Formal Reasoning about Expectation Properties for Continuous Random Variables

Hasan, Osman; Abbasi, Naeem; Akbarpour, Behzad; Tahar, Sofiène; Akbarpour, R.

doi:10.1007/978-3-642-05089-3_28

Cited by 20 publications

(10 citation statements)

References 14 publications

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“…[17,18,19]). Hurd's formalization of probability theory [17] has been utilized to verify sampling algorithms of a number of commonly used discrete [17] and continuous random variables [20] based on their probabilistic and statistical properties [21,22]. Moreover, this formalization has been used to conduct the reliability analysis of a number of applications, such as memory arrays [23], soft errors [24] and electronic components [25].…”

Section: Introductionmentioning

confidence: 99%

Towards the Formal Reliability Analysis of Oil and Gas Pipelines

Ahmad

Hasan

Tahar

et al. 2014

Lecture Notes in Computer Science

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It is customary to assess the reliability of underground oil and gas pipelines in the presence of excessive loading and corrosion effects to ensure a leak-free transport of hazardous materials. The main idea behind this reliability analysis is to model the given pipeline system as a Reliability Block Diagram (RBD) of segments such that the reliability of an individual pipeline segment can be represented by a random variable. Traditionally, computer simulation is used to perform this reliability analysis but it provides approximate results and requires an enormous amount of CPU time for attaining reasonable estimates. Due to its approximate nature, simulation is not very suitable for analyzing safety-critical systems like oil and gas pipelines, where even minor analysis flaws may result in catastrophic consequences. As an accurate alternative, we propose to use a higher-order-logic theorem prover (HOL) for the reliability analysis of pipelines. As a first step towards this idea, this paper provides a higher-order-logic formalization of reliability and the series RBD using the HOL theorem prover. For illustration, we present the formal analysis of a simple pipeline that can be modeled as a series RBD of segments with exponentially distributed failure times.Comment: 15 page

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Section: Introductionmentioning

confidence: 99%

Towards the Formal Reliability Analysis of Oil and Gas Pipelines

Ahmad

Hasan

Tahar

et al. 2014

Lecture Notes in Computer Science

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“…A number of higher-order-logic formalizations of probability theory are available in higher-order logic (e.g., [72,73,74]) and have been utilized to verify sampling algorithms of a number of commonly used discrete [72] and continuous random variables [75] based on their probabilistic and statistical properties [76,77]. Moreover, this formalization has been used to conduct the reliability analysis of a number of applications, such as memory arrays [78], soft errors [79], electronic components [80] and oil and gas pipelines [81].…”

Section: Higher-order-logic Theorem Provingmentioning

confidence: 99%

Reliability modeling and analysis of communication networks

Ahmed

Hasan

Pervez

et al. 2017

Journal of Network and Computer Applications

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In recent times, the functioning of various aspects of modern society-ranging from the various infrastructural utilities such as electrical power, water to socio-economical aspects such as telecommunications, business, commerce, education-has become critically reliant on communication networks, and particularly on the Internet. With the migration of critical facilities to the Internet, it has become vitally important to ensure the reliability and availability of networks. In this paper, we study various modeling and analysis techniques that can aid in the study of reliability of communication networks. In this regard, we provide background on the modeling techniques (such as reliability block diagrams, fault trees, Markov chains, etc.) and analysis techniques (such as mathematical analytical methods, simulation methods, and formal methods). Apart from providing the necessary background, we also critically evaluate the pros and cons of different approaches, and provide a detailed survey of their applications in communication networks. To the best of our knowledge, this is the first in-depth review of the application of reliability modeling and analysis techniques in communication networks. work, the ability of a network to maintain an acceptable reliability level under extreme environmental conditions and assess the impact of design changes on the reliability of the overall network [17]. Similarly, the availability prediction allows us to evaluate various maintenance design options to achieve the desired availability of the network [18].The qualitative and quantitative reliability analysis requires the selection of an appropriate mathematical modeling and analysis technique. The modeling technique must be able to effectively capture the important parameters of the real system and the analysis technique should be capable of providing insights into the system behavior without running (or executing) the real system. There are numerous techniques that can provide analysis in the early phase, when only initial details are available of the design, and there are other techniques that cater the analysis of the later design phases, when more precise implementation details are available [16]. Some of the most widely used formalisms/techniques for modeling reliability and availability of communication networks are: Reliability Block Diagram (RBD) [19], Fault Tree (FT) [20], and Markov Chain (MC) [21]. Traditionally, the models developed using these techniques are analyzed using analytical methods or simulation tools.Recently, the computer networks community has shown great interest in the utilization of formal methods [22] as a reliability analysis technique for communication networks. Formal methods use mathematical logic to precisely model the system's intended behavior and deploy mathematical reasoning to construct an irrefutable proof that the given system satisfies its requirements. This kind of mathematical modeling and analysis makes formal methods an accurate and rigorous analysis method compared to the traditional a...

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“…The expectation of a continuous random variable has been formally defined in [Hasan, 2009b] using the Lebesgue integral, which has strong relationship with the measure theory fundamentals [Galambos, 1995]. This definition is general enough to cater for both discrete and continuous random variables and is thus far more superior than the commonly used Rieman integral based definition that is only applicable to continuous random variables with well-defined PDF.…”

Section: Statistical Properties For Continuous Random Variablesmentioning

confidence: 99%

“…Though, the main limitation of the Lebesgue integral based definition is the complex reasoning process involved for verifying expectation properties. This limitation has been tackled in [Hasan, 2009b] and the main idea is to verify two relatively simplified expressions for expectation by building on top of the Lebesgue integral based definition. The first expression is for the case when the given continuous random variable is bounded in the positive interval [a,b] and the second one is for an unbounded random variable.…”

Section: Statistical Properties For Continuous Random Variablesmentioning

confidence: 99%

Reconfigurable Embedded Control Systems

2011

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Product or company names used in this set are for identification purposes only. Inclusion of the names of the products or companies does not indicate a claim of ownership by IGI Global of the trademark or registered trademark. Library of Congress Cataloging-in-Publication Data Reconfigurable embedded control systems : applications for flexibility and agility / Mohamed Khalgui and Hans-Michael Hanisch, editors. p. cm. Includes bibliographical references and index.

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Formal Reasoning about Expectation Properties for Continuous Random Variables

Cited by 20 publications

References 14 publications

Towards the Formal Reliability Analysis of Oil and Gas Pipelines

Towards the Formal Reliability Analysis of Oil and Gas Pipelines

Reliability modeling and analysis of communication networks

Reconfigurable Embedded Control Systems

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