Towards the Formal Reliability Analysis of Oil and Gas Pipelines

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

Formal Availability Analysis using Theorem Proving

Availability analysis is used to assess the possible failures and their restoration process for a given system. This analysis involves the calculation of instantaneous and steady-state availabilities of the individual system components and the usage of this information along with the commonly used availability modeling techniques, such as Availability Block Diagrams (ABD) and Fault Trees (FTs) to determine the system-level availability. Traditionally, availability analyses are conducted using paper-and-pencil methods and simulation tools but they cannot ascertain absolute correctness due to their inaccuracy limitations. As a complementary approach, we propose to use the higher-order-logic theorem prover HOL4 to conduct the availability analysis of safety-critical systems. For this purpose, we present a higher-order-logic formalization of instantaneous and steady-state availability, ABD configurations and generic unavailability FT gates. For illustration purposes, these formalizations are utilized to conduct formal availability analysis of a satellite solar array, which is used as the main source of power for the Dong Fang Hong-3 (DFH-3) satellite.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1505.0264

Formal Probabilistic Analysis of a Wireless Sensor Network for Forest Fire Detection

Wireless Sensor Networks (WSNs) have been widely explored for forest fire detection, which is considered a fatal threat throughout the world. Energy conservation of sensor nodes is one of the biggest challenges in this context and random scheduling is frequently applied to overcome that. The performance analysis of these random scheduling approaches is traditionally done by paper-and-pencil proof methods or simulation. These traditional techniques cannot ascertain 100% accuracy, and thus are not suitable for analyzing a safety-critical application like forest fire detection using WSNs. In this paper, we propose to overcome this limitation by applying formal probabilistic analysis using theorem proving to verify scheduling performance of a real-world WSN for forest fire detection using a k-set randomized algorithm as an energy saving mechanism. In particular, we formally verify the expected values of coverage intensity, the upper bound on the total number of disjoint subsets, for a given coverage intensity, and the lower bound on the total number of nodes.Comment: In Proceedings SCSS 2012, arXiv:1307.802

Formalization of Normal Random Variables

Engineering systems often have components that exhibit random behavior. This randomness in many cases is normally distributed. To verify such systems, proba- bilistic analysis is used. Such engineering systems have applications in domains like transportation, medicine and military. Despite the safety-critical nature of these ap- plications, most of the analysis is done using informal techniques like simulation and paper-and-pencil analysis, and thus cannot be completely relied upon. The unreliable results produced by such methods may result in heavy financial loss or even the loss of a human life. To overcome the limitation of traditional methods, we propose to conduct the analysis of such systems within the trusted kernel of a higher-order-logic theorem prover HOL4. The soundness and the deduction style of the theorem prover guarantee the validity of the analysis and the results of this type of analysis are generic and valid for any instance of the system. For this purpose, we provide HOL4 formalization of Lebesgue measure and normal random variables along with the proof of their classical properties. We also ported the theory of Gauge integral and other required foundational concepts from HOL Light and Isabelle/HOL theorem provers. To illustrate the usefulness of our formalization, we conducted the formal analysis of two applications, i.e., error probability of binary transmission in the presence of Gaussian noise and probabilistic clock synchronization in wireless sensor networks