METHODS AND MODELS FOR ASSESSMENT OF RELIABILITY OF STRUCTURAL-COMPLEX SYSTEMS

The article presents the main propositions of logical-probabilistic method of analysis the assurance and enhancement of reliability of structurally complex systems, in which the structure of the system is described by means of mathematical logic and quantitative assessment of reliability is performed using probability theory. An example build script the dangerous condition and performed a quantitative investigation of the reliability of complex systems with interdependent basic events. The methods and models are implemented in a computer system that provides the ability to objectively assess the reliability and safety of structurally complex systems and solving problems of operational decision-making in complex emergencies.The article presents the main propositions of logical-probabilistic method of analysis the assurance and enhancement of reliability of structurally complex systems, in which the structure of the system is described by means of mathematical logic and quantitative assessment of reliability is performed using probability theory. An example build script the dangerous condition and performed a quantitative investigation of the reliability of complex systems with interdependent basic events. The methods and models are implemented in a computer system that provides the ability to objectively assess the reliability and safety of structurally complex systems and solving problems of operational decision-making in complex emergencies

IST Austria Thesis

This dissertation concerns the automatic verification of probabilistic systems and programs with arrays by statistical and logical methods. Although statistical and logical methods are different in nature, we show that they can be successfully combined for system analysis. In the first part of the dissertation we present a new statistical algorithm for the verification of probabilistic systems with respect to unbounded properties, including linear temporal logic. Our algorithm often performs faster than the previous approaches, and at the same time requires less information about the system. In addition, our method can be generalized to unbounded quantitative properties such as mean-payoff bounds. In the second part, we introduce two techniques for comparing probabilistic systems. Probabilistic systems are typically compared using the notion of equivalence, which requires the systems to have the equal probability of all behaviors. However, this notion is often too strict, since probabilities are typically only empirically estimated, and any imprecision may break the relation between processes. On the one hand, we propose to replace the Boolean notion of equivalence by a quantitative distance of similarity. For this purpose, we introduce a statistical framework for estimating distances between Markov chains based on their simulation runs, and we investigate which distances can be approximated in our framework. On the other hand, we propose to compare systems with respect to a new qualitative logic, which expresses that behaviors occur with probability one or a positive probability. This qualitative analysis is robust with respect to modeling errors and applicable to many domains. In the last part, we present a new quantifier-free logic for integer arrays, which allows us to express counting. Counting properties are prevalent in array-manipulating programs, however they cannot be expressed in the quantified fragments of the theory of arrays. We present a decision procedure for our logic, and provide several complexity results

Compositional Probabilistic Analysis of Temporal Properties over Stochastic Detectors

Run-time monitoring is a vital part of safety-critical systems. However, early-stage assurance of monitoring quality is currently limited: it relies either on complex models that might be inaccurate in unknown ways, or on data that would only be available once the system has been built. To address this issue, we propose a compositional framework for modeling and analysis of noisy monitoring systems. Our novel 3-value detector model uses probability spaces to represent atomic (non-composite) detectors, and it composes them into a temporal logic-based monitor. The error rates of these monitors are estimated by our analysis engine, which combines symbolic probability algebra, independence inference, and estimation from labeled detection data. Our evaluation on an autonomous underwater vehicle found that our framework produces accurate estimates of error rates while using only detector traces, without any monitor traces. Furthermore, when data is scarce, our approach shows higher accuracy than non-compositional data-driven estimates from monitor traces. Thus, this work enables accurate evaluation of logical monitors in early design stages before deploying them

On quantum statistics in data analysis

Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the other hand, it is well known that the lattices of concepts, that arise in data analysis, are in general also non-distributive, albeit for completely different reasons. In his recent book, van Rijsbergen argues that many of the logical tools developed for quantum systems are also suitable for applications in information retrieval. I explore the mathematical support for this idea on an abstract vector space model, covering several forms of data analysis (information retrieval, data mining, collaborative filtering, formal concept analysis...), and roughly based on an idea from categorical quantum mechanics. It turns out that quantum (i.e., noncommutative) probability distributions arise already in this rudimentary mathematical framework. We show that a Bell-type inequality must be satisfied by the standard similarity measures, if they are used for preference predictions. The fact that already a very general, abstract version of the vector space model yields simple counterexamples for such inequalities seems to be an indicator of a genuine need for quantum statistics in data analysis.Comment: 7 pages, Quantum Interaction 2008 (Oxford, April 2008) v3: added two diagrams, changed some wording

Implementation of Knowledge-Based Expert System Using Probabilistic Network Models

The latest development in machine learning techniques has enabled the development of intelligent tools which can identify anomalies in the system in real time. These intelligent tools become expert systems when they combine the algorithmic result of root cause analysis with the domain knowledge. Truth maintenance, fuzzy logic, ontology classification are just a few out of many techniques used in building these systems. Logic is embedded in the code in most of the traditional computer program, which makes it difficult for domain experts to retrieve the underlying rule set and make any changes. These system bridge the gap by making information explicit rather than implicit. In this paper, we present a new approach for developing an expert system using decision tree analysis with probabilistic network models such as Bayes-network. The proposed model facilitate the process of correlation between belief probability with the unseen data by use of logical flowcharting, loopy belief propagation algorithm, and decision trees analysis. The performance of the model will be measured by evaluation and cross validation techniques