Abstract
Cause-consequence Diagram (CCD) is widely used as a deductive safety analysis technique for decision-making at the critical-system design stage. This approach models the causes of subsystem failures in a highly-critical system and their potential consequences using Fault Tree (FT) and Event Tree (ET) methods, which are well-known dependability modeling techniques. Paper-and-pencil-based approaches and simulation tools, such as the Monte-Carlo approach, are commonly used to carry out CCD analysis, but lack the ability to rigorously verify essential system reliability properties. In this paper, we propose to use formal techniques based on theorem proving for the formal modeling and step-analysis of CCDs to overcome the inaccuracies of the simulation-based analysis and the error-proneness of informal reasoning by mathematical proofs. In particular, we use the HOL4 theorem prover, which is a computer-based mathematical reasoning tool. To this end, we developed a formalization of CCDs in Higher-Order Logic (HOL), based on the algebraic approach, using HOL4. We demonstrate the practical effectiveness of the proposed CCD formalization by performing the formal reliability analysis of the IEEE 39-bus electrical power network. Also, we formally determine the Forced Outage Rate ( $\mathcal {FOR}$ ) of the power generation units and the network reliability index, i.e., System Average Interruption Duration Index ( $\mathcal {SAIDI}$ ). To assess the accuracy of our proposed approach, we compare our results with those obtained with MATLAB Monte-Carlo Simulation (MCS) as well as other state-of-the-art approaches for subsystem-level reliability analysis.
Highlights
NOWADAYS, in many safety-critical systems, which are prevalent, e.g. in smart grids [1] and automotive industry [2], a catastrophic accident may happen due to coincidence of sudden events and/or failures of specific subsystem components
Remark that all above-mentioned Consequence Diagram (CCD) new formulations have been formally verified in HOL4, where the proof-script amounts to about 12,000 lines of HOL4 code, which can be downloaded for use from [32]. This code can be extended, with some basic knowhow about HOL4, to perform dynamic failure analysis of dynamic subsystems where no dependencies exist in different subsystems using Dynamic Fault Trees (DFT), such as PAND and SP, i.e, CCD reliability analysis of Type B
In this paper, we developed a formal approach for Cause-Consequence Diagrams (CCD), which enables safety engineers to perform N -level CCD analysis of safety-critical systems within the sound environment of the HOL4 theorem prover
Summary
NOWADAYS, in many safety-critical systems, which are prevalent, e.g. in smart grids [1] and automotive industry [2], a catastrophic accident may happen due to coincidence of sudden events and/or failures of specific subsystem components. The main discipline for safety design engineers is to perform a detailed Cause-Consequence Diagram (CCD) [3] reliability analysis for identifying the subsystem events that prevent the entire system from functioning as desired. HiP-HOPS lacks the modeling of multi-state system components and cannot provide generic mathematical expressions that can be used to predict the reliability of a critical-system based on any probabilistic distribution [9]. We propose to use formal techniques based on theorem proving for the formal reliability CCD analysisbased of safety-critical systems, which provides us the ability to obtain a verified subsystem-level failure/operating consequence expression. Comparison between our formal CCD reliability assessment with the corresponding results obtained from MATLAB MCS and other notorious approaches
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