Plant Probabilistic Risk Assessment Research Articles

Exhaustive Test Case Generation for Nuclear Safety Software Based on the Software Logic Model

An issue regarding the incorporation of software reliability within the nuclear power plant (NPP) probabilistic risk assessment model has emerged in the licensing processes of digitalized NPPs. Since software failure induces common-cause failure of the processor modules, the reliability of the software used in the NPP safety-critical instrumentation and control systems must be quantified and verified with proper test cases and environments. In this study, a software testing method based on the minimal cut set (MCS)–based exhaustive test case generation scheme is proposed where the software logic model is developed from available information on the software development and the MCSs that represent the necessary and sufficient conditions for the software variables’ states to produce safety software outputs are generated. The MCSs are then converted into the test cases, which can be used as inputs to the test bed to verify that the test cases produce correct outputs after software execution. The effectiveness of the proposed method is demonstrated with the safety-critical trip logic software of the APR-1400 reactor protection system. The method provides a systematic way to conduct exhaustive software testing and prove the functionality of the nuclear safety software based on the test result without uncertainties.

Multi-unit seismic probabilistic risk assessment: A Bayesian network perspective

The Fukushima Dai-ichi highlighted multi-unit accidents in nuclear power plant (NPP) probabilistic risk assessment (PRA). This paper focuses on multi-unit seismic PRA because seismic events are contributors to NPP site risk. This paper integrates works on modeling ground motion spatial variability at a NPP site and dependent seismic failures into a coherent and rigorous framework using Bayesian networks, and explores the relative importance of different types of correlation on NPP site-based risk metrics. A study of a hypothetical dual unit NPP site considered 15 cases with varying degrees of correlation in spatial ground motion (GM) and seismic failures. Based on the results, the current assumption of perfect GM correlation across a NPP site underestimates risk metrics that consider either unit experiencing core damage (CD) (site CD), which is not conservative. The risk metric that considers both units experiencing CD (concurrent CD) shows differences between the partial and perfect GM correlation assumptions when multiple component failures contribute to the CD in each unit. Within a GM correlation assumption, the site CD increases as the fragility correlation increases, a counterintuitive trend. The risk assessment case outlined in this paper provides more realistic results than the cases reflecting the current state of practice.

Identifying human failure events (HFEs) for external hazard probabilistic risk assessment

In recent years, several advancements in nuclear power plant (NPP) probabilistic risk assessment (PRA) have been driven by increased understanding of external hazards, plant response, and uncertainties. However, major sources of uncertainty associated with external hazard PRA remain. One important source is how risk-significant human actions that are carried out to enable plant response and recovery from natural hazards cause the close coupling of physical impacts on plants and overall plant risk during these hazard events. This makes human reliability and human-plant interactions important elements to consider in resolving PRA gaps in external hazards. One of the challenges in considering human response in external hazard probabilistic risk assessment (XHPRA) is that most existing human reliability analysis (HRA) models were not developed for assessing actions outside the control room (termed ex-control room actions) and hazard response. To support this new scope, HRA models will need to be developed or modified to support identification of human activities, causal factors, and uncertainties inherent in external hazard response, thereby providing insights regarding event timing and physical event conditions as they relate to human performance. In this study, there are two main objectives: (1) evaluate the applicability of an existing cognitive-based HRA method, Phoenix, to ex-control room actions, and (2) identify sources of uncertainty to be characterized or reduced in order to make this method suitable for XHPRA. The first step of such work is performed by assessing the suitability of existing HRA methods to support identifying human failure events (HFEs) for human response to flooding hazards. These HFEs are human actions or inactions that are involved in human responses to flooding hazards and could contribute to the loss of a critical function for the plant in the scenario being examined. In this work, decomposition analyses using the cognitive-based Phoenix HRA model are used to identify HFEs. The Phoenix method was found to be suitable for analyzing ex-control room actions as well as identifying specific HFEs and underlying crew failure modes (CFMs). However, the method's suitability for use in ex-control room actions would benefit from expanding the available CFMs to accommodate a larger variety of physical and communication tasks.

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. 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.

A Bayesian Network Approach for Modeling Dependent Seismic Failures in a Nuclear Power Plant Probabilistic Risk Assessment

The importance of modeling dependency between seismic failures of multiple components in a nuclear power plant (NPP) probabilistic risk assessment (PRA) has been discussed since the 1980s. In NUREG/CR-7237, Budnitz et al. found the Reed-McCann method to be the most promising method for modeling dependent seismic failures in NPP PRA. However, there are issues with the Reed-McCann method's quantification of the seismic fragility of a system of multiple components. To address this issue and to facilitate an overall realism increase in modeling dependencies in seismic PRA, this paper proposes a Bayesian network (BN) approach to model dependent seismic failures. To illustrate the proposed approach, we calculate the fragility of a parallel system and a series system using the Reed-McCann method, the BN approach, the First-Order Reliability Method (FORM) and Monte Carlo simulation (MCS). Then, we compare the system fragility results from these four approaches/methods to the lower and upper bounds of the system fragility. We found that the BN approach performed better than the Reed-McCann method with respect to providing results that stay within the lower and upper bounds of the system fragility. Further, the BN approach gives similar results to FORM and MCS. This paper proposes a BN approach because, in combination with our previous work about extending a probabilistic seismic hazard analysis to account for the spatial variability of ground motion at an NPP hard-rock site, it can be used to simultaneously and realistically account for dependent seismic failures and spatial variability of ground motion in both single-unit and multi-unit seismic PRAs.

A method for improved realism in modeling transient fires in nuclear power plant probabilistic risk assessments

In current fire probabilistic risk assessments (PRAs) for nuclear power plants in the United States, fires due to transient combustibles are one of the top contributors to calculated plant risk. This does not comport with industry experience on the severity of transient fires. A two-phase project was developed to improve the realism of modeling transient fires in PRAs. In the summer of 2018, a large fire testing program was executed to test 99 fuel packages representative of transient combustibles in nuclear power plants. This paper develops a method to weight the test results using operational experience in the form of a fire events database maintained by the Electric Power Research Institute. The weighted test results were used to create probabilistic distributions of heat release rate, total energy release, and zone of influence (maximum distance for causing target damage). Additionally, the weighted test results were used to develop a generic approach for modeling the time-dependent behavior of a transient fire.

Integrated Risk-Informed Design (I-RID) methodological framework and computational application for FLEX equipment storage buildings of Nuclear Power Plants

In this research, an Integrated Risk-Informed Design (I-RID) methodological framework is developed for generating and evaluating design options for Nuclear Power Plant (NPP) structures and for providing plant decision makers with a quantitative comparison among design options based on multiple decision criteria, e.g., safety risk and cost. In the I-RID framework, simulations of underlying failure mechanisms are integrated with Probabilistic Risk Assessment (PRA) (consisting of event trees and fault trees) and a cost assessment model in a unified framework. The failure mechanisms are simulated by conducting Finite Element Analysis (FEA), and a probabilistic interface between FEA and the existing plant PRA is generated using structural reliability techniques. A causal model for cost assessment is developed, which allows for the modeling of multi-layer causal relationships among underlying contributing factors and, therefore, creates an explicit connection between cost and safety risk outputs. This paper applies the I-RID framework to the design of a storage building for the Diverse and Flexible Coping Strategies (FLEX) equipment in an NPP subjected to a potential tornado impact. Over two hundred design options are generated and evaluated, and three suggested design options with the lowest values of safety risk and cost are identified.

An algorithm for enhancing spatiotemporal resolution of probabilistic risk assessment to address emergent safety concerns in nuclear power plants

Emergent safety concerns often involve complex spatiotemporal phenomena. In addressing these concerns, the classical Probabilistic Risk Assessment (PRA) of Nuclear Power Plants (NPPs) has limitations in generating the required resolution for risk estimations. The existing dynamic PRAs have yet to demonstrate their feasibility for implementation in a plant. In addition, due to the widespread use of classical PRA in the nuclear industry and by the regulatory agency, a transition to a fully dynamic PRA would require a significant investment of resources. As a more feasible alternative, the authors have developed the Integrated PRA (I-PRA) methodology to add realism to risk estimations by explicitly incorporating time and space into underlying models of the events in the plant PRA while avoiding significant changes to its structure. In I-PRA, the failure mechanisms associated with the areas of concern (e.g., fire, Generic Safety Issue 191) were modeled in separate simulation modules, which were then integrated with the plant PRA through a probabilistic interface. This paper (i) provides theoretical foundations for the incorporation of time and space into PRA and (ii) introduces an algorithm that helps execute I-PRA in a way to gradually enhance spatiotemporal resolution of plant PRAs to efficiently address emergent safety concerns.

Methodological and Practical Comparison of Integrated Probabilistic Risk Assessment (I-PRA) with the Existing Fire PRA of Nuclear Power Plants

Nearly half of the U.S. nuclear power plants (NPPs) are in the process of transitioning, or have already transitioned, to a risk-informed, performance-based fire protection program. For this transition, Fire Probabilistic Risk Assessment (Fire PRA) is used as a foundation for fire risk evaluation. To increase realism in Fire PRA by reducing conservative bias, the authors have developed an Integrated Probabilistic Risk Assessment (I-PRA) methodological framework that does not require major changes to the existing plant Probabilistic Risk Assessments (PRAs). The underlying failure mechanism models associated with fire events are developed in a separate module, which can be interfaced and connected to the existing plant PRA. This paper explains the areas of methodological advancements in I-PRA, comparing them with the existing Fire PRA of NPPs. This comparison is further demonstrated in a realistic case study that applies the I-PRA framework to a critical fire-induced scenario at an NPP. The core damage frequency (CDF) for the selected scenario, computed by the I-PRA framework, is compared with the results of the Full Compartment Burn screening method and the existing Fire PRA methodology. Using the I-PRA framework, the CDF for the selected scenario has decreased by a factor of 20 compared with the Full Compartment Burn screening approach and by a factor of 2 compared to the existing Fire PRA methodology based on NUREG/CR-6850 and the subsequent NUREGs that have updated the data and methods for individual steps.

Statistical characterization of the time to reach peak heat release rate for nuclear power plant electrical enclosure fires

Since publication of NUREG/CR-6850 (EPRI 1011989), EPRI/NRC-RES Fire PRA Methodology for Nuclear Power Facilities in 2005, phenomenological modeling of fire growth to peak heat release rate (HRR) for electrical enclosure fires in nuclear power plant probabilistic risk assessment (PRA) has typically assumed an average 12-min rise time [1]. One previous analysis using the data from NUREG/CR-6850 from which this estimate derived indicated this could be represented by a gamma distribution with alpha (shape) and beta (scale) parameters of 8.66 and 1.31, respectively [2]. Completion of the test program by the US Nuclear Regulatory Commission (USNRC) for electrical enclosure heat release rates, documented in NUREG/CR-7197, Heat Release Rates of Electrical Enclosure Fires (HELEN-FIRE) in 2016, has provided substantially more data from which to characterize this growth time to peak HRR [3]. From these, the author develops probabilistic distributions that enhance the original NUREG/CR-6850 results for both qualified and unqualified cables.2 The mean times to peak HRR are 13.3 and 10.1 min, respectively, with a mean of 12.4 min when all data are combined, confirming that the original NUREG/CR-6850 estimate of 12 min was quite reasonable.Via statistical-probabilistic analysis, the author shows that the time to peak HRR for qualified and unqualified cables can again be well represented by gamma distributions with alpha and beta parameters of 1.88 and 7.07, and 3.86 and 2.62, respectively. Working with the gamma distribution for All cables given the two cable types, the author performs simulations demonstrating that non-suppression probabilities, on average, are 30% and 10% higher than the use of a 12-min point estimate when the fire is assumed to be detected at its start and halfway between its start and the time it reaches its peak, respectively. This suggests that adopting a probabilistic approach enables more realistic modeling of this particular fire phenomenon (growth time).

Multiunit Accident Contributions to Quantitative Health Objectives: A Safety Goal Policy Analysis

In 1986 the U.S. Nuclear Regulatory Commission (USNRC) implemented a safety goal policy in response to the 1979 Three Mile Island accident. This policy addresses the question, “How safe is safe enough?” by specifying quantitative health objectives (QHOs) for comparison with average individual early fatality and latent cancer fatality risk results computed from nuclear power plant (NPP) probabilistic risk assessments (PRAs). Comparisons of PRA results to the QHOs or other subsidiary numerical objectives are used to determine whether proposed regulatory actions should be rejected based on potential safety benefit relative to the level of residual risk to the public, before performing detailed cost-benefit analyses to determine whether they could be justified on their net value basis. Lessons learned from recent operational experience—including the 2011 Fukushima accident—indicate that concurrent accidents involving multiple units at a shared site can occur with non-negligible frequency. Yet, risk contributions from such scenarios are excluded by policy from safety goal evaluations for the nearly 60% of the U.S. NPP sites that include multiple units. The objectives of this paper are to (1) present an approach for estimating multiple unit risk metrics for comparison with the safety goal QHOs using accident scenarios from the State-of-the-Art Reactor Consequence Analyses (SOARCA) Project; and (2) using this approach, evaluate the effects of including risk contributions from concurrent multiunit accidents in safety goal evaluations. The approach is demonstrated using a two-unit case study involving two representative NPP sites that are each comprised of two co-located operating reactor units. This paper (1) summarizes results and insights obtained from the two-unit case study; (2) describes additional considerations for applying methods to sites comprised of two or more units, including other major radiological sources; and (3) identifies potential areas for further research.

Advances in multi-unit nuclear power plant probabilistic risk assessment

The Fukushima Dai-ichi accident highlighted the importance of risks from multiple nuclear reactor unit accidents at a site. As a result, there has been considerable interest in Multi-Unit Probabilistic Risk Assessment (MUPRA) in the past few years. For considerations in nuclear safety, the MUPRA estimates measures of risk and identifies contributors to risk representing the entire site rather than the individual units in the site. In doing so, possible unit-to-unit interactions and dependencies should be modeled and accounted for in the MUPRA. In order to effectively account for these risks, six main commonality classifications—initiating events, shared connections, identical components, proximity dependencies, human dependencies, and organizational dependencies—may be used. This paper examines advances in MUPRA, offers formal definitions of multi-unit site risk measures and proposes quantitative approaches and data to account for unit-to-unit dependencies. Finally, a parametric approach for the multi-unit dependencies has been discussed and a simple example illustrates application of the proposed methodology.

An event classification schema for evaluating site risk in a multi-unit nuclear power plant probabilistic risk assessment

Today, Probabilistic Risk Assessments (PRAs) at multi-unit nuclear power plants consider risk from each unit separately and consider dependencies and interactions between the units informally and on an ad hoc basis. The accident at the Fukushima nuclear power station underlined the importance and possibility of multi-unit accidents. These interactions make the operation of multiple units dependent on each other and should be formally accounted for in PRAs. In order to effectively account for these risks in a multi-unit PRA, six main dependence classifications have been identified: initiating events, shared connections, identical components, proximity dependencies, human dependencies, and organizational dependencies. This paper discusses these six classifications and the nature of their resulting dependence between multiple units. As a validation of the classification, this paper will also discuss multi-unit events that have occurred in operating plants. Finally, the paper will present existing methodologies that could be used to more formally quantify unit-to-unit dependencies in the PRAs for each classification.

Lessons Learned from the U.S. Nuclear Regulatory Commission’s Digital System Risk Research

For the past several years, the U.S. Nuclear Regulatory Commission and its contractors have been actively engaged in research to determine the capabilities and limitations of the state of the art of digital systems risk and reliability modeling. This program was developed to assess the capabilities of various modeling methods and to develop regulatory acceptance criteria for the use of digital system risk and reliability modeling in risk-informing digital system reviews. The program investigated both traditional and advanced modeling methods for the evaluation of digital system risk and reliability in the context of including these methods in current generation probabilistic risk assessments (PRAs). The methods investigated included traditional event tree/fault tree analysis, Markov modeling, and dynamic flow graph methodology. As part of the investigation into the capabilities of these methods, we have also reviewed the availability, capability, and practicality of the needed supporting data and analysis methods, including failure mode identification, data generation methods, and uncertainty analysis. The review indicated that for some digital systems traditional PRA modeling methods may be appropriate but that a number of potential issues exist that must be carefully evaluated in modeling these systems. Both the traditional and advanced modeling methods review found that the order of component failures can be important and that simulation either as part of the reliability model or as part of the supporting analysis is needed to determine the effects of combinations of component failures and the timing of digital system failures. Finally, the research showed that better data and models of fault-tolerant features of digital systems and software are needed to support more complete and accurate modeling of digital instrumentation and control for use in nuclear power plant PRAs.

Probabilistic risk assessment modeling of digital instrumentation and control systems using two dynamic methodologies

The Markov/cell-to-cell mapping technique (CCMT) and the dynamic flowgraph methodology (DFM) are two system logic modeling methodologies that have been proposed to address the dynamic characteristics of digital instrumentation and control (I&C) systems and provide risk-analytical capabilities that supplement those provided by traditional probabilistic risk assessment (PRA) techniques for nuclear power plants. Both methodologies utilize a discrete state, multi-valued logic representation of the digital I&C system. For probabilistic quantification purposes, both techniques require the estimation of the probabilities of basic system failure modes, including digital I&C software failure modes, that appear in the prime implicants identified as contributors to a given system event of interest. As in any other system modeling process, the accuracy and predictive value of the models produced by the two techniques, depend not only on the intrinsic features of the modeling paradigm, but also and to a considerable extent on information and knowledge available to the analyst, concerning the system behavior and operation rules under normal and off-nominal conditions, and the associated controlled/monitored process dynamics. The application of the two methodologies is illustrated using a digital feedwater control system (DFWCS) similar to that of an operating pressurized water reactor. This application was carried out to demonstrate how the use of either technique, or both, can facilitate the updating of an existing nuclear power plant PRA model following an upgrade of the instrumentation and control system from analog to digital. Because of scope limitations, the focus of the demonstration of the methodologies was intentionally limited to aspects of digital I&C system behavior for which probabilistic data was on hand or could be generated within the existing project bounds of time and resources. The data used in the probabilistic quantification portion of the process were gathered partially from fault injection experiments with the DFWCS, separately conducted under conservative assumptions, partially from operating experience, and partially from generic data bases. The purpose of the quantification portion of the process was, purely to demonstrate the PRA-updating use and application of the methodologies, without making any particular claim regarding the specific validity and predictive value of the data utilized to illustrate the quantitative risk calculations produced from the qualitative information analytically generated by the models. A comparison of the results obtained from the Markov/CCMT and DFM regarding the event sequences leading to DFWCS failure modes show qualitative and quantitative consistency for the risk scenarios and sequences under consideration. The study also shows that: (a) the risk significance of the timing of system component failures may depend on factors that include the actual variability of initiating conditions of a dynamic transient, even within the nominal control range and (b) the range of dynamic outcomes may also be dependent on the choice of the assumed basic system-component failure modes included in the models, regardless of whether some of these would or would not be considered to have direct safety implications according to the traditional safety/non-safety equipment classifications.

A Benchmark System for Comparing Reliability Modeling Approaches for Digital Instrumentation and Control Systems

There is an accelerating trend to upgrade and replace nuclear power plant analog instrumentation and control systems with digital systems. While various methodologies are available for the reliability modeling of these systems for plant probabilistic risk assessments, there is no benchmark system that can be used as the basis for methodology comparison. A system representative of the steam generator feedwater control systems in pressurized water reactors is proposed for such a comparison. Dynamic reliability modeling of the benchmark system for an example initiating event is illustrated using the Markov/cell-to-cell mapping technique and dynamic flowgraph methodologies.

Calculating and addressing uncertainty for risk-based allowable outage times

Abstract This article examines the calculation and treatment of uncertainty in risk-based allowable outage times (AOTs) for operational control at nuclear power plants, where an AOT is defined as the time that a component or system is permitted to be out of service. The US Nuclear Regulatory Commission (NRC) has explored the possibility of using a nuclear power plant's probabilistic risk assessment results to determine component or system AOTs. The analysis and results from previous work prepared for the NRC on determining risk-based AOTs are presented. As part of the discussion, the article examines the inherent uncertainty in calculating risk-based AOTs and presents the difficulties in calculating these risk-based AOTs. It is noted that care should be taken when dealing with uncertainty analysis results where a time-interval is the outcome of the analysis. In addition, potential improvements in the mechanism of calculating risk-based AOTs are suggested.

ASME Risk‐Based Inservice Inspection and Testing: An Outlook to the Future

Significant research work has been completed in the development of risk‐based inservice inspection (ISI) and testing (IST) technology for nuclear power plant applications through the ASME Center For Research and Technology Development. This paper provides technology that has been developed for these engineering applications. The technology includes risk‐based ranking methods, beginning with the use of plant probabilistic risk assessment (PRA), for the determination of risk‐significant and less risk‐significant components for inspection and the determination of similar populations for pumps and valves for inservice testing. Decision analysis methods are outlined for developing ISI and IST programs. This methodology integrates nondestructive examination data, structural reliability/risk assessment results, PRA results, failure data, and expert opinion to evaluate the effectiveness of ISI programs. Similarly, decision analysis uses the output of failure mode and causes analysis in combination with data, expert opinion, and PRA results to evaluate the effectiveness of IST programs. Results of pilot applications of these ASME methods to actual nuclear plant systems and components are summarized. The results of this work are already being used to develop recommended changes in ISI and IST requirements by the ASME Section XI and the ASME Operation and Maintenance Code organizations. A perspective on Code and regulatory adoption is also outlined. Finally, the potential benefits to the nuclear industry in terms of safety, person‐rem exposure, and costs are summarized.

A methodology for modeling operator errors of commission in probabilistic risk assessment

Abstract This paper describes a methodology to incorporate operator errors of commission (EOCs) in nuclear power plant probabilistic risk assessments (PRAs). This is done by taking appropriate information from the plant PRA, operating procedures, information about plant configuration in terms of systems and functions, as well as physical and thermal-hydraulic information. This is combined with a set of performance influencing factors (PIFs), and results in an initial condition set which is fed into the primary tool for the methodology, called H uman I nteraction T ime LINE (HITLINE) to systematically generate sequences of human actions, including errors. Screening is applied to combinations of hardware failures, instrument failure, and PIFs to select the combinations that meet the criteria developed for the purpose. The criteria are based on the operator action or inaction causing a transition from one event tree (ET) branch to another. The strategy of utilizing mapping tables to accomplish all major steps of implementation decomposes the analysis into two separate parts. Values used in different scenario-dependent (error) likelihoods, and adjustors for these likelihoods to account for the influence of the scenario-independent PIFs, are separately assigned. While developing the HITLINE, the methodology then involves the use of mapping tables to generate a set of PIFs, given the relevant information about plant and emergency operating procedures (EOPs). This set is then used to select predetermined weights and adjustors to compute the final weight to be assigned to each branch at a single branching point. Quantification at each branching point is done through the multiple factors assigned to systematically assign the weights for different actions. Dependencies are carried from one branch point to another through the use of operator related variables such as operator diagnosis, and expectation about plant behavior. Size of HITLINE is managed by applying merging, truncation and termination rules at each time step. Similar end states with respect to the ET are terminated and their weights are combined. Combination is also applied among HITLINEs constructed for different initial condition sets for a given initiating event. Incorporating the results back into the ET either causes a reordering of sequence probabilities or including additional operator related top events to the ET. The methodology is demonstrated through a hypothetical example.

PRA importance measures for maintenance prioritization applications

Abstract Various importance measures are standardly calculated in a standard probabilistic risk assessment (PRA). Approaches are developed in this paper for using two of these measures—the minimal cutset contribution and the risk reduction importance—for prioritizing the risk importances of maintenances. One approach which is developed prioritizes maintenances based on the risk importance of the associated contributor. The second approach prioritizes maintenances based on the risk impact if the maintenance is ineffective. The core damage frequency is used as the risk measure for prioritization. The demonstration studies, which are carried out using the Surry Plant PRA, indicate that the two approaches give similar results if appropriate cutoff criteria are used. As an additional evaluation, risk unimportant maintenances are identified using the risk increase importance, or risk achievement worth, calculated in the PRA.