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
Dynamic fault trees (DFTs) have emerged as an important tool for capturing the dynamic behavior of system failure. These DFTs are then analyzed qualitatively and quantitatively using stochastic or algebraic methods to judge the failure characteristics of the given system in terms of the failures of its subcomponents. Model checking has been recently proposed to conduct the failure analysis of systems using DFTs with the motivation to provide a rigorous failure analysis of safety-critical systems. However, model checking has not been used for the DFT qualitative analysis and the reduction algorithms used in model checking are usually not formally verified. Moreover, the analysis time grows exponentially with the increase of the number of states. These issues limit the usefulness of model checking for analyzing complex systems used in safety-critical domains, where the accuracy and completeness of analysis matters the most. To overcome these limitations, we propose a comprehensive methodology to perform the qualitative and quantitative analysis of DFTs using an integration of theorem proving and model checking based approaches. For this purpose, we formalized all the basic dynamic fault tree gates using higher-order logic based on the algebraic approach and formally verified some of the simplification properties. This formalization allows us to formally verify the equivalence between the original and reduced DFTs using a theorem prover, and conduct the qualitative analysis. We then use model checking to perform the quantitative analysis of the formally verified reduced DFT. We applied our methodology to five benchmarks and the results show that the formally verified reduced DFT was analyzed using model checking with up to six times less states and up to 133000 times faster.
Abstract. Fault Tree (FT) is a standard failure modeling technique that has been extensively used to predict reliability, availability and safety of many complex engineering systems. In order to facilitate the formal analysis of FT based analyses, a higher-order-logic formalization of FTs has been recently proposed. However, this formalization is quite limited in terms of handling large systems and transformation of FT models into their corresponding Reliability Block Diagram (RBD) structures, i.e., a frequently used transformation in reliability and availability analyses. In order to overcome these limitations, we present a deep embedding based formalization of FTs. In particular, the paper presents a formalization of AND, OR and NOT FT gates, which are in turn used to formalize other commonly used FT gates, i.e., NAND, NOR, XOR, Inhibit, Comparator and majority Voting, and the formal verification of their failure probability expressions. For illustration purposes, we present a formal failure analysis of a communication gateway software for the next generation air traffic management system.
Abstract. Dependability is an umbrella concept that subsumes many key properties about a system, including reliability, maintainability, safety, availability, confidentiality, and integrity. Various dependability modeling techniques have been developed to effectively capture the failure characteristics of systems over time. Traditionally, dependability models are analyzed using paper-and-pencil proof methods and computer based simulation tools but their results cannot be trusted due to their inherent inaccuracy limitations. The recent developments in probabilistic analysis support using formal methods have enabled the possibility of accurate and rigorous dependability analysis. Thus, the usage of formal methods for dependability analysis is widely advocated for safety-critical domains, such as transportation, aerospace and health. Given the complementary strengths of mainstream formal methods, like theorem proving and model checking, and the variety of dependability models judging the most suitable formal technique for a given dependability model is not a straightforward task. In this paper, we present a comprehensive review of existing formal dependability analysis techniques along with their pros and cons for handling a particular dependability model.
Depending on the operational environment, installation location, and aging of oil and gas pipelines, they are subject to various degradation mechanisms, such as cracking, corrosion, leaking, and thinning of the pipeline walls. Failure of oil and gas pipelines due to these degradation mechanisms can lead to catastrophic events, which, in the worst case, may result in the loss of human lives and huge financial losses. Traditionally, paper-and-pencil proof methods and Monte Carlo based computer simulations are used in the reliability analysis of oil and gas pipelines to identify potential threats and thus avoid unwanted failures. However, paper-and-pencil proof methods are prone to human error, especially when dealing with large systems, while simulation techniques primarily involve sampling-based methods, i.e., not all possible scenarios of the given systems are tested, which compromises the accuracy of the results. As an accurate alternative, we propose to use a higher-order-logic theorem proving for the reliability analysis of oil and gas pipelines. In particular, this paper presents the higher-order-logic formalization of commonly used reliability block diagrams (RBDs), such as series, parallel, series-parallel, and k-out-of-n, and provides an approach to utilize these formalized RBDs to assess the reliability of oil and gas pipelines. For illustration, we present a formal reliability analysis of a pipeline transportation subsystem used between the oil terminals at the Port of Gdynia, Poland, and Dębogó rze.
Importance measures provide a systematic approach to scrutinize critical system components, which are extremely beneficial in making important decisions, such as prioritizing reliability improvement activities, identifying weak-links and effective usage of given resources. The importance measures are then in turn used to obtain a criticality value for each system component and to rank the components in descending manner. Simulations tools are generally used to perform importance measure based analysis, but they require expensive computations and thus they are not suitable for large systems. A more scalable approach is to utilize the importance measures to obtain all the necessary conditions by proving a generic relationship describing the relative importance between any pair of components in a system. In this paper, we propose to use higher-order-logic (HOL) theorem proving to verify such relationships and thus making sure that all the essential conditions are accompanied by the proven property. In particular, we formalize the commonly used importance measures, such as Birnbaum and Fussell-Vesely, and conduct a formal importance measure analysis of a railway signaling system at a Moroccan level crossing as an application for illustration purpose.
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