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DOE OSTI2025

AUTOMATIC GENERATION OF EVENT TREES AND FAULT TREES: A MODEL-BASED APPROACH

In the past few decades, increasing complexity in modern engineering systems has been driven by the integration of a large number of components and by the fact that the system operations involve many disciplines (e.g., thermal-hydraulics, plant operations, cyber-security). Current safety/reliability modeling approaches to such systems are labor intensive, difficult to learn, and rely heavily on simplistic Boolean logic to depict failure propagation and accident progression. While these methods serve well for simple systems (i.e., linear causal systems with limited small inter- and intra-system interactions), their results are difficult to verify when modeling complex systems (typically performed through the extensive use of modeling assumptions). The development of new methods is addressed to meet these challenges through a model-based system engineering (MBSE) lens. Under MBSE philosophy, every aspect of the system (form or function) is represented by a model that completely characterizes its architecture or behavior. MBSE approach greatly improves the management of design, analysis and verification of complex systems. An integration of Dynamic Probabilistic Risk Assessment (DPRA) methods with MBSE models is proposed to perform safety/reliability analyses of engineering systems. In particular, MBSE representation of the system (performed using Systems Modeling Language [SysML]) is coupled with DPRA methods to automatically generate event trees and fault trees.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Automatic Generation of Event Trees and Fault Trees: A Model-Based Approach

In the past few decades, the increasing complexity of modern engineering systems has been driven by the integration of a large number of components whose operations may involve many disciplines (e.g., thermal hydraulics, plant operations, cybersecurity). Most computational tools used by industry and regulators for system safety and reliability assessments are still based on the traditional fault tree (FT) and event tree (ET) approach, which may not be able to capture complex interactions among system constituents. The use of simulation tools has widely increased in the past few decades to improve the fidelity of the reliability and safety analyses. However, the direct use of simulation tools as part of dynamic probabilistic risk assessment (DPRA) methods is not getting traction since (1) modeling the whole system under consideration with DPRA methods may be computationally expensive and unnecessary, and (2) the manual integration of DPRA models into existing state-of-practice probabilistic risk assessment models (i.e., based on FTs and ETs) can be time consuming and prone to errors. Here, in this paper we propose a procedure to overcome this limitation by presenting several algorithms designed to automatically construct subsystem ETs and FTs from DPRA methods for integration into an existing ET/FT system model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Eucalyptus – An Analysis Suite for Fault Trees with Uncertainty Quantification

Eucalyptus is a novel code developed at Lawrence Livermore National Laboratory to incorporate uncertainty quantification into Fault Tree Analysis (FTA). This tool addresses the challenge of imperfect knowledge in “grey-box” systems by allowing analysts to incorporate and propagate uncertainty from component-level assessments to system-level effects. Eucalyptus facilitates a consistent evaluation of the impact of subject matter expert judgment and knowledge gaps on overall system response by Monte Carlo generation of possible system fault trees, sampling probabilities of the existence of subsystems and components. Here, the code supports the specification of fault trees through text and allows export to various formats, including auto-generated images, easing analysis and reducing errors. It has undergone extensive verification testing, demonstrating its reliability and readiness for deployment, and leverages on-node parallelism for rapid analysis. Example analyses are shown that include the identification of system failure paths and quantification of the value of further information about system components.

Fault Tree Analysis↗

DOE OSTI2020

Identification of potential CO 2 leakage pathways and mechanisms in oil reservoirs using fault tree analysis

Geological storage of CO 2 technologies has become an important and effective way to reduce the greenhouse gas emissions, especially when it is combined with CO 2 enhanced oil recovery (EOR), which can not only trap CO 2 but also enhance oil recovery. However, the risk of CO 2 leakage has always been a prominent issue. In this paper, the mechanisms and pathways of CO 2 leakage during geological storage in oil reservoirs were analyzed using fault tree analysis (FTR). Besides, monitoring technologies were discussed and deployed in a CO 2 EOR demonstration project. The analysis results showed that the sealing failures of oil producer and CO2 injector wells, like well cement failure and casing failure, are the main reasons for the CO 2 leakage, which has been observed in the oil field monitoring project. The monitoring results indicated that there is no large-scale CO 2 leakage, while relatively high and abnormal CO 2 concentration in soil gas near some wellbores are observed, which indicates there is some leakage of CO 2 through incomplete cement ring and well casing string. FTR results provide guidelines for monitoring and preventing of CO 2 leakage during geological storage in oil reservoirs. Finally, the near-surface monitoring methods, especially the soil gas monitoring technologies, can effectively detect the leakage of CO 2 , and are a proper method for CO 2 leakage monitoring.

58 GEOSCIENCES↗

DOE OSTI2020

Limitations of traditional tools for beyond design basis external hazard PRA

Probabilistic risk assessment (PRA) is being used increasingly by the nuclear industry for safety during normal operations as well as for the protection against external hazards. Computation of total risk in an external hazard PRA is dependent on hazard assessment, fragility assessment, and systems analysis. A systems analysis for propagation of component fragilities is conducted using event and fault trees. The event and fault trees for an actual power plant can be fairly large in size, which imposes computational challenges. Hence, certain assumptions are employed for computational efficiency. These assumptions typically represent the conditions imposed during the design basis (DB) scenario. The traditional PRA tools based on these assumptions are also widely applied to perform risk assessment in the context of beyond design basis (BDB) scenarios. However, some of these assumptions may not be valid for certain BDB scenarios. In addition, the probability of dependent failures also increases in BDB scenarios due to common cause failures (CCF) which usually results from design modifications, human errors, etc. In this manuscript, a simple and a relatively more complex illustrative examples are used to show the limitation of these assumptions in the numerical quantification of risk for the case of BDB conditions. Case studies with CCF events across multiple fault trees are also presented to illustrate the effect of these assumptions when traditional approach is used in BDB risk assessment. It is shown that the assumptions are valid for the case of DB conditions but may lead to excessively conservative risk estimates in the case of BDB conditions. Finally, a Bayesian network based top-down algorithm is proposed as an alternative tool for accurate numerical quantification of total risk in systems analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Linking classical PRA models to a dynamic PRA

Here, this paper presents a series of methods designed to incorporate classical Probabilistic Risk Assessment (PRA) models such as Event Trees (ETs) and Fault Trees (FTs) into dynamic PRA. In contrast to classical PRA, dynamic PRA couples stochastic methods with system simulators to determine the risks associated with complex systems such as nuclear power plants. Compared with classical PRA methods, they can evaluate with higher resolution the safety impact of timing and sequencing of events on the progression of the accident. As part of a dynamic PRA analysis, it is not uncommon that parts of the system to be analyzed might not require a computationally expensive simulation model. These parts could be in fact modeled by employing classical PRA models (e.g., a FT). Here, we present a set of methods and tools that can be used to link the most common classical PRA models (ETs, FTs, reliability block diagrams and Markov models) to simulation codes such as RELAP5-3D: creating a “hybrid PRA.” In order to show the potential of such an hybrid PRA we employ this method to verify ET modeling assumptions (e.g., success criteria) using a large break loss of coolant accident initiating event as a test case. In this respect, we link a set of FTs from the original PRA to the RELAP5-3D code and perform a hybrid PRA. The FTs are employed to model the control logic of several safety systems and to propagate component failures throughout the system. Provided the generated dynamic PRA data, we show how conservative assumptions in the original PRA can be identified and how such original PRA can be modified by updating success criteria captured by the set of RELAP5-3D simulation runs.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dynamic PRA Methods to Evaluate the Impact on Accident Progression of Accident Tolerant Fuels

Accident tolerant fuels (ATFs) are new nuclear fuels developed in response to the accident at the Fukushima power station in March 2011. The goal of ATFs is to withstand accident scenarios through better performance compared to currently employed fuels (e.g., small-scale hydrogen generation). This paper targets a method for evaluating and comparing ATF performance from a probabilistic risk assessment (PRA) perspective by employing a newly developed combination of event trees and dynamic PRA methods. Compared to classical PRA methods based on event trees and fault trees, dynamic PRA can evaluate with higher resolution the safety impacts of physics dynamics and the timing/sequencing of events on the accident progression without the need to introduce overly conservative modeling assumptions and success criteria. In this paper, we analyze the impact on the accident progression of three different cladding configurations for two initiating events [a large break loss-of-coolant accident (LB-LOCA) and a station blackout (SBO)] by employing dynamic PRA methods. The goal is to compare the safety performance of ATFs (FeCrAl and Cr-coated cladding) and the currently employed Zr-based clad fuel. We employ two different strategies. The first focuses on the identification of success criteria discrepancies between the accident sequences generated by the classical PRA model and the set of simulation runs generated by dynamic PRA using ATF. The second one, on the other hand, directly uses dynamic PRA to evaluate the impact of timing of events (e.g., recovery actions) on accident progression. In conclusion, by applying these methods to the LB-LOCA and SBO initiating events, we show how dynamic PRA methods can provide analysts with detailed and quantitative information on the safety impact of ATFs.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Failure Mechanism Traceability and Application in Human System Interface of Nuclear Power Plants using RESHA

In recent years, there has been considerable effort to modernize existing and new nuclear power plants with digital instrumentation and control systems (DI&C). However, there has also been considerable concern both by industry and regulatory bodies for the risk and consequence analysis of these systems. Of particular concern are digital common cause failures (CCFs) specifically related to software defects. These “misbehaviors” by the software can occur in both the control and monitoring of a system. While many new methods have been proposed to identify potential software failure modes, such as Systems-theoretic Process Analysis (STPA), Hazard and Consequence Analysis for Digital Systems (HAZCADS), etc., these methods are focused primarily on the control action pathway of a system. In contrast, the information feedback pathway lacks unsafe control actions (UCAs), which are typically related to software basic events; thus, assessment of software basic events in such systems is unclear. In this work, we present the idea of intermediate processors and unsafe information flow (UIF) to help safety analysts trace failure mechanisms in the feedback pathway and how they can be integrated into a fault tree for improved assessment capability. The concepts presented are demonstrated in two comprehensive case studies, a smart sensor integrated platform for unmanned autonomous vehicles and another on a representative advanced human system interface (HSI) for safety critical plant monitoring. The qualitative software basic events are identified, and a fault tree analysis is conducted based on a modified Redundancy-guided Systems-theoretic Hazard Analysis (RESHA) methodology. The case studies demonstrate the use of UIF and intermediate processors in the fault tree to improve traceability of software failures in highly complex digital instrumentation feedback. The improved method can also clarify fault tree construction when multiple component dependencies are present in the system.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Failure Mechanism Traceability and Application in Human System Interface of Nuclear Power Plants using RESHA

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Big Data For Operation and Maintenance Cost Reduction

The purpose of this research is to develop a first-of-a-kind framework for integrating Big Data capability into the daily activities of our current fleet of nuclear power plants. Big Data is traditionally defined as data sets with high volume, velocity, and heterogeneity, and the existing Big Data analytics capabilities are now widely popular in fields such as finance, weather, e-commerce, healthcare and sports. In the nuclear industry, while the volume and velocity of data may present computational challenges for existing analytics capabilities, data heterogeneity are seen to present the major challenge. This research project mainly focuses on incorporating the wide range of data heterogeneities in nuclear power plants into an integrated Big Data Analytics capability. The primary end-product of this project is a Big Data framework that is capable of dealing with the large volume and heterogeneity of the data found in nuclear power plants to extract timely and valuable information on equipment performance. The framework can generate system insights that are actionable relations between measurable impacts and the corresponding maintenance action plans and enable optimization of plant operation and maintenance based on the extracted information. The developed framework is capable of handling heterogeneous data including both image data and time-series sensor data. Specifically, this developed framework includes the following components. The first component is an overarching maintenance ontology which includes system insights required by maintenance optimization. The maintenance ontology interacts with other components in the developed framework. The second component handles Piping & Instrumentation Diagram (P&ID) data. It can be used to extract system components and their relations automatically from the P&IDs. This extracted information is stored in the first component, i.e., maintenance ontology, and is also used as input to the third component, i.e., a tool for generating the fault tree for the corresponding system. The generated fault tree in turn is stored in the ontology for assessing risk that is used as a criterion in maintenance policy optimization. The fourth component is a tool for inferring the parameters in the Markov degradation model for a nuclear system. It uses basic information from the ontology. The fifth component is a tool for assessing the degradation level using sensor measurement data, for example, pressure, flowrate. This tool can be used for determining corrective maintenance actions. The results obtained from components four and five are returned to the ontology. The sixth component of the framework is a tool for optimizing the maintenance policy for a nuclear system of interest. It takes certain basic information from the ontology, e.g., costs of maintenance actions and system failures, as input, and returns the optimal maintenance policy to the ontology. This tool can be used for determining predictive maintenance actions. A set of experiments have also been conducted to verify the algorithms developed in this project for nuclear system degradation monitoring. The experiments are based on four solenoid valves, similar to the ones used in nuclear power plants. The analyses based on the experimental data using two algorithms, i.e., the Randomized Window Decomposition (RWD) algorithm and the particle filtering algorithm, and the results are introduced in the report. The Big Data framework developed in this project can be used as a support tool in daily activities of plant operation and maintenance and will reduce current costs while maintaining or improving safety levels. Overall, the project will not only benefit existing reactors, however it will open new frontiers to realize the long overdue value of Big Data Analytics in the nuclear sphere.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

A Causal Approach to Integrate Component Health Data into System Reliability Models

Two of the challenges of current plant reliability approaches are the ability to integrate plant health data, and to support decision making. Condition based data and diagnostic/prognostic information are in fact not considered into plant reliability models to inform system engineers on the most critical components. Currently, the propagation of quantitative health data from the component to the system level is a challenge given the diverse nature/structure of the data. On the other hand, plant reliability methods (which are typically based on fault-trees or reliability block diagrams) can effectively propagate data from the component to the system level, but values of failure rates or failure probabilities are an approximated integral representation of the past industry-wide operational experience, and it neglects the present component health status (e.g., diagnostic and condition-based data) and health projection (when available from prognostic data). Our first claim is that system reliability models should propagate health information from the component to the system/plant level in order to provide a quantitative snapshot of system/plant health and identify the most critical components. Our second claim is that component health should be informed solely by that specific component current and historical performance data and should not be an approximated integral representation of the past industry-wide operational experience. This paper is directly supporting these two claims by proposing a different approach to perform reliability modeling which relies on available component diagnostic, prognostic and condition-based data to measure component health, and it propagates this information through fault tree models. The propagation of health data from the component to the system level is performed not in terms of probability, but in terms of margins where margin is defined as the “distance” between the present actual status and an undesired event (e.g., failure or unacceptable performance). Through a cause-effect lens, while classical reliability models target the effect associated to a component performance, a margin-based approach focuses on the cause of an undesired component performance (i.e., component health). Hence, thinking of reliability in terms of margins implies decision making based on causal reasoning. We will show how fault tree models can be solved using a margin language and how this process can effectively assist system engineers to identify the most critical components.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Reliability modeling in a predictive maintenance context: A margin-based approach

Current system reliability methods (typically based on fault trees or reliability block diagrams) can effectively propagate reliability data from the asset to the system level in order to identify system critical points. However, employed asset reliability data are an approximated integral representation of the past industrywide operational experience, and they neglect the present asset health status (available, for example, from online monitoring data and diagnostic assessments) and forecasted health projection (when available from prognostic models). Asset health should be informed solely by that specific asset’s current and historical performance data and should not be an approximated integral representation of the past industrywide operational experience (as currently performed by system reliability models through Bayesian updating processes). Sensor data, diagnostic assessments, and prognostic assessments are in fact not considered in plant reliability models used to inform system engineers on the most critical assets. In addition, the propagation of quantitative health data from the asset to the system level is a challenge given the diverse nature and structure of health data elements (e.g., vibration spectra, temperature readings, expected failure time). Ideally, in a predictive maintenance context, system reliability models should support decision making by propagating available health information from the asset to the system level in order to provide a quantitative snapshot of system health and identify the most critical assets. Here, this paper is directly addressing these two goals by proposing a different approach for reliability modeling that relies on asset diagnostic and prognostic assessments, along with monitoring data to measure asset health. The propagation of health data from the asset to the system level is performed through fault tree models not in probability terms, but in terms of margin where margin is the “distance” between the present status and an undesired event (e.g., failure or unacceptable performance). Through a cause-effect lens, while classical reliability models target the effect associated with asset performance, a margin-based approach focuses on the cause of an undesired asset performance (i.e., its health). Hence, thinking of reliability in terms of margins implies decision-making based on causal reasoning. We will show how fault tree models can be solved using a margin language and how this process can effectively assist system engineers to identify the most critical assets.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Refining Processing Engines from SAPHIRE: Initialization of Fault Tree/Event Tree Solver

SAPHIRE has been extensively employed for over 35 years to model risk-important systems and quantify risk models. As a well-established and thoroughly documented Probabilistic Risk Assessment (PRA) tool, SAPHIRE has continuously tracked computational trends and received regular updates. Despite its ongoing evolution, there remains a need for further enhancements, particularly in dealing with the quantification of exceptionally large models. These improvements could take the form of algorithmic advancements, harnessing the power of parallel computing, and exploring the potential benefits of cloud computing solutions. Considering these aspirations, the notion of a remote solve option was introduced and subsequently evolved into a dedicated project within the SAPHIRE development team. A significant outcome of this initiative is SAPHSOLVE, an engine extracted from the SageRisk API designed specifically for remote solving capabilities. The ongoing project is nearing its culmination, marked by a series of discoveries that have brought undocumented aspects to light. Among these revelations is the intricacy of the input and output format for the SAPHSOLVE engine. This document serves the crucial purpose of meticulously delineating the precise formats for both input and output, as they form an indispensable foundation. The importance of documenting these formats cannot be overstated, as it is a pivotal step in facilitating rigorous testing and comparison. Whether it involves scrutinizing SAPHSOLVE results against those of the internal integrated solver or other external solvers, the ability to construct models or transform existing ones into a compatible SAPHSOLVE format is imperative. Chapter 1 offers a succinct introduction to both SAPHIRE and SAPHSOLVE, followed by Chapter 2 which outlines the roadmap for enhancing SAPHSOLVE. The core of this report is Chapter 3, which intricately elucidates the intricacies of the input and output file formats. To provide a tangible illustration of these formats, a rudimentary example has been compiled and is available in Appendix. SAPHSOLVE represents a novel external solving mechanism developed by the SAPHIRE team, although it has not yet reached the full spectrum of capabilities possessed by SAPHIRE's internal solver. However, the SAPHIRE team has set a comprehensive course for incorporating the functionalities of SAPHSOLVE. A comprehensive outlook on the future of SAPHSOLVE is expounded upon in Chapter 4.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Generic Pressurized Water Reactor Model for SAPHIRE

Generic Pressurized Water Reactor Model for SAPHIRE This report contains a data dump from a SAPHIRE Generic Pressurized Water Reactor (PWR) model. The intent is to have this information reviewed for export control and classification so that the generic model can be used external to INL. The facility model is not applicable to any existing nuclear reactors. The Generic PWR model does not represent any existing power plant and was created to support research and training purposes. Three distinct types of data are used to create a SAPHIRE risk model: - Event trees representing typical PWR sequences - Fault trees representing generic system performance - Basic events (e.g., component failure information) Where possible, we have taken information from publicly available documents and referenced that information tagged to a specific item.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2025

Redefining Design for Remanufacturing: A Practical Methodology for Prioritizing Remanufacturing Design Rules

Products are often discarded when they fail or no longer meet user needs. These outcomes are frequently shaped by early design decisions. While remanufacturing offers a sustainable alternative by restoring products to like‐new condition, its potential is often limited by designs that do not consider remanufacturing from the outset. This research addresses that challenge by introducing a structured Design for Remanufacturing (DfRem) methodology and a CAD‐integrated tool to support real‐time design decisions. The DfRem framework introduces a new primary design function focused on preserving product functionality across its life cycle. It is supported by a fault tree that identifies failure modes that limit remanufacturing potential and a hierarchy of design principles including Prevent, Minimize, Relocate, Restore, and others. Each principle is linked to actionable design rules that help engineers reduce the need for remanufacturing or improve its efficiency when necessary. To operationalize this framework, we developed CAD plugins for Autodesk Inventor and PTC Creo. These tools use a state machine model to present prioritized design rules based on selected failure modes and user input. By embedding DfRem logic directly into widely used CAD environments, the tool enables engineers to make sustainability‐informed decisions without disrupting existing workflows. Furthermore, this approach highlights the critical role of design in enabling circular and resource‐efficient product development, making remanufacturing a more practical and accessible strategy during the early stages of product design.

CAD↗

DOE OSTI2021

Data requirements for improving the Quantitative Risk Assessment of liquid hydrogen storage systems

Quantitative Risk Assessment (QRA) supports the development of risk-informed safety codes and standards which are employed to enable the safe deployment of hydrogen technologies essential to decarbonize the transportation sector. System reliability data is a necessary input for rigorous QRA. Here, the lack of reliability data for bulk liquid hydrogen (LH 2 ) storage systems located on site at fueling stations limits the use of QRAs. In turn, this hinders the ability to develop the necessary safety codes and standards that enable worldwide deployment of these stations. Through a QRA-based analysis of a LH 2 storage system, this work focuses on identifying relevant scenario and probability data currently available and ascertaining future data collection requirements regarding risks specific to liquid hydrogen releases. The work developed consists of the analysis of a general bulk LH 2 storage system design located at a hydrogen fueling station. Failure Mode and Effect Analysis (FMEA) and traditional QRA modeling tools such as Event Sequence Diagrams (ESD) and Fault Tree Analysis (FTA) are employed to identify, rank, and model risk scenarios related to the release of LH 2 . Based on this analysis, scenario and reliability data needs to add LH 2 -related components to QRA are identified with the purpose of improving the future safety and risk assessment of these systems.

08 HYDROGEN↗

DOE OSTI2021

A Redundancy-Guided Approach for the Hazard Analysis of Digital Instrumentation and Control Systems in Advanced Nuclear Power Plants

We report digital instrumentation and control (I&C) upgrades are a vital research area for the nuclear industry. Despite their performance benefits, deployment of digital I&C in nuclear power plants (NPPs) has been limited. Digital I&C systems exhibit complex failure modes including common cause failures (CCFs), which can be difficult to identify. This paper describes the development of a redundancy-guided application of the Systems-Theoretic Process Analysis and fault tree analysis for the hazard analysis of digital I&C in advanced NPPs. The resulting Redundancy-Guided Systems-Theoretic Hazard Analysis (RESHA) is applied for the case study of a representative state-of-the-art digital reactor trip system. The analysis qualitatively and systematically identifies the most critical CCFs and other hazards of digital I&C systems. Ultimately, the RESHA can help researchers make informed decisions for how, and to what degree, defensive measures such as redundancy, diversity, and defense in depth can be used to mitigate or eliminate the potential hazards of digital I&C systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

On the Language of Reliability: A System Engineer Perspective

In its classical definition, risk is defined by three elements: what can go wrong, what are its consequences, and how likely is it to occur? While this definition makes sense in a regulatory-based framework where for the current fleet of operating light water reactors (LWRs), the risks associated with nuclear power plants typically are characterized in terms of core damage and large early release frequency (LERF), this approach does not provide a useful snapshot of the health of the plant from a broader perspective. This is due to the very narrow context in which the term “risk” typically is defined as nuclear safety aspects that have the potential to impact public health. In this paper, we take the viewpoint of nuclear safety that is reflective of the current fleet of operating LWRs for which core damage frequency and LERF are appropriate metrics. For other advanced reactor designs, other more applicable technology neutral metrics of reactor safety metrics would be specified. A possible alternate path would start by redefining the word risk with a broader meaning that better reflects the needs of a system health and asset management decision-making process. Rather than asking how likely an event could occur (in probabilistic terms), we can ask how far this event is from occurring. Our approach starts by defining and quantifying component and system health in terms of a “distance” between its actual and limiting conditions, i.e., determination of the margin that exists between the current state/condition and the state where the component/system is no longer capable of achieving its intended function. A margin is a measure that is more reflective of the current state or performance of a component, and therefore more closely tied to decisions that are made on an ongoing basis. Further, we will show how, given the data available from plant equipment reliability and monitoring (e.g., pump vibration data) and prognostic (e.g., component remaining useful life estimation) data, a margin can be described and determined for all types of maintenance approaches (e.g., corrective or predictive maintenance). We show how classical reliability models (e.g., fault trees) can be used to quantify the system margin provided component margin values. In the approach described in this paper, the propagation of margin values through classical reliability models are not performed using classical probabilistic calculations applied to sets (as performed in a typical plant probabilistic risk assessment). Instead, we show how it is possible to propagate margin values through Boolean logic gates (i.e., AND and OR operators) through distance-based operations.

97 MATHEMATICS AND COMPUTING↗