

Mechatronic design processes have become shorter and more parallelized, induced by growing time-to-market pressure. Methods that enable quantitative analysis in early design stages are required, should dependability analyses aim to influence the design. Due to the limited amount of data in this phase, the level of uncertainty is high and explicit modeling of these uncertainties becomes necessary. This work introduces new uncertainty-preserving dependability methods for early design stages. These include the propagation of uncertainty through dependability models, the activation of data from similar components for analyses and the integration of uncertain dependability predictions into an optimization framework. It is shown that Dempster-Shafer theory can be an alternative to probability theory in early design stage dependability predictions. Expert estimates can be represented, input uncertainty is propagated through the system and prediction uncertainty can be measured and interpreted. The resulting coherent methodology can be applied to represent the uncertainty in dependability models.

Mechatronic design processes have become shorter and more parallelized, induced by growing time-to-market pressure. Methods that enable quantitative analysis in early design stages are required, should dependability analyses aim to influence the design. Due to the limited amount of data in this phase, the level of uncertainty is high and explicit modeling of these uncertainties becomes necessary. This work introduces new uncertainty-preserving dependability methods for early design stages. These include the propagation of uncertainty through dependability models, the activation of data from similar components for analyses and the integration of uncertain dependability predictions into an optimization framework. It is shown that Dempster-Shafer theory can be an alternative to probability theory in early design stage dependability predictions. Expert estimates can be represented, input uncertainty is propagated through the system and prediction uncertainty can be measured and interpreted. The resulting coherent methodology can be applied to represent the uncertainty in dependability models.

The book focuses on system dependability modeling and calculation, considering the impact of s-dependency and uncertainty. The best suited approaches for practical system dependability modeling and calculation, (1) the minimal cut approach, (2) the Markov process approach, and (3) the Markov minimal cut approach as a combination of (1) and (2) are described in detail and applied to several examples. The stringently used Boolean logic during the whole development process of the approaches is the key for the combination of the approaches on a common basis. For large and complex systems, efficient approximation approaches, e.g. the probable Markov path approach, have been developed, which can take into account s-dependencies be-tween components of complex system structures. A comprehensive analysis of aleatory uncertainty (due to randomness) and epistemic uncertainty (due to lack of knowledge), and their combination, developed on the basis of basic reliability indices and evaluated with the Monte Carlo simulation method, has been carried out. The uncertainty impact on system dependability is investigated and discussed using several examples with different levels of difficulty. The applications cover a wide variety of large and complex (real-world) systems. Actual state-of-the-art definitions of terms of the IEC 60050-192:2015 standard, as well as the dependability indices, are used uniformly in all six chapters of the book.

Learn about the techniques used for evaluating the reliability and availability of engineered systems with this comprehensive guide.

The first part of the book defines the concept of uncertainties and the mathematical frameworks that will be used for uncertainty modeling. The application to system reliability assessment illustrates the concept. In the second part, evidential networks as a new tool to model uncertainty in reliability and risk analysis is proposed and described. Then it is applied on SIS performance assessment and in risk analysis of a heat sink. In the third part, Bayesian and evidential networks are used to deal with important measures evaluation in the context of uncertainties.

This book presents the latest research findings in the field of maintenance and safety of aging infrastructure. The invited contributions provide an overview of the use of advanced computational and/or experimental techniques in damage and vulnerability assessment as well as maintenance and retrofitting of aging structures and infrastructures such

Modelling has permeated virtually all areas of industrial, environmental, economic, bio-medical or civil engineering: yet the use of models for decision-making raises a number of issues to which this book is dedicated: How uncertain is my model ? Is it truly valuable to support decision-making ? What kind of decision can be truly supported and how can I handle residual uncertainty ? How much refined should the mathematical description be, given the true data limitations ? Could the uncertainty be reduced through more data, increased modeling investment or computational budget ? Should it be reduced now or later ? How robust is the analysis or the computational methods involved ? Should / could those methods be more robust ? Does it make sense to handle uncertainty, risk, lack of knowledge, variability or errors altogether ? How reasonable is the choice of probabilistic modeling for rare events ? How rare are the events to be considered ? How far does it make sense to handle extreme events and elaborate confidence figures ? Can I take advantage of expert / phenomenological knowledge to tighten the probabilistic figures ? Are there connex domains that could provide models or inspiration for my problem ? Written by a leader at the crossroads of industry, academia and engineering, and based on decades of multi-disciplinary field experience, Modelling Under Risk and Uncertainty gives a self-consistent introduction to the methods involved by any type of modeling development acknowledging the inevitable uncertainty and associated risks. It goes beyond the “black-box” view that some analysts, modelers, risk experts or statisticians develop on the underlying phenomenology of the environmental or industrial processes, without valuing enough their physical properties and inner modelling potential nor challenging the practical plausibility of mathematical hypotheses; conversely it is also to attract environmental or engineering modellers to better handle model confidence issues through finer statistical and risk analysis material taking advantage of advanced scientific computing, to face new regulations departing from deterministic design or support robust decision-making. Modelling Under Risk and Uncertainty: Addresses a concern of growing interest for large industries, environmentalists or analysts: robust modeling for decision-making in complex systems. Gives new insights into the peculiar mathematical and computational challenges generated by recent industrial safety or environmental control analysis for rare events. Implements decision theory choices differentiating or aggregating the dimensions of risk/aleatory and epistemic uncertainty through a consistent multi-disciplinary set of statistical estimation, physical modelling, robust computation and risk analysis. Provides an original review of the advanced inverse probabilistic approaches for model identification, calibration or data assimilation, key to digest fast-growing multi-physical data acquisition. Illustrated with one favourite pedagogical example crossing natural risk, engineering and economics, developed throughout the book to facilitate the reading and understanding. Supports Master/PhD-level course as well as advanced tutorials for professional training Analysts and researchers in numerical modeling, applied statistics, scientific computing, reliability, advanced engineering, natural risk or environmental science will benefit from this book.

The book deals with the application of various measures of information like the entropy, divergence, inaccuracy, etc. in modelling lifetimes of devices or equipment in reliability analysis. This is an emerging area of study and research during the last two decades and is of potential interest in many fields. In this work the classical measures of uncertainty are sufficiently modified to meet the needs of lifetime data analysis. The book provides an exhaustive collection of materials in a single volume to make it a comprehensive source of reference. The first treatise on the subject. It brings together the work that have appeared in journals on different disciplines. It will serve as a text for graduate students and practioners of special studies in information theory, as well as statistics and as a reference book for researchers. The book contains illustrative examples, tables and figures for clarifying the concepts and methodologies, the book is self-contained. It helps students to access information relevant to careers in industry, engineering, applied statistics, etc.